Derivative Structures in the Market and Their Place in Corporate Portfolio Management


Derivatives are financial instruments that do not hold independent value, but where instead the value of the instrument is based on the underlying value of a given asset, which can range from financial assets such as stocks, bonds and market indexes to commodity assets such as oil, gold or wheat, to more obscure or exotic assets such as weather or other exotic assets. The four main categories of derivative include forwards, futures, options and swaps, each of which is used for a different risk control technique and each of which has its own unique structure, risk, and potential for return. Derivatives are commonly used in financial firms to balance portfolios and reduce risk by spreading it across the market, or in order to mitigate potential risk by limiting it (for example, placing a ceiling or floor on currency exchanges or purchases).

This paper explores the use of derivatives in the financial market, including their use in portfolio management. Following a thorough definition of the derivative, the paper explores the use of derivatives in portfolio management and other banking activities, and offers a substantive risk assessment that addresses the potential difficulties that the use of these instruments may pose as well as a description of the benefits of using derivatives.

The paper also explores ways in which actual financial institutions use derivatives through examination of public reports and other available information, in order to determine what current practice is in the use of these reports. The report concludes with recommendations for portfolio managers within financial institutions regarding the use of these instruments for risk management as well as the potential dangers of their use. The study is intended to provide an overview guide to this material and an analysis of existing research that can be used for further research and understanding of the subject material.

Chapter 1 Introduction to the Research Project

The use of derivatives in corporate risk management has come under scrutiny recently in the news, following reports of credit risk derivatives being used improperly by some firms and banks during the mortgage lending collapse of 2007-2008. However, while these instruments may be misused, they also hold an important role in both financial and non-financial firms in hedging risk and balancing corporate portfolios and investments. Derivatives can be used in a number of different applications. These applications include balancing risk across a number of different investors, gaining access to foreign currency or reducing currency exchange risk exposure, and reallocating loan risk across lending portfolios within or among banks.

While these instruments clearly have benefits in terms of balancing, spreading and reducing risk to the individual investor, corporation or bank, there are still considerable risks that must be considered. For example, credit risk derivatives were at fault for revenue losses because they were improperly calculated to be less risky than they actually were. Conversely, a currency option, one type of derivative that reduces the potential for risk in currency exchange rates, could end up being a poor rate if the market does not change in the expected manner. These are just a few of the risks that can be encountered within the use of derivatives in financial and non-financial firms.

This paper presents an overview of the types of derivatives available, the risk involved in using the derivative, and other important factors that must be considered in its use.

Research Aims

The main aim of this research is to explore and identify the derivative structures in the financial market and examine different corporate responses to the changes in the market and uses of these derivatives. The research also examines the impact posed by changes in the market on the corporate portfolio strategy. By first providing an overview of the different types of derivative structures available, and then analyzing corporations in order to identify how they use these structures, the research paper analyzes corporate portfolio diversification as a strategy and explores the potential for derivatives in financial markets.

Research Objectives

The main research objectives of this project include:

Definition of the structure and application of derivatives

Definition of the risk posed by application of derivatives in a competitive market

Description of the common usage and potential impact of derivatives on the financial institution

Examination of the impact of market changes in the corporate portfolio within the financial institution

Identification of the limitations and risks of derivatives as used in the corporate portfolio

Identification of appropriate risk management and portfolio management strategies

Importance of the paper

Sustained changes in the financial and competitive environment of industries, increasing globalization and increasing complexity of financial markets has led to an unprecedented period of currency and interest rate volatility worldwide. In order to counter this increase in risk, innovative foreign exchange risk and interest rate risk hedging techniques have developed at a rapid pace. Although these derivatives are intended to assist in risk management and risk minimization, particularly in terms of uncertain cash flows and currency exchange rates, their use has been uncertain, as instruments grow increasingly exotic.

This paper will provide a guide to derivatives and their use in the financial market, as well as provide a clear understanding of the risks involved in the use of derivatives and their appropriate application to risk management, as well as discussion of how the risk of the derivatives themselves may be handled. This information can be used by investment risk managers and others in order to guide policies regarding the use of these instruments and allow for an increased understanding of the underlying issues involving these instruments.

Methodology overview

The methodology that will be used is that of desk research and meta analysis. This method will assemble information from a large number of sources, including primarily secondary research, and organize and analyze it in such a way as to create an understanding of the research material in the general case. This information will be able to be used for description of the operation and formulation of derivatives in a number of markets.

Data collection

The main data collection technique used in this discussion will be secondary research or desk research.

This method was chosen both because of the limited time available to perform the survey and because of the amount of information already available on the subject matter. Secondary information will include primarily a literature review, which will provide background and theoretical information that can be used in order to form an overall picture of the theory and practice of using derivatives and derivative structures. Other secondary data will be used to examine the issues at hand for analysis, including materials such as company reports, journal articles and time series, and previously conducted surveys that address the subject matter.

However, it should be noted that derivatives are not ordinarily considered reportable assets, and so may leave little trace on company reports and discussions. As such, generalized information from sources such as the Bank for International Settlements will be used as much as possible rather than specific firm information.

Data analysis

Following the collection of data using the method described above, the data will be analyzed using a number of techniques. Analysis methods are intended to be both quantitative and qualitative, in accordance with the data available for analysis.

Quantitative analysis will be exploratory and descriptive, using data summaries in such methods as charts, tables, and descriptive statistics. Qualitative analysis techniques that will be used will include categorization, development and analysis of relationships, and descriptive techniques. This data analysis will be used in order to create an overall view of the data that can be used in order to explore the research questions.

Organization of the paper

The table below presents the organization of the remainder of the paper in terms of chapter numbers and contents.



Chapter 2

Literature review and context review

Chapter 3

Methodology overview

Chapter 4

Presentation of results of analysis, discussion of results and examination of risk and risk mitigation strategies for firms using derivatives

Chapter 5

Conclusions and recommendations for further study

Table 1 Organization of the paper


This chapter has presented an overview of the aims and objectives of the paper as well as the methods that will be used to explore the research objectives. It will provide a guide to the remainder of the paper. The next chapter, the Literature Review, provides insight into the structure and definition of derivatives as well as providing insight into their use in financial markets.

Chapter 2 Review of the Literature

In order to provide background and theoretical information for the discussion in the following chapters, this chapter presents an overview of the current state of affairs concerning derivatives and their use in the financial firm. This includes a description of the definition of derivative, the varying types of derivatives and what their uses and significance are, and a description of their current use in the banking context in order to examine the overall importance of derivatives in portfolio management.

This chapter will also provide an overview of the concepts of portfolio management in order to examine issues involved in the use of derivatives.

Definition of derivatives

Although there are a number of different definitions of derivatives, the basic principle of the derivative is that it is not, in and of itself, an asset or investment; instead, it is a financial instrument that is based on the value of an underlying asset or instrument (Hunt & Kennedy, 2004, p. 1). As such, it should be clear that as a derivative has no independent financial value, it should not be considered to be an investment per se; if the firm wishes to make an investment in the underlying asset, it is more appropriate to do so directly. Instead, derivatives are used to gain potential access to cash flows, risk, currency exchanges or other valuable items or to distribute risks across a number of different users, markets, or geographic areas rather than assigning all risk to a single portfolio or individual (Hunt & Kennedy, 2004, p. 3).

Derivatives may be based on the value of a wide range of underlying instruments, including stocks, bonds, indexes, exchange rates, interest rates or the prices of commodity such as wheat, oil or livestock (Hunt & Kennedy, 2004). More exotic underlying instruments include credit risks of packaged assets and even long-range weather forecasts; however, these exotic underlying instruments fall outside the scope of this discussion and will not be examined in-depth.

Underlying concepts

There are a number of underlying concepts that must be understood if the idea of the derivative is to be fully described. The first such idea is that of replication. In brief, replication is the portfolio of assets (trading strategy that will pay out an identical amount to the payout of the derivative in any potential trading circumstance (Hunt & Kennedy, 2004, p. 3). In other words, the balance of the portfolio, on which option pricing theory is based, is dependent on its ability to mirror the price of the option that it is compared against.

The second important underlying idea is that of arbitrage. Hunt and Kennedy (2004, p. 3) defined arbitrage as a trading strategy that generates profit from nothing with no risk involved. Arbitrage opportunities are assumed not to exist in the trading of derivatives; although it is clear that some random arbitrage opportunities might exist, they cannot be counted upon in a trading strategy and should not be considered for the purposes of this analysis.

The underlying security is defined as the security involved in an option or other derivative transaction (Chorafas, 2008, p. 36).

In other words, the underlying security (or underlying asset) is the security or asset from which the derivative derives its value, like a commodity such as oil, gold or wheat. These underlying securities rarely actually change hands (although it may occasionally occur). As Chorafas noted, while the underlying security may be based in an asset or liability, it cannot be considered to be an asset or liability itself, but is instead intended only to hedge risks from other market areas. Chorafas demonstrated that the relationship between the underlying security and the derivative is likely to be nonlinear; that is, the price of the derivative will not depend immediately on the price of the underlying security, but will instead be offset by other factors. The figure below demonstrates this nonlinear relationship.

Figure 1 Nonlinear relationship between the value of derivatives and underlying instruments (Chorafas, 2008)

The idea of notional principle amount, or face amount, is the amount of money on which the trade is based; however, this money is never actually intended to change hands, it only provides a basis for such characteristics of the derivative as interest rate calculation or other bases for engaging in the trade (Chorafas, 2008, p. 36). This may be specified not only in currency, but also in any other relevant measurement, such as shares, kilos, gallons, bushels, or whatever the natural means of measuring the underlying asset might be.

Types of derivatives

There are a wide range of types of derivatives, and custom derivatives are often assembled in order to meet the requirements of the parties involved in the trade that do not easily coincide with the definition of any standard type.

However, the four major categories of derivatives include options, forwards, futures and swaps. Each of these types has a different structure and different uses within the market, and each is traded differently within the market. The description, structure and main uses of each of these types of derivatives are described in detail below.


An option is an instrument that gives the buyer the opportunity (but not the requirement) to purchase a given instrument at a specific time for a specific price (Chorafas, 2008, p. 39). An option may be a call option (guaranteeing the buyer the right to buy the underlying good at the set price) or a put option (guaranteeing the owner the right to sell the underlying good at the strike price) (Kolb, 2003, p. 4).

The buyer of an option may decide to exercise it (in which case they take delivery of the underlying) or to not exercise it (in which case it expires); if the buyer does exercise the option (decide to take delivery) the seller must give it to them for the agreed-upon price. The price at which the buyer may exercise the option is the strike price, while the price paid to the seller for the option is known as the premium (Chorafas, 2008, p. 40). The expiration date is the date by which the option must be exercised is the expiration date. The type of option will determine whether the option can be exercised only on that date, at any time prior to that date, or at certain specific times prior to the expiration date. American options can be exercised at any point up to the expiration date, while European options allow exercise only on the expiration date (Kolb, 2003, p. 507).

A Bermuda option has set intermediate dates between the purchase and the expiration date at which it may be exercised (Kolb, 2003). There are also a number of exotic options that provide more customized payment, delivery and exercise agreements that may rely on the price of the underlying asset; for example, a barrier option's exercise depends on the value of the underlying asset reaching a price specified in the contract, while an Asian option depends on the average price of the underlying security (Kolb, 2003). A so-called plain vanilla option, however, depends only on the current price of the underlying and other characteristics of the option such as exercise price and time until expiration (Kolb, 2003, p. 577). Caps, floors and collars are particular characteristics of a given option, which are intended to limit exposure to upside and downside risk (Smith & Walter, 2003, p. 84).

A cap, commonly used in an interest rate swap as well as other options, fixes the upper rate of exchange, while a floor similarly fixes the lower rate of exchange; as can be envisioned, a collar fixes both the upper and lower rates of exchange in order to reduce the potential for risk. Options are extremely popular derivatives that are used in both financial and nonfinancial firms for portfolio balance.


A forward, or more properly a forward contract or option, is structured in much the same way as an option; however, rather than the exercise of the instrument being optional at the expiration date, exercise is mandatory at that time (Kolb, 2003). A basic definition of a forward was given by Kolb, who remarked, A forward contract... always involves a contract initiated at one time; performance in accordance with the terms of the contract occurs at a subsequent time.

Furthermore, the type of forward contracting to be considered here always involves an exchange of one asset for another. The price at which the exchange is set at the time of the initial contracting. Actual payment and delivery of the good occurs later (Kolb, 2003, p. 2). Forward contracts are commonly used in currency exchange operations and other transactions in which the individuals involved wish to reduce uncertainty; for example, in a currency exchange forward, the seller ensures the present value of the trade, as does the buyer. Although the currency exchange rates may fluctuate over the time between the contract and the expiration date, the risk for each party will be reduced because they will be able to protect themselves from changes in the currency exchange (Kolb, 2003).

As such, forwards are commonly used for securing access to foreign currency or other underlying assets that an individual will need in the future at a risk-controlled price. In effect, the use of forwards removes uncertainty from the future business climate, therefore reducing risk. Forwards may also be used in order to create a position in the weaker currency when performing interest rate hedging (Smith & Walter, 2003, p. 43). In effect, the investor attempts to determine when a weak currency is going to undergo a currency collapse (such as the 1997-1998 Asian market collapse, which began with a weakened currency in Thailand), and then purchases interest rate forwards in this currency, then waits for the interest rate in the country to drop as monetary policy shifts to propping up the currency rather than attempting to slow growth.

However, this strategy is not without risk because there is always the potential that the currency may not depreciate or, if it does, that the requisite interest rate drop will not occur, or will not be sufficient to make the investment worthwhile.


Futures are an even more specialized form of the option. Futures contracts, which always trade on organized exchanges rather than in over the counter transactions, are a type of forward contract with highly standardized and specified contract terms... futures contracts are highly standardized with a specified quantity of a good, and with a specified delivery date and delivery mechanism (Kolb, 2003, p. 3).

According to Kolb, performance on a futures contract is also guaranteed with by a clearing house, or a financial institution that guarantees the integrity of the market, and are protected by margin, or security payments posted by traders as a good-faith indication of willingness to trade (Kolb, 2003, p. 3). Futures, unlike other forms of derivatives, trade in a regulated market and as such may not be as complex to handle as other forms of derivatives such as forwards. Futures are most commonly used for trade in commodities, and are often used by nonfinancial institutions rather than financial institutions.


Unlike the other forms of derivatives, a swap is not just a specialized form of option, but is instead a different type of instrument. A swap is an over-the-counter instrument involving the exchange of one stream of payment liability for another (Smith & Walter, 2003, p. 75). According to Smith and Walter, this derivative has only developed since the 1980s, with an increasing use of derivatives by non-financial corporations in order to reduce risk and reduce cost of listing on stock and bond markets. Swaps, as contingent values, are also not listed on financial reports, which allow firms to manoeuvre their full investment in a given position if desired (Smith & Walter, 2003, p. 76).

Common swaps include interest rate swaps and currency exchange swaps. Currency swaps allow firms to exchange their exposure to currency risk (for example, by limiting the amount paid in interest from one position to another) by exchanging currency rates from one to the other. Historical currency swap rates demonstrate the overall growth in currency swaps. The table below demonstrates the growth in currency rate swaps over the top ten traded currencies in 2000. As can be seen, the Euro almost immediately became prominent, with rapidly increasing amounts of currency swaps overtaking the currency as it was instituted. The use of currency swaps is extremely common in financial and non-financial firms that require protection from currency risk. For example, those with operations in multiple countries (Smith & Walter, 2003).


Notional Amount Traded Per Year (Historical Figures)




Australian dollar




Canadian dollar




Danish Kroner








Hong Kong dollar




Japanese yen




New Zealand dollar




Norwegian Kroner




Pound Sterling




Swiss franc




Table 2 Historical trades in currency swaps, 1998-1999 (Smith & Walter, 2003)

Interest rate swaps allow for firms to exchange interest rates on funds, often in exchange for future value of a payment stream. As noted by Smith and Walter, these instruments are advantageous because they allow for the transfer of potential immediate interest risk, as well as offering individuals access to funds at lower interest rates.

In addition to an immediate swap, a pair of traders may engage in what is called a forward swap, in which payments at some time in the future are fixed rather than immediately exchanging hands (Smith & Walter, 2003, p. 83).

These derivatives are not commonly used in the financial world, but may take place for example in order to fix interest rates through the duration of a long-term building project or perform similar interest rate fixation.

Credit derivatives

Of particular current concern is the credit derivative, which protect the lender against loan default in much the same way as a loan guarantee. According to Smith and Walter (85), the major types of credit derivatives include total return swaps (in which the potential returns from a risky underlying loan instrument are exchanged for a lower, but less risky, guaranteed return); credit default swaps (in which an upfront fee is exchanged for coverage in the case of a default on the underlying loan instrument); and the credit linked note (in which the buyer makes a series of payments to the seller, which are returned if there are no credit difficulties during the lifetime of the loan) (Smith & Walter, 2003, p. 86).

Banks have commonly used these derivatives in the recent past in order to limit their exposure to consumer debt; however, as the recent subprime mortgage crisis in the United States has shown, reckless use of credit derivatives may not be appropriate. Many hedge funds (estimated by Douglas to be a tenth of the total market) specialize in credit derivatives, following a number of different strategies for engaging in credit derivatives trading and arbitrage. The authors noted that of the participants in the credit derivative markets, the majority of funds that specialized in credit derivatives worked in emerging debt markets and convertible arbitrage opportunities, rather than in less risk, but less rewarding, areas such as distressed debt and high yield debt (Douglas, 2007).

The risks of credit derivative instruments will be explored more fully in Chapter 3, Data and Analysis.

Derivative trading

Derivatives are traded in one of two ways. Over the counter derivatives (OTC derivatives) are derivatives that are traded directly between private parties, rather than being traded through an exchange (Smith & Walter, 2003). Some of the most commonly traded derivative structures that are traded over the counter include swaps (which are usually custom-packaged in order to meet the needs of both parties involved in the trade) and exotic options and other custom-packaged derivative products (Smith & Walter, 2003). These instruments are best traded over the counter because of their custom nature; the OTC sale format allows for customization of the package in order to meet the needs of the purchaser in terms of portfolio balance and risk adjustment (Chorafas, 2008, p. 58).

However, this flexibility comes with a cost in risk undertaking, as there is no open market value of the instrument in order to ensure that the buyer does not overpay (Chorafas, 2008, p. 59). Although precise figures on the trade of OTC derivative instruments are difficult to obtain due to the private and non-reported nature of the trades, evidence points to a very large market for these instruments. According to the Bank for International Settlements, the estimated international trade in OTC derivatives as of December 2007 was approximately 596,004 billion US dollars (Bank for International Settlements, 2007).

The second form of derivative trading is exchange-traded derivative trading, in which derivatives are listed on exchange for buyers and sellers in much the same fashion as stock or bond markets (Chorafas, 2008).

The potential for overpricing that exists in OTC derivatives is not present in exchange-traded derivatives, because the existence of the open market results in the establishment of a fair market value for the derivative (Chorafas, 2008, p. 60). However, many types of derivatives are traded in derivative exchanges; most commonly, interest rate swaps and commodity forwards and futures are available on derivative exchanges (Chorafas, 2008, p. 75). While customization of derivative packages is not possible, for some purposes the use of a traded derivative is entirely sufficient to meet the needs of the portfolio management problem, and should be considered as lower cost than creating a customized over the counter derivative sale.

According to the Bank for International Settlements, the exchange trading activity in derivatives during the 2nd quarter of 2008 (March to June) totalled 600,465 billion US dollars, which represented a total trade volume of 2,397 million contracts in total (Bank for International Settlements, 2008).

Portfolio management

The main use of derivatives is in portfolio management, in particular hedging (balancing and spreading) risk involved in the portfolio. Modern portfolio theory, a theory developed by Markowitz, Sharpe and others, is based on the principle of reducing exposure to systematic risk by diversifying and spreading risk.

This portfolio management practice, which is used by both individual and institutional investors, focuses on the riskiness of a given asset and the ability to determine the appropriate price of the risky asset (Elton & Gruber, 1999). The theory is based on the mean and variance of performance in a given portfolio of assets, which must be balanced in order to ensure a reduced risk in return (Elton & Gruber, 1999, p. 442). The efficient frontier, or Markowitz frontier, is the point at which there is the lowest risk for a given level of return; it is at this point that a perfectly diversified portfolio will lie (Elton & Gruber, 1999, p. 448). However, the exact determination of this line is difficult due to the amount of information required in order to determine the true riskiness of any given asset. As such, there are variables that stand in for the complex information required for this calculation.

One such approximation is the risk-free asset, or an instrument that is expected to return a risk-free rate (typically a government-securitized asset with a short-term payment period, such as a United States Treasury bill (T-bill) (Elton & Gruber, 1999). Another such is the beta of a given stock, which is the degree of variance from the risk-free asset (Elton & Gruber, 1999). Systematic risk and specific risk are the two different types of risk involved in modern portfolio theory. Systematic risk is risk that is held in common to all securities within a given single market, and as such cannot be removed entirely from the portfolio, while specific risk is risk that is associated with the given security (for example, poor corporate governance of a firm issuing a stock) (Elton & Gruber, 1999).

The use of hedging, or investment strategies intended to cover the systematic risk of a given investment with another instrument, is commonly used in order to reduce the risk in portfolio management (Koziol, 1990, p. 2). Banks in particular may use hedging as a means to control their exposure to risk through asset-liability mismatches; for example, they may pursue a hedging strategy to cure the mismatch between long-term lending practices and short-term deposits (Smith & Walter, 2003, p. 73). It should be noted that this strategy is not without risk; in particular, it must be remembered that hedging is not a profit-making strategy, but is instead a risk reduction strategy, and it can be quite costly in the event that risk is not encountered.

Use of derivatives in portfolio management

Derivatives are commonly used in portfolio management as a hedging strategy. This emphasizes the fact that derivatives should be considered not as an asset or as a profit opportunity (although the use of them may sometimes result in a profit opportunity), but rather as a risk reduction strategy. One common example of derivative use in portfolio management is in currency exchange management (Smith & Walter, 2003). For example, if a firm wishes to undertake a building project or expand their market opportunities into another country, this will expand their portfolio and increase the number of markets in which they operate. However, this will require access to a considerable amount of the foreign currency over the life of the project, particularly if it is a capital-heavy project such as building new locations or expanding infrastructure or logistics.

However, this can be risky because of fluctuating exchange rates; over the course of a long-term building or expansion project, a firm may undergo a significant loss if the currency of the foreign country grows in strength (reducing the firm's buying power within the country). This risk can be mitigated by purchasing currency exchange forwards or engaging in a currency exchange swap with another party that has the same need to reduce the risk of fluctuation between the two currencies (Smith & Walter, 2003).

This is considered to be a hedging strategy, because it reduces the risk of both parties in the case of exposure to fluctuating currency rates; it helps to balance the portfolio of the firm by reducing the exposure to systematic risk (currency fluctuations, which cannot be adequately predicted or controlled), but does not offer a significant opportunity for profit. The use of derivatives to spread exposure to risk among several investors, limit exposure and cost changes, and engage in other risk-reduction activities is common among both financial and non-financial firms and is one of the main ways in which a firm's portfolio may be balanced.

In the banking context, derivatives are used to plan the balance of investments and protect from market uncertainty (Kim, 2007).

This is particularly true for the investment bank, of which Kim described the main goal as the planning an undertaking of securities that can satisfy both investors and the company ... if the OTC derivatives are efficient from the viewpoint of a securities company and an investment bank that have issued designed-structured securities with built-in derivatives, the risk can be efficiently hedged (Kim, 2007, p. 30). In particular, over the counter derivatives are used to control risk and market exposure in a way that can be tailored to the needs of the individual bank without undergoing considerable shifts in the portfolio instruments themselves (Kim, 2007, p. 31).

Kim also held that derivatives are important for balancing and reducing the volatility of the capital market, which is becoming an increasing concern as the volatility of the market increases. This use of OTC derivatives in particular within the investment bank indicates that the bank is using the instruments to hedge risk, rather than gain profit. This is the appropriate place for the use of derivatives, which should not be considered to be a profit-making opportunity but should instead be considered only as a way to reduce risk exposure.

The credit risk derivative in the portfolio management process

The uses of credit risk derivatives in the portfolio management process differ depending on the level of financial institution. In particular, commercial banks use credit risk derivatives in order to shed credit risk, or reduce their credit risk load (Gibson, 2007, p. 27).

In the general case, they transfer risk from large corporate loans, counterparty credit risk and other sources of risk to other areas within the market in order to reduce the overall risk level of the portfolio. Investment banks, on the other hand, use credit derivatives in order to manage security underwriting risk, by hedging the credit risk involved in the short-term assumption of instruments onto the bank's books before selling them on (Gibson, 2007, p. 25).

There are other considerations other than the specific type of bank involved in the choice of credit derivatives use as well. For example, one study reported that size of the bank was directly related to the level of credit derivative use, because the barriers to entry to the market were high, and larger banks would gain more from their use (Ashraf, Altunbas, & Goddard, 2007).

Generic considerations in the bank's choice of credit derivative use may include the availability of tax incentives, reduction of risk through defaults, and the fund management incentive behaviour described below, in which fund managers are incentivized to take extra risks (Ashraf, Altunbas, & Goddard, 2007).

Although there is evidence to suggest that the credit derivative market should be regulated, this regulation has yet to occur in most markets, meaning that firms may also view it as a way to improve profits or ensure profits without regulation (Huang, 2001).

Potential risks of derivatives

Although derivatives are generally considered to be a good way to hedge other investment risks in the portfolio, this is not meant to imply that derivatives do not have risks in and of themselves. This is demonstrated by the financial engineering difficulties in the early 1990s, when companies such as Metalgesellschaft, Gibson Greetings and Proctor & Gamble suffered significant losses due to mismanagement of derivative funds and portfolio balance (Weithers, 2007, p. 42).

These incidents were largely due to mismanagement of funds; for example, Metalgesellschaft was surprised by a cash flow mismatch between their derivative holdings (specifically, they over-positioned in long-term forwards and under-positioned in short-term exchange-traded futures) (Weithers, 2007).

However, while mismanagement does pose a significant risk it is only one of the potential risks that can be encountered in the management of derivatives within portfolios.

There are a number of risks that are specific to the structure and use of derivatives. Sill (1997) highlighted a number of potential risks of derivatives. One of these risks was inappropriate pricing of derivatives, either due to inaccurate pricing models or, in the case of OTC derivatives, the lack of open market pricing availability for customized derivative packages); underperformance of pricing models and risk management models leading to exposure to more risk than anticipated (Sill, 1997, p. 24).

This unanticipated exposure to risk was the problem faced by many banks following the collapse of the subprime mortgage market in the United States, which led to a worldwide housing market depression in 2007 that is still ongoing. Another type of risk that may be involved in the use of derivatives is that of credit risk - that is, one party may default on the obligation (Sill, 1997, p. 24).

As Sill noted, this is not such a problem in an organized securities exchange, where the use of margin and financial underwriting by an overseeing financial institution will prevent harm from default; however, in the OTC market this is considerably more risky because these safeguards do not exist. This may be particularly problematic because of the reliance of investment banks on the OTC derivative market. A third risk is that of liquidity risk; simply put, a derivative may not be able to be traded on the open market, another issue that may particularly impact the OTC market (Sill, 1997, p. 25).

As noted by Sill, this does not necessarily pose a problem on the market level; however, on the individual participant level, this could cause a problem in which the eventual sale price of an illiquid derivative (as with any illiquid asset) may be very different from the book value or purchase price of that derivative. This may be particularly a problem in the OTC market as well, because of the essentially custom nature of many OTC derivatives, which may make them inherently more illiquid than exchange-traded derivatives. This, of course, would reduce the liquidity of the investment bank portfolio.

There are other risks involved in derivatives trading as well, which may not have any direct connection to the underlying assets or derivatives themselves. For example, the type of collateral used in the contract may be an exposure to counterparty risk, particularly when dealing with OTC credit derivatives; the use of cash may result in an unacceptable loss for the firm if this is realized (Linden, 2008, p. 10).

Another potential risk is that fund managers that use derivatives, when freed from the burdens of risk management, may engage in increasingly riskier portfolio management strategies in order to increase their own gain through compensation strategies such as bonuses, which are common in the portfolio management industry (Benson, Faff, & Nowland, 2007).

In particular, Benson et al found that managers that had experienced a long downturn in fund returns may be more inclined to increase the riskiness of their trades when using derivatives; however, the authors did caution that the results were not definitive and should be carefully considered. Regardless, this is a potential that should be considered in the use of derivatives. Another potential risk is that the use of derivatives for risk hedging may simply not work; according to one study, the amount of risk faced by a given firm using derivatives as a hedging strategy was not reduced for several years, and only commodity hedging actually provided the required during those yearly years (Bali, Hume, & Martell, 2007).

As such, it should be considered whether the firm's use of derivatives for hedging is actually driven by financial concerns or whether it is driven by non-financial concerns such as shareholder expectation or portfolio manager training.


This chapter has presented a thorough overview of the structure and uses of derivatives, both in the general case and in the investment banking market. This included discussion of the different common types of derivatives, methods of derivative trading and sale, and use of derivatives in portfolio management and in investment banks. It also discussed the potential risks of derivative use.

It is counterintuitive to consider that something that is intended to reduce the overall risk of a portfolio should come with risk itself; however, on further consideration this makes sense. It is not the job of the derivative to remove all evidence of risk from a portfolio, but rather to balance the risk that is already inherent in the portfolio. For example, a futures contract does not reduce the potential for risk in the sale of the goods; it only imposes a known structure on the eventual transaction by setting a specific time, place, price and method of delivery for a set amount of goods. This evens the risk by introducing certainty, but does not remove it completely. As such, it makes sense that the use of derivatives should come with risks in and of themselves. The next chapter presents the methodology used in the study and discusses issues involved in this methodology.

Chapter 3 Methodology

This chapter presents an overview of the methodology used in the analysis including a description of the data sources and analysis methods.

Research method

The research method used could be considered to be a meta analysis of existing information, in which secondary information was analyzed and synthesized in order to provide an overall view of the picture. According to Zikmund, this method is appropriate for use in business research particularly when engaging in pragmatic or analytic research in order to provide a basis for decision-making aids (Zikmund, 2002).

The research method relied on secondary data, both as a means of reducing analytical error through introduction of bias through the research method and as a way to maximize the available time and resources for the report. The use of secondary data is supported in this research method, as Zikmund noted, because it can be difficult to gather the amount and variety of information required for a given analysis. As such, this method was considered to be the most appropriate for the analysis of this research subject.

Data sources

The data sources used were numerous. For information regarding the use of derivatives and structure, a literature review using secondary data was used. The results of this literature review are presented in Chapter 2. This literature review was used to first provide information regarding the subject matter and second to provide background and insight into the potential issues discussed in the analysis of the issues. This data was obtained from a number of sources including books and journal articles.

A second source of information was databases maintained by the Bank for International Settlements, which maintains records and statistics regarding a number of banking-related issues, including trade volume and type of both exchange-traded and over the counter securities internationally back to 1984.

Data analysis

A number of statistical techniques were used to examine the data gathered from BIS. These techniques included the use of Excel to conduct descriptive analysis on current trading as well as techniques such as time series analysis intended to explore growing trends in the derivatives market.

This information is then informed with discussion from previous research regarding the use of derivatives in financial and non-financial firms, with particular emphasis on financial firms, in order to explore the research questions. The analysis of this data is presented in Chapter 4 (Analysis and Discussion).


This chapter presented an overview of the methodology that will be used to analyze the use of derivatives in the market generally, as well as examine their use in investment banks. The following chapter will present this analysis, first involving the examination of data sets obtained from the BIS and secondarily examining the resulting information's links to current research and the use of derivatives in investment banking.

Chapter 4 Results and Discussion

This chapter presents the results of descriptive and trend analysis in the use of derivatives, as well as examination of the implications of these results for investment banking and portfolio management. It also presents the results of some previous research in comparison with this analysis and explores the meanings of these findings in light of the research objectives. It also provides recommendations for the appropriate use of derivatives in portfolio management strategies.


Te analysis of derivatives was broken down into categories depending on the type of derivative, following the BIS format for data organization and display. Although information was available for both exchange-traded derivatives and OTC derivatives, OTC derivatives were the main focus of this research because investment banks primarily use OTC derivatives, rather than exchange-traded derivatives, in order to maintain portfolio balance through hedging. All funds are represented in US dollars (the BIS index currency).

Description of the data set

According to Gibson (2007), the majority of the BIS information is obtained from reporting dealers of OTC derivatives, with about fifty-five individual dealers reporting data. This, Gibson stated, reflects the interdealer nature of the market (Gibson, 2007, p. 25).

Dealer reported data includes a small amount of information for dealers themselves, but also represents a significant amount of data from the dealers' customers and account holders. Other information is obtained from non-reporting financial institutions as well as other sources. This information is then broken out into counterparties and examined in a time series basis.

Foreign exchange derivatives

Foreign exchange derivatives tracked by the BIS include forwards and swaps, currency swaps, and options. The analysis below describes each of these outcomes, including notional value (the value represented by the underlying instrument) and gross market value of the instruments (at best approximation).

Notional value

The charts below describe the growth in use of foreign exchange (currency exchange) derivatives from June 1998 to June 2007.

These figures, which are reported quarterly, demonstrate significant growth in the sectors. This chart represents the notional value, or the value of the instruments based on value of the underlying assets that are chosen for exchange (although these funds are never intended to change hands). The first chart represents these figures for all trading partners (including both financial and non-financial institutions), while the second chart shows the growth across this time period for financial institutions only.

Figure 2 Growth in quarterly notional value of OTC derivative transfers for foreign exchange derivatives, Jun 98 - Jun 07 (All market participants)

Figure 3 Growth in quarterly notional value of OTC derivative transfers for foreign exchange derivatives, Jun 98 - Jun 07 (Financial institutions)

As can be seen from these graphs, the overall growth in the notional value of exchange derivatives of various types for financial institutions was even higher than in the average firm. This may be due to increasing globalization of financial institutions. Charts containing data from which these charts were derived are attached in Appendix A (Research Data).

Gross value

While the information above discussed the notional value of the traded instruments during the two time periods (that is, the value on which the derivatives were valued, rather than the amount paid for the instruments), the charts below examine the growth of the gross value of the trade in derivatives over the same time period as discussed above. The charts below demonstrate the same relationships as the charts in the notional value discussion, with the first chart representing the total trade for all individuals and the second chart representing total gross value of trades within the financial institution.

Figure 4 Gross value of foreign exchange derivative trading (June 1998-December 07)

Figure 5 Gross value of foreign exchange derivative trading (June 1998-June 2007)

As can be seen from these charts, the growth of foreign exchange currencies over this time period has not been significantly out of line between banking institutions and other institutions during this time period. In fact, the financial use of forwards and swaps even dropped slightly across this time period. However, both financial and non-financial markets have undergone considerable growth in the value of these instruments, and as such this should be considered in discussion of the outcomes of the impact of derivatives on the financial market.

Single-currency interest rate derivatives

Similar trends are seen in the BIS reporting of single-currency interest rate derivatives, which are commonly used to limit exposure to interest rate risk or to gain access to a more acceptable exchange rate. The graphs below demonstrate the growth in notional value and gross market value of single-currency interest rate derivatives across all markets and financial markets (measured on a quarterly basis) from June 1998 to June 2007.

Supporting data for these graphs, which demonstrate the growth across the time period, are shown in Appendix A.

Notional value

As can be seen from the line chart below, the growth of notional value of single-currency interest rate derivatives has been a steadily increasing curve, which is suggestive of (but not conclusive to) linear growth.

Figure 6 Growth of notional value in single-interest currency rate derivatives, Jun-98-Dec-07

Figure 7 Growth of notional value in single-interest currency rate derivatives quarterly (Jun-98 compared to Jun-07)

As can be seen from this comparison, the use of interest rate derivatives within the market grew substantially, from almost no market in 1997 to a market of over 350 million USD in notional value in 2007.

As can be seen in the figure below, the main growth in this instrument in banking has been the use of interest rate swaps.

Figure 8 Growth of notional value in single-interest currency rate derivatives (Jun-98 compared to Jun-07), banking institutions only

Gross market value

As can be seen from the line graph below, the growth of gross value of interest rate derivatives has not been nearly as steady as the growth in notional value. There are significant dips in the graph that indicate that the gross value of the underlying instruments for this category has fluctuated sharply over time.

Figure 9 Gross value of single-currency interest rate derivatives, June 1998-December 2007

Figure 10, below, examines the growth of single-currency across all interest rate swaps in the market (including financial and non-financial firms).

This shows that high rates of growth in the gross market value of interest rate swaps are only marginally paced by options and other instruments, and that forward rate agreements show almost no presence within this figure.

Figure 10 Gross market value of quarterly sales of single-currency interest rate swaps, Jun-98 and Jun-07 (all counterparties)

The growth of the financial market echoes the growth of the overall interest rate swap market, and as can be seen accounts for approximately eighty percent of the traffic within this market.

Figure 11 Gross market value of quarterly sales of single-currency interest rate swaps, Jun-98 and Jun-07 (Financial firms only)

Credit default swaps

The final category of derivatives that will be considered in this context is the credit default swap, one of the main categories of derivative that are included in the BIS reports. Information on these derivatives is only available from the BIS beginning on December 2004, which is congruent with the relatively recent advent of this type of derivative. However, figures were not broken out for financial institutions only until December 2005. As such, the comparison of these instruments will be performed using a December 2005-December 2007 timeframe, rather than the timeframe used for the previous instruments.

Notional value

As can be seen in the line chart below, the growth of credit default swaps over the past several years has been enormous, with the quarterly notional value of the most recent measurement (December 2007) totalling 9.5 times the first measurement in December 2004.

Figure 12 Growth in credit default derivatives, Dec-04 to Dec-07

Figure 13 Growth in quarterly credit default derivatives, notional value (Dec-05 to Dec-07)

Figure 14 Growth in quarterly credit default derivatives, notional value (Dec-05 to Dec-07), financial institutions

As can be seen from the charts above, as well as the information available in the Appendix, almost all of the face value of credit default derivatives is assigned to the financial market. This could have significant consequences in terms of the stability of investment bank and other financial firm portfolios if these credit risk instruments are not appropriately evaluated for the actual level of risk.

Another way in which to consider the issue of credit default derivatives is in the maturity dates of the instruments, which demonstrate the portfolio's long-term versus short-term hedging strategies. The two figures below demonstrate the overall growth in varying maturity categories. As can be seen, the highest growth in notional value in outstanding bought options has been in the category of maturity between 1 year and five years. A similar pattern is seen in the growth in standing sold derivatives, as can be expected if it is assumed that outstanding bought and outstanding sold should be approximately equal.

Figure 15 Growth in outstanding bought credit default derivatives by maturity date, Dec-05 - Dec-07

Figure 16 Growth in outstanding sold credit default derivatives by maturity date, Dec-05-Dec-07

Gross market value

The gross market value of quarterly total trades in credit default swaps grew substantially over this period as well, as can be seen in Figure 17 below.

This market grew from quarterly revenues of almost nothing to over 2,000,000 million US dollars over a period of 3 years.

Figure 17 Growth in quarterly trade in credit default swaps, gross market value (December 2004-December 2007)

Figure 18, below, demonstrates the growth in these instruments across the time period for both all parties and financial parties. As can be seen, the growth was noticeable in all categories; however, the financial counterparties showed a considerably higher growth rate of these instruments, outstripping the growth of the non-financial institutions by several times.

Figure 18 Growth in credit default swaps, Dec-05 to Dec-07 (All parties)

Data from which these results are derived is available in Appendix A.


The results of the above analysis yielded a clear demonstration that the use of credit derivatives, as well as other types of derivatives, is growing rapidly, particularly in the financial market. First of all, it becomes clear that the main participant in the credit derivative market, particularly in terms of credit default swaps, is the financial institution.

While the BIS data did not provide the required granularity to determine what the overall distribution between commercial, consumer and investment banks as well as other financial institutions was the actual distribution of the data, it is clear that the majority of participants in this market are in fact financial institutions. This is in contrast to Gibson's (2007) assertion that a wide range of participants uses the market. However, in accordance with Gibson's argument, it is true that discussion of the use of credit risk derivatives should not rely on data from a single source (Gibson, 2007, p. 25). Gibson presented information derived from three different sources that may offer a more thorough picture of the overall participation in the market of other participants, in contrast to the BIS data that primarily reflected only the financial firms.

However, it should also be considered that the difficulty in tracking the OTC derivatives market is that these trades are not regulated and as such may not be fully reported or appropriately reported in all cases; as such, it could be the case that individuals or private non-financial firms that interact with the credit derivatives market under-report their involvement, leading to a skewing of the data available from the BIS. According to Gibson, banks primarily use credit derivatives to reduce their credit risk load, and while some large banks took on credit risk, these increased credit risk loads tended to be only between 2 and 6 percent of traditional lending practice risk (Gibson, 2007, p. 26).

It is also clear that the growth of credit risk derivatives between 2004 and 2007 is out of line with that of other derivatives, in some cases nearing the level of growth over two years that other types of derivatives saw in nine. This increased growth must be considered carefully for its implications as well as examined in case, as evidence points to now, the use of these derivatives is not appropriate for the banking context.


There are a number of recommendations for the use of derivatives in financial portfolio management that can be derived from this study. The first is that, as should be obvious from the uses of derivatives in the financial market as a whole and from prior research into the area, care should be taken in order to ensure that the risk of the underlying asset and the potential for performance should be appropriately determined. Without this determination, it is not possible to ensure that the firm can engage in appropriate risk management through a hedging strategy, because there will be no way to determine whether the instrument holds the appropriate amount of risk or whether it does not.

This should be of primary concern in regard to inclusion of derivatives in the portfolios of banks, in particular; this is especially true of credit risk derivatives, which as shown above might inadvertently expose the bank to a greater level of risk than had been intended by the portfolio manager.

Another recommendation is somewhat based in the structure of compensation for fund managers and corporate culture of the bank, however. As noted above, derivatives are often used in banking investment portfolios for non-financial reasons, including manager training and incentives to take riskier positions than would otherwise be accepted and the assumption on the part of the shareholder or other overseers that the portfolio must include certain types of derivatives in order to be appropriately diversified. As can be seen from the above, this is not necessarily the case, and the use of inappropriate diversification and risk management strategies may actually hinder the portfolio's performance more than it helps.

In particular, it may take several years for the effects of a given hedging effort to take place. There are also the potential for mismanagement, such as that which occurred with Metalgesellschaft in the early 1990s. All of these factors indicate that a firm should consider before it uses hedging whether this is truly necessary, or whether the firm can reduce its risk in other ways, particularly as applies to credit risk derivatives. While interest rate and currency hedging strategies may in many ways be safer and more reliable (as well as serving a more defined business need), these strategies too should be considered carefully before engaging in them.

Chapter 5 Conclusions

This paper has explored the structure, uses and risks of the derivative market as it applies to financial institutions. It provided an overview of the structure of the derivative and derivative trading strategies and markets, and explored the use of derivatives in financial management. Research and analysis concluded that the use of derivatives has increased substantially within all markets in the last decade, in some cases showing gains in quarterly trading volume of almost ten times from the previous decade. The credit risk derivative market in particular showed surprisingly high gains in growth over time.

All of this information can lead to the conclusion that the use of derivatives is a rapidly growing strategy that cannot be expected to slow at this point. The use of derivatives for managing portfolio risk in a number of different ways has become entrenched in portfolio management. This is a positive situation because it leads to more stable portfolios that are closer to the efficient portfolio, and it reduces and spreads risk. However, the risks and potential difficulties of using credit derivatives should not be ignored. In particular, the use of credit derivatives for non-financial reasons, such as rote manager training or reducing the perceived riskiness of a high-risk portfolio, should be frowned upon and should not be considered to be an appropriate use of the instruments.

Without the limiting of the use of these instruments, there is the potential that the market could show drastically decreased performance as exposure to credit risk grows exponentially along with the use of credit risk derivatives. In particular, the actual level of risk of credit risk derivatives should be carefully examined in order to ensure that the firm is not placing itself at risk for increased exposure that is outside its intended exposure. This type of unintentional risk cannot be considered to be systematic risk, and must be considered to be risk that is specific. As such, it must be guarded against in order to avoid the perception of less risk in the portfolio than is actually present.

Derivatives must not be considered to be a risk-free asset, but instead should be used to balance other risks that occur naturally within the portfolio. This is clear within the literature of derivative structure and use, and is clearly best practice among trading strategy analysts. However, how often this is considered in practice is a matter of debate. For example, the use of credit derivatives to spread risk among the banking industry ignores the fact that this risk is still present; even if it is moved to other individuals or firms, the resulting risk will still negatively impact somewhere.

This was seen with the United States subprime mortgage collapse in 2007; with a higher than expected rate of loan default, the credit risk derivatives associated with these debts accelerated faster than many banks were prepared to handle, and many banks ended up with a higher level of risk within their portfolios than they had anticipated. A repeat of this incident could easily result in similar outcomes if the use of derivatives is not adjusted appropriately.

Recommendation for further study

One area for further study that turned up during the process of this examination is the potential for use of derivatives in non-financial firms.

The information obtained from the BIS was firmly in the financial category. However, there is the potential that the use of derivatives is not only limited to financial firms, as would be suggested by the BIS data, but is actually common throughout the business world. This is hinted at by Gibson's (2007) assertion that only approximately five to ten percent of the reporting dealers' volume was due to their own hedging activities, and that the remainder was related to client activities and other firms.

This indicates that a significant portion of what is currently considered to be financial sector activity in this study may in fact be non-financial in nature. However, extracting this information from the current data set would not be possible. Examination of data from one or more reporting dealers should shed some light on the matter and help to determine whether the participation in the credit derivatives market in particular is in fact heavily weighted toward bank participation or if the financial sector participation reflected in the study above is a juxtaposition of banking sector data and the data of clients of the banking sector. This information would allow for a determination of exactly how much risk the financial services industry is actually in, and how much risk is spread among other industries and markets.


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Appendix A Research Data

This section provides charts, graphs and figures to supplement the information in Chapter 4. This information was used in the research process. Where necessary, information that is not relevant to the current examination has been trimmed in order to increase the clarity of the description. All figures are in US dollars.

Instrument type (OTC)



June 98 Notional value

June 07

Notional Value

June 98

Gross market value

June 07

Gross market value

All instruments

All counterparties (net)





Total foreign exchange including gold

All counterparties (net)





Forwards and swaps

All counterparties (net)





Forwards and swaps

Reporting dealers (net)





Forwards and swaps

Other financial institutions





Forwards and swaps

Non-financial institutions





Forwards and swaps inc. gold

All counterparties (net)





Currency swaps

All counterparties (net)





Currency swaps

Reporting dealers (net)





Currency swaps

Other financial institutions





Currency swaps

Non-financial institutions





Total options

All counterparties (net)





Options sold

All counterparties (gross)





Options sold

Reporting dealers (gross)





Options sold

Other financial institutions





Options sold

Non-financial institutions





Options sold inc. gold

All counterparties (gross)





Options bought

All counterparties (gross)





Options bought

Reporting dealers (gross)





Options bought

Other financial institutions





Options bought

Non-financial institutions





Options bought inc. gold

All counterparties (gross)





Table 3 Data for analysis of foreign exchange derivatives trading, 1998-2007

Instrument (OTC)


Jun 98 Notional value

Jun 07 Notional Value

Jun 98 Gross market value

Jun 07 Gross Market Value

All instruments

All counterparties (net)





Forward rate agreements

All counterparties (net)





Forward rate agreements

Reporting dealers (net)





Forward rate agreements

Other financial institutions





Forward rate agreements

Non-financial institutions





Interest rate swaps

All counterparties (net)





Interest rate swaps

Reporting dealers (net)





Interest rate swaps

Other financial institutions





Interest rate swaps

Non-financial institutions





Total options

All counterparties (net)





Options sold

All counterparties (gross)





Options sold

Reporting dealers (gross)





Options sold

Other financial institutions





Options sold

Non-financial institutions





Options bought

All counterparties (gross)





Options bought

Reporting dealers (gross)





Options bought

Other financial institutions





Options bought

Non-financial institutions





Table 4 Selected data for single-currency interest rate derivatives

Data type


Counter party

Dec 05

Dec 07

Notional amounts outstanding bought


All counterparties (gross)



Notional amounts outstanding bought

Maturity of one year or less

All counterparties (gross)



Notional amounts outstanding bought

Maturity over 1 year and up to 5 years

All counterparties (gross)



Notional amounts outstanding bought

Maturity over 5 years

All counterparties (gross)



Notional amounts outstanding bought


All counterparties (gross)



Notional amounts outstanding bought


All counterparties (gross)



Notional amounts outstanding sold


All counterparties (gross)



Notional amounts outstanding bought


Banks and security firms



Notional amounts outstanding sold


Banks and security firms



Notional amounts outstanding bought


Insurance and financial guaranty firms



Notional amounts outstanding sold


Insurance and financial guaranty firms



Notional amounts outstanding bought


Non-financial institutions



Notional amounts outstanding sold


Non-financial institutions



Notional amounts outstanding bought





Notional amounts outstanding sold





Notional amounts outstanding bought


Other financial institutions



Notional amounts outstanding sold


Other financial institutions



Notional amounts outstanding bought


Reporting dealers (gross)



Notional amounts outstanding sold


Reporting dealers (gross)



Table 5 Notional figures for credit risk derivatives


Dec 05 Gross market value

Dec 07 Gross market value

All instruments



All instruments



All instruments



All instruments



All instruments



All instruments



All instruments



Single-name credit default swaps



Multi-name credit default swaps



Table 6 Gross market value figures for credit risk derivatives