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Dissertation Proposal, equity default swaps and barrier options, a comparison of the two.

To present this framework for this empirical study on hedging strategies, the author will compare equity default swaps and barrier options. Today’s Financial Managers, unlike their forerunners, have the ability to resource funding from the broadest and most liquid capital markets in history almost to the extent that bank relationships have become a non-essential commodity. Therefore their choice of option is based on previous results and predicted outcomes.

Banks have started to provide multi-dimensional relationships and offer better performance. Today there is an alternative; non-bank financial services firms provide specialised financial products. Organisations need to address this expanding portfolio of borrowing options, and can consider a blended relationship; this can help them to satisfy the needs of the company.

Therefore financial decisions are made in relation to choosing a provider and then ultimately what strategy will be utilised in the portfolio.  This hypothesis is based on the later, the hedging decisions of equity default swaps and barrier options. A digital barrier option is an option that consists of a barrier, if this barrier is reached it affects the existence of the option. Whereas equity default swap are technically an equity derivative, which behaves similar to a fusion of credit and an equity derivatives.

This study will analysis these forms of hedging using the binomial model, which was further developed by Cox, Ross, and Rubinstein, this model has its roots in the Black-Scholes model, but takes into account dividends, variable-interest-rate and non-constant-volatility assumptions.

Literature Review

The organisations financial policies on risk management of cash borrowings and foreign exchange, are intended to support their objective of maintaining shareholder value by managing, controlling and limiting their financial risks. The onset of the worldwide economic recession, including high interest rates, and the suspension of the UK from exchange controls in 1979 has led to a more cautious approach to borrowing. This was reinforced by a series of well-publicised financial disasters (Bryant, M 1998).

Within the UK debt is kept high for further financial advantages. There is evidence that organisations have a target level of capital gearing at the aggregate level, which in the long run depends on the tax advantages of debt and on the probability of bankruptcy, which will be related to the expected costs of financial distress (Bunn, P and Young, G 2004).

Approaches

Arnott & Bernstein, (2002) suggested that equity risk premium is “for the forward-looking, expected or required returns and equity excess return for historical performance numbers”. The total equity premium is the compensation investors require for risk and for non-risk items such as term structure expectations, trading costs, and taxes. Equities, bonds, and cash have one important general characteristic in common; they each provide a flow of income over a period of time. Any income-producing asset can be calculated for their future expected cash flows at an appropriate rate, when taking into account all relevant information, for example credit rating, interest rate risk, discretionary variability of dividend income, trading, and tax costs (Arnott, R. & Bernstein, P 2002:22).

Equity default swaps
Equity default swaps use the credit default swap technology, but not to transfer credit risk, they transfer the risk of major diminution in the market value of shares. Another feature of equity default swap (EDS) application has been that credit default swaps CDOs have been included in equity default swaps in their overall portfolio, together with, the total rate of return swaps (Davydov, D & Linetsky, V 2001).

The first major transaction of CDO integrate EDS was Moody’s Odysseus deal arranged by Morgan, which consisted of a portfolio of 100 reference entities, with 10% of these being EDS. In 2004 in Japan Daiwa Securities took the EDS concept further when it launched the first publicly rated arbitrage CDO 100% collateralised by EDS. Zest Investments issued 31.5 billion notes in five different classes, backed by EDS on a portfolio of 30 quoted blue chip companies’. Payment to the protection will be triggered if the share price of any of the companies in the EDS portfolio falls by more than 70% from its initial price and if the share price fails to recover to the initial level by December 2008 (Camara A 2005).

Barrier options
Barrier options are a well-accepted type of path-dependent options traded over-the-counter on stocks, stock indexes, currencies, commodities, and interest rates. There are several reasons to use barrier options rather than standard options. First, barrier options strongly match investor beliefs about the future behaviour of the asset. Second, barrier option premiums are generally lower than those of standard options because an additional condition has to be met for the option holder to receive the payoff. The premium can be reduced considerably, in particular when the volatility is high (Davydov, D & Linetsky, V 2001).

A digital barrier option is a digital option that includes a barrier, which, if reached during the life, affects the existence of the option. The barriers may be placed either above the strike or below, meaning that prior to expiry, an active digital can be knocked out or an inactive digital can be knocked in. Because the use of barriers decreases the probability that the digital will pay off, the gearing factor will be higher than a regular digital. A digital option is an option that pays out a fixed amount if the option at maturity is in the money (ITM). It is similar to a European option in that at expiration it must be ITM to payout, and similar to a One-Touch Binary in that it pays a fixed amount (Camara A 2005).

For example an investor thinks that EUR/USD will be above 0.9900 in 3 months’ time, although not to the extent that they would profit from buying a European option. Instead they purchase a 3-month, 0.9900 Digital Option that has a gearing factor of 7:1. The investment made is €25,000 with a Spot Reference:0. 9250 These Digital options usually suit those having very specific spot views and/or premium constraints. Result if spot is above 0.9900, then the investor receives a payment of €175,000, if spot is below 0.9900 then the option expires and is worthless (Camara A 2005).

Barrier options are path dependent option that has one of two characteristics: (1) Either a knockout, which causes the option to immediately terminate if the underlier reaches a specified barrier level, or (2) knock-in feature causes the option to become effective only if the underlier reaches a specified barrier level. Premiums are paid in advance, although due to the contingent nature of the option, they tend to be lower than for example a corresponding vanilla option. Whereas equity default swap is a variety of over the counter derivative, although technically an equity derivative, it behaves like a fusion of a credit derivative and an equity derivative. The title “equity default swap” appears a contradiction, how can equity default; the product is a resemblance to credit default swaps, whose structures it imitates (Camara A 2005).

An equity default swap is a mode for one party to provide another party protection against a possible event relating to their reference asset. As with a credit default swap, the reference asset is a debt instrument, and protection is provided against a credit event for example a default. With equity default swaps, the reference asset is part of the company's stock, and therefore it provides protection against a marked decline in the price of the stock. An illustration of this is if the equity default swap provides protection against a 50% drop in the stock price, from the date when the equity default swap was initiated; this event will be protected, this is also known as the trigger event or knock-in event (Camara A 2005).

Which Model to apply
Amongst the major models that have been developed to help the financial markets is the Black-Scholes model in 1973. Although financial historians have traced the origins of this model to the seminal work of Bachelier (1900) and to the extensions of Sprenkle (1962), Boness (1964), and Samuelson (1967), it is clearly the insights provided by Black and Scholes as well as Merton (1973) that revolutionised the financial markets. The key factor is the notion that an option can be perfectly hedged with a unit of the underlying asset (Chance, D 1999).

The Black-Scholes model is increasingly being viewed as the model of choice, but it is questioned whether it merits should earn this status. Outside the investment industry, the model isn't well understood, and vital considerations such as the impact of vesting on option values remain unresolved. The original model’s inputs are the volatility of the underlying stock's returns, the option strike price, and the stock's market price, a risk-free interest rate and the option's term (Young C 1993).

Versions of the model allow the use of less-restrictive assumptions in valuing stock options. These include adjustments for dividends, as well as variable-interest-rate and non-constant-volatility assumptions. Although many users employ modified versions of the model that permit relaxing the underlying assumptions, generally the resulting values do not differ radically from the original model adjusted for dividends. When valuing executive stock options, this version seems to appropriately balance the trade-offs between ease of use and theoretical accuracy (Young C 1993).

Rubinstein (1976) remarked that “the Black-Scholes model can be obtained in an equilibrium economy, when agents have power utility functions characterised by CPRA and aggregate wealth and the stock price are jointly distributed” (Rubinstein (1976) cited in Camara A 2005:1686).  In their paper, Black and Scholes (1973) assume that "the stock price follows a random walk in continuous time ... and thus that the distribution of possible stock prices is lognormal” (Black and Scholes (1973) cited in Camara A 2005:1686).

Closely linked to the Black-Scholes model was a parallel development of the binomial model. The binomial model demonstrates, using an asset with only two possible future prices, how an option is combined with the asset to form a risk-free hedge, leading to a process for obtaining the option price. It is considered a discrete time model, allowing trading only at finite time intervals. This model was developed further by Cox, Ross, and Rubinstein (1979), and is well respected in the financial world. In their papers the life of an option is split into an increasing number of smaller and smaller time intervals, the option price obtained from the binomial procedure joins to the Black-Scholes price (Chance, D 1999).

The binomial and Black-Scholes models offer insight on the derivatives, which can be priced using a risk neutral approach. Risk neutrality, is the detestation to modern portfolio theory, it is the conception that investors do not care about risk and are content to price a risky asset as the accepted payoff of the asset discounted at the risk-free rate.  Although it is argued that theorists do not assume risk neutrality. They accept that (1) the prices of underlying assets are determined in a fair market and are observable, and (2) arbitrage opportunities do not exist (Chance, D 1999).

Therefore the binomial model developed Cox, Ross, and Rubinstein will be used for this study. This model includes more financial factors and events, which can influence and affect the price, than the Black-Scholes model. The binomial model will give a more advanced analysis of the financial outcomes when comparing the equity default swaps and barrier options.

Methodology

Secondary Research

The secondary methodologies that are used for the research are an extensive literature review, to discuss contemporary and historical research on the topic. This will include books, journals, financial papers and Internet sites (Saunders, M. et al 1997). This review will start wide discussing the well-used financial options that are available, and then focus equity default swaps and barrier options

The literature review is expected to meet the following criteria

1. Review the most used, existing theories and models on hedging strategies
2. Introduce and discuss equity default swaps and barrier options
3. Discuss the advantages and disadvantages of the model chosen for the research

Primary Research

The first stage of primary research will be a questionnaire sent to a cross section of practioners in the financial markets (Saunders, M. et al 1997).

The questionnaire will

1. Reveal primary information on financial decisions
2. Identify which method of hedging practioners prefer
3. With the rationale for these choices
4. Compare this to the contemporary theorists

The majority of the primary research will be the application of the developed binomial model to equity default swaps and barrier options, within a set of predetermined events in separate money markets. These hypothetical investments will be in as similar conditions as possible; to reduce any predicted difference on return (Saunders, M. et al 1997). 

The primary research will

1. Reveal primary information hedging methods
2. Identify the most consistent method for hedging
3. Compare this to the contemporary theory

The Cox, Ross, and Rubinstein (CRR) binomial model is easy to construct and is probably the most widely accepted and popular binomial model. To set up the CRR model in Microsoft Excel, enter the data in cells A7 to B12 (D'Urso, J 2005).

Then, enter the labels as shown in cells A16 to A21. Finally, the following formulas will be entered the in the corresponding cells:
B17 =B11/B12
B18 =(EXP (B10*SQRT (B17)))
B19 =1/B18
B20 =(EXP (B9*B17)-B19)/(B18-B19)
B21 =EXP (-B9*B17)

The next stage is to set up a “stock price tree” this will generate various stock prices for example up and down prices at each step over the life of the option. The end result is a standard binomial model that can be adapted to fit any organisation. This is not the full formula; this is available in D'Urso (2005) journal article, and easily converts CRR binomial model into Microsoft excel spread sheet, this will be used to calculate the formula (D'Urso, J 2005).

Conclusions
The choice of model used is favoured by practioners, although it is not universally used. The questionnaires will help to identify the rationale behind this, and offer further discussion on the compared hedging options and alternatives.

Using the CRR binomial model to compare the two chosen methods of hedging equity default swaps and barrier options will reduce bias and increase the validity and accuracy of the findings. This will then be compared to the theory presented in the literature review.

Bibliography

Arnott, R. & Bernstein, P (2002) What Risk Premium is 'Normal'
Financial Analysts Journal, March/April 2002

Bostock, P (2004The equity premium: what level should investors require?
Journal of Portfolio Management, Winter 2004 v30 i2

Bryant, M (1998) The evolving role of the corporate treasurer
Management Accounting (British), Feb 1998 v76 n2

Bunn, P and Young, G (2004)
Bank of England, Quarterly Bulletin London, Autumn 2004.Vol.44, Iss. 3

Camara A (2005) Option prices sustained by risk-preferences   
The Journal of Business, Sept 2005 v78 i5

Chance, D (1999) Research Trends in Derivatives and Risk Management Since Black-Scholes(Special Theme: Derivatives & Risk Management) Journal of Portfolio Management, May 1999

Davydov, D & Linetsky, V (2001) Pricing and Hedging Path-Dependent Options Under The CEV Process (constant elasticity of variance) Management Science, July 2001 v47 i7

D'Urso, J (2005) Valuing Employee Stock Options
The CPA Journal. New York: Jul 2005.Vol.75, Iss. 7

Lekkos, I & Milas, C (2004) Common Risk Factors in the US and UK Interest Rate Swap Markets The Journal of Futures Markets Vol.24, Iss. 3

Saunders, M. et al (1997) Research Methods For Business Students
Pitman Publishing. London

Young. C (1993) What’s the right Black-Scholes value? (Valuation of executive stock options) (Corporate Reporting) Financial Executive, Sept-Oct 1993 v9

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