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Your rich uncle has left you a one third interest in an offshore oil property with estimated reserves of 50 million barrels.
The present value of the development cost is $12/bbl, and the development lag (the time between when development begins until the wells begin producing) is two years.
Your uncle's partners have an option of up to twenty years to develop the resource, and the marginal value per barrel is at present $12.
Once developed, net production revenue each year will be 5 per cent of the value of the reserves. The riskless rate of interest is 8 per cent and the variance in the in (natural logarithm) of oil prices is 0.03.
What is the value of your uncle's interest in the investment opportunity?
The first general equilibrium option valuation formula was published by Fischer Black and Myron Scholes in 1973. It is known as Black-Scholes formula. They recognize that to riskless portfolio can be constructed when shares and calls will join. They create skills in using analysis which gives a no-arbitrage value for European-Style call options on shares.
The Black-Scholes model is usually observed closely as either in starting or in the end of the story. This formula solved a problem with which economists didn't found the answer for at least three-quarters of a century. To consider the Black-Scholes model in the context of a family tree of option pricing models is very useful. By selling options that should exercise early and then hoping they won't be, gives money to some people. Where the stock price is under the strike price then instead of buying stock we can sell put options. If then puts didn't came in action, we will get an extra profit, which can be balanced in other cost of trading.
The formula deceives that by placing orders, either stock or prices will be unaffected. Though at a special time, we can affect prices with orders. The assumptions are not complicated for this problem. But the formula is tough to understand as it includes the complex mathematics for calculation.
The Assumption Behind The Black-Scholes Model:
- No Dividends: This assumption says that during option's life cycle, stock does not pay dividends. Generally, shareholders get dividends from mostly all companies. The basic model later accommodate for dividends. The assumption relates to basic Black-Scholes model to get dividends. If we like to adjust the Black-Scholes model for dividends, then just we need to less the discounted value of a future dividend from the stock price.
- Efficient Markets: The Black-Scholes modelsuggests that people cannot continuously forecast the direction of a particular stock or market. This model assumes stock moves as a manner related to a random walk. This means that at any particular provided time, the price of present stock can go up or down with same probability rate.
- Interest Rates Constant and Unknown: this assumption is similar to volatility, interest rates are assumed to be same constant. The model uses the risk-free rate to exhibit. This constant and known rate. There is no such thing in real world but can use US Government treasury bills 30 day rate since government there is deemed to be credible enough. Increased volatility can change by these treasury.
- Liquidity: The Black-Scholes model assumes that markets are absolutely liquid and possible to buy or sell any value of stock or options or their denominator at any particular time.
- Lognormally distributed returns: The Black-Scholes model assumes that returns on the underneath stocks are casually distributed. This assumption is quite reasonable in the real world.
- No Commissions and Transaction costs: The model assumes there are no obstruction to do trading and no fees for buying and selling options.
- European-Style options: The Black-Scholes model that only European-style market can only be set in action on the expiration date. American-style options can be taken into action any time during the life cycle. Due to the greater flexibility, American options become more worthy.
- Constant Volatility: This is the most expressive assumption. It is a measure of the expectations to move of a stock in near-term, which is constant over time. While it can also be dependently constant in very short period, but never can be constant in long-term.
The oil property is not viable at current market price, but still it is profitable to accept this property, because the potentiality in oil generates value if oil prices go up. As the oil prices goes up, it will generate potentiality so profitable to keep this oil property.
- Brealey, R.A., Myers, S.C. & Allen, F. (2008) Principles of Corporate Finance, New York: McGraw-Hill/Irwin
- Maxi-Pedia (2009) What are The Assumptions Behind The Black-Scholes Model [online] (cited 14 December, 2009) Available from http://www.maxi-pedia.com/Black+Scholes+model+assumptions
- QuickMBA (2009) Black-Scholes Option Pricing Formula [online] (cited 14 December, 2009) Available from http://www.quickmba.com/finance/black-scholes/
- Rubinstein, M. Ed., (1992) From Black-Scholes to Black Holes, New York: Risk Magazine Ltd.
- Bodie, Z., Kane, A. & Marcus, A.J. (2009) Investments, 8th Edition, New York: McGraw-Hill.
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