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Sample_Questions_Exam2_f5108_08_sol - Sample Questions Exam...

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Sample Questions Exam 2 Finance 5108 1. The Black-Scholes-Merton is based on certain assumptions. What are those assumptions? 1.Security prices follow a Weiner process that depends on the following equation. + dS S dt S dt μ σ = . This is a process in which securities have a return of u and a random component that has a variance of σ. 2. Short selling can be done with use of the full proceeds 3. Frictionless markets with perfectly divisible securities 4. No dividends 5. Exercise can only be at expiration 6. No arbitrage condition 7. Securities are traded continuously 8. Flat yield curve whose return is constant 2. What is the value of a call option on a non dividend paying stock that has a strike price of $50, the stock is currently trading at $49, has an implied volatility of 25%, risk free rate of 3% and a time to expiration of 4 months? What would be the value of a put option with the same parameters? 2 1 2 4 -.03( ) 12 49 .25 4 ln + .03 + 50 2 12 = .00148 4 .25 12 4 = .00148 .25 -.1429 12 Using the attached chart N(.00) = .5000 N(-.14) = 1- .5557 = .4443 c = 49(.5000) - 50e (.4443) = 24.50 - 21.99 d d = - = = 2.51 3. What is implied volatility and why is it used in the pricing of option instead on the volatility calculated using standard statistical techniques? The problem with the continuous time assumption is that securities do not trade continuously but trade in discrete time increments. This leads to the problem that the traditional method of using statistics to estimate the volatility. The implied instantaneous volatility is an estimate using the current price of the underlying asset to back into the instantaneous volatility. Using a model such as the Black-
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