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Advanced Financial Modeling

In: Business and Management

Submitted By gallen
Words 384
Pages 2
Problem Set 1: Options

1. The strike price of a call option on GM common stock is $50. a) What is the payoff at expiration of this call if, on the expiration date, GM stock sells for $45? b) What is the payoff at expiration of this call if, on the expiration date, GM stock sells for $55? c) Draw the payoff diagram for this option.

2. Use the Black-Scholes model to price a call with the following characteristics: Stock price = $65 Strike price = $70 Time to expiration = 120 days Stock price variance = 0.35 Risk-free interest rate = 0.05

3. Suppose there is a call option on Go-East Airlines with a strike price of $22. Today’s date is May 3, 2015 and the call expires on May 18, 2015. The current risk free rate on a T-bill that matures the on the option’s expiration day is 1.8%, annualized. Go-East Airlines’ stock is currently trading $23 per share. The historical standard deviation for the stock is 22%. Assume that the option is European and that Go-East does not pay dividends. a) Use the Black-Scholes option pricing formula to determine the value of the call option. b) What is the value of a put option on Go-East Airlines that matches in maturity and strike price?

4. On August 7 2015, the Nokia Corporation’s stock traded at $15.36. At the time the stock price was quoted, the most actively traded option for this stock was a call option with September 2015 maturity and a strike price of $17.50. Assume that the option matures in exactly 30 days, and assume a US Treasury Bill with the same maturity has an annualized return of 1.20%. The variance of the stock price is 10% annually. You can assume that options for Nokia have European type exercise structure. a) Calculate the Black-Scholes price for the call option described above. b) Calculate the price of a put option that has the same strike price and maturity as…...

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