1 Problem Set I on Chapters 20,21 – Option Valuation 1. You are considering the sale of a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends,...

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1 Problem Set I on Chapters 20,21 – Option Valuation 1. You are considering the sale of a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it will either increase to $120 or decrease to $80. The risk-free rate of interest is 10%. a. Describe the specific steps involved in applying the binomial option pricing model to calculate the option’s value, and show the value. b. Compare the binomial option pricing model to the Black-Scholes option pricing model. (No Black-Scholes calculations are necessary). 2. Describe the condition under which it would be rational to exercise both an American-style put and call stock option before the expiration. In both cases, comment specifically on the role that dividends pay. 3. Explain why a change in the time to expiration (i.e., T) can have either a positive or negative impact on the value of a European-style put option. In this explanation, it will be useful to contrast the put’s reaction with that of a European-style call option, for which an increase in T has an unambiguously positive effect. 4. Consider the following questions on the pricing of options on the stock of ARB, inc.: a. A share of ARB stock sells for $75 and has a standard deviation of returns equal to 20 percent per year. The current risk-free rate is 9% and the stock pays two dividends: (1) a $2 dividend just prior to the option’s expiration day, which is 91 days from now (i.e., exactly one-quarter of a year); and (2) a $2 dividend 182 days from now (i.e., exactly one-half year). Calculate the Black-Scholes value for a European-style call option with an exercise price of $70. b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price? c. Calculate the change in the call option’s value that would occur if ARB’s management suddenly decided to suspend dividend payments and this action had no effect on the price of the company’s stock. d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: 1) the volatility of ARB stock increases to 30 percent, and (2) the risk-free rate decreases to 8 percent.