Mr. Franklin gained experience with basic option strategies at his previous job. As an exer se, he decides to review the fundamentals of option valuation using a simple example. Mr. Franklin ,c-ognizes that the behavior of an option's value is dependent on many variables and decides to sp nd some time closely analyzing this behavior, particularly in the context of the Black-Scholes op on pricing model (and assuming continuous compounding). His analysis resulted in the informa on shown below:
Exhibit 1: Input for Option Pricing Stock price $100 Strike price $100 Interest rate 7% Dividend yield 0% Time to maturity (years) 1.0 Standard deviation of stock 0.20
Exhibit 2: Option Sensitivities Call Put Delta 0.6736 -0.3264
1. Mr. Franklin wants to compute the value of the call option using the information in Exhibit I. Which of the following is closest to his answer? a. $4.78 b. $5.55 c. $11.54
2. Mr. Franklin wants to compute the value of the put option that corresponds to the call value ca culated in the previous question. Which of the following is the closest to his answer? a. $4.78 b. $5.55 c. $11.54
3. Mr. Franklin is interested in the sensitivity of the put option to changes in the volatility of the underlying equity's returns. If the volatility of the underlying equity's returns increases, the value of the put option: a. Decreases. b. Increases. c. Does not change. 4. Mr. Franklin wants to know how the put option in Exhibit 1 behaves when all the parameters a held constant except delta. Which of the following is the best estimate of the change in the put option's price when the underlying equity increases by $1? a. $.33 b. -$.33 c. -$3.61
What's on the Web?
1. Black-Scholes Model Go to www.numa.com and find the option pricing calculator. There is a call and a put option on a stock that expire in 30 days. The strike price is $55, and the current stock price is $58.70. The standard deviation of the stock is 45 percent per year, and the risk-free rate is 4.8 percent per year, compounded continuously. What is the price of the call and th put? What are the deltas for the call and the put?
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