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Problem 16-05

Consider the following data relevant to valuing a European-style call option on a nondividend-paying stock: X = 40, RFR = 10%, T = six months (i.e., 0.5), and = 0.28.

1. Compute the Black-Scholes option and hedge ratio values for the series of hypothetical current stock price levels shown below. You may use Appendix D to answer the question. Do not round intermediate calculations. Round the Black-Scholes option values to the nearest cent and the hedge ratio values to four decimal places.

   Stock Price	Call		Hedge Ratio
   $25	$
   $30	$
   $35	$
   $40	$
   $45	$
   $50	$
   $55	$

2. Determine how your answer in Part a would differ under the following separate circumstances: (1) the time to expiration increases, and (2) the volatility of a nondividend-paying stock increases.

   An increase in time to expiration causes a(an) -Select-decreaseincreaseItem 15 in the call value. An increase in the volatility causes a(an) -Select-decreaseincreaseItem 16 in the call value.

3. For S = 40, calculate the Black-Scholes value for a European-style put option. How much of this value represents time premium? Do not round intermediate calculations. Round your answers to the nearest cent.

   Put value: $

   Time premium: $