Consider a stock currently trading at 25 that can go up or down by 15 percent pe
ID: 2800097 • Letter: C
Question
Consider a stock currently trading at 25 that can go up or down by 15 percent per period. The risk-free rate is 10 percent. Use one-period binomial model.
a, Determine the two possible stock prices for the next period.
b. Determine the intrinsic values at expiration of a European call with an exercise price of 25.
c. Find the value of the option today.
d. Construct a hedge by combining a position in stock with a position in the call. Calculate the hedge ratio and show that the return on the hedge portfolio is the risk-free rate regardless of the outcome, assuming that the call trading at the price obtained in part c.
e.Determine the rate of return from a risk-free hedge if the call is trading at 3.50 when the hedge is initiated.
Explanation / Answer
Determine the two possible stock prices for the next period. up 15%: Su = 25 × 1.15 =28.75 down 15%: Sd = 25 × 0.85 =21.25 Determine the intrinsic values at expiration of a European call with an exercise price of 25. up 15%: Cu= Max(0, Su – X) = 28.75 – 25 =3.75 down 15%: Cd= Max(0, Sd – X) = 21.25 – 25 =0 Find the value of the option today. p = [(1 + r) – d] ÷ (u – d) =(1.10 – 0.85) ÷ (1.15 – 0.85) = 0.8333 à1 – p = 1 - 0.8333 = 0.1667 C = {(p × Cu) + [(1 – p) × Cd]} ÷ (1 + r) = [(0.8333 × 3.75) + (0.1667 × 0)] ÷ 1.10 =2.84