Consider a stock currently worth $80 (S = 80) that can go up or down by 25 percent per period. The exercise price is $80 (X = $80) and the risk-free rate is 5 percent (r = .05). The option will expire at the next period (t = 1). You try to find a theoretically fair value of the call using a one-period binomial option pricing model. Answer the following questions. (Hint: See Ch 16 Teaching Notes and Excel Spreadsheet)
Compute the u and d in the binomial option pricing model such that the stock prices at the next period are Su and Sd.
What are two possible stock prices at the next period?
What are the intrinsic values at expiration of a European call option if the stock goes up and down?
Compute two values at expiration of a European call option (Cu and Cd)?
Compute the binomial probability (p)?
Find the theoretical fair value of the call option today using the one-period binomial pricing model.
Compute the riskless hedge ratio (h).
In order to construct a riskless hedge position by buying stocks and selling 1,000 calls using the riskless hedge ratio (h). How many stocks should you buy at what price? At what price should you sell the calls?
Compute the initial value of the riskless hedge position (V0).
Compute the market values of the riskless hedge position at the next period if the stock goes up (Vu) and goes down (Vd).
Find the rate of return on the riskless hedge position (R).