Question

You have the following information about forward and options contracts on the same stock. All derivatives have one-year maturity. Risk-free rate is 10%. S₀ = $45.25, F_0,1 = %50, C_K=45 = $7.70, C_K=45 = $5.40, P_K=45 = $3.20, and P_K=50 = $5.40.

What is the profit if you hedge a short position of the stock with a 45-strike call if the stock price at maturity is $47?

Answer 1

Since we are having a short position on the stock we are afraid of stock price rising. To protect against this we will go long a call option.

Premium paid on call option of exercise price 45 = $7.70

If the stock price at maturity is $47, call option is exercised and payoff will be
Payoff from call option = Share Price – Exercise Price
                                                = 47 – 45
                                                = $2

Loss from call option = Premium paid – Payoff from call option
                                          = $7.70 - $2
                                          = $5.70