Question

Solve for the call option premium given the following information:
Current Stock Price: $63 (non-dividend paying stock)

Strike Price: $65

Risk Free-rate: 5.00%

Time to expiration: 9 months

Put premium: $5.50

If the above call option is an American-style call option, would it make sense for the holder of the option to exercise the option before expiration? Why or why not? Based on what you know about the relationship between American and European options, what is the call option premium of an American-style option given the above data?

Answer 1

Current Stock Price, S₀: $63 (non-dividend paying stock)

Strike Price, K: $65

Risk Free-rate, r : 5.00%

Time to expiration, T : 9 months = 9/12 = 0.75 year

Put premium, P₀: $5.50

PV (K) = Present value of K = K / (1 + r)^T = 65 / (1 + 5%)^0.75 = $  62.66

If C₀ is the call premium, let's recall the Call put parity equation on a European option:

C₀ + PV (K) = P₀ + S₀

Or, C₀ + 62.66 = 5.50 + 63 = 68.50

Hence, C₀ = 68.50 - 62.66 = $ 5.84

For a non dividend paying stock, it doesn't make sense for a holder of American call option to exercise early i.e. before expiration. This is because the option holder will make more money by selling the option rather than exercising the option earlier. At any point in time, the option has two values = intrinsic value (S - K) + time value. On exercise the money a call option holder makes = S - K = intrinsic value of the option only. By selling the option, the option holder will make not only the intrinsic value but also the time value.

The American call option premium = European call option premium = $ 5.84.