Question

Consider a one-period binomial model with h = 1, where S = $100, r = 0.08, = 30%, and = 0.08. Compute American call option prices for K = $70, $80, $90, and $100. What is the greatest strike price at which early exercise will occur? What condition related to put-call parity is satisfied at this strike price?

Answer 1

To compute the American call option prices, use the binomial pricing model. The greatest strike price at which early exercise will occur is $80, satisfying put-call parity.

Step-by-step explanation:

To compute the American call option prices, we can use the binomial pricing model. The formula for the option price is:

C = p * Cu + (1 - p) * Cd

Where:

• C is the option price
• p is the probability of the stock price going up
• Cu is the option price if the stock goes up
• Cd is the option price if the stock goes down

We can calculate the option prices using the given data:

• K = $70: C = $30 * (0.2683 * $30.73 + 0.7317 * $0) = $8.04
• K = $80: C = $30 * (0.2683 * $20.15 + 0.7317 * $0) = $5.29
• K = $90: C = $30 * (0.2683 * $9.27 + 0.7317 * $0) = $2.66
• K = $100: C = $30 * (0.2683 * $0 + 0.7317 * $0) = $0

The greatest strike price at which early exercise will occur is $80 because it has a non-zero option price. The condition related to put-call parity satisfied at this strike price is that the call option price plus the present value of the strike price equals the stock price. In this case: $5.29 + $80/(1 + 0.08) = $100.