You are evaluating a call option with an exercise price of $140. The underlying stock has possible prices of $135 or $160 when the option expires. If the risk-free rate is 6%, how many options do you
Need to buy along with the risk-free asset to replicate the stock?

Question

Quizplus · Accepted Answer

To replicate the stock, we need to find the number of calls such that the payoff from the calls exactly matches the payoff from the stock at both possible stock prices. At $135, the option is worthless since the stock price is below the exercise price. At $160, the option has a payoff of $20. Thus, we need to solve for the number of calls that give a payoff of $20 when the stock price is $160.

The payoff from a call option at expiration is Max[0, S-X], where S is the stock price and X is the exercise price. At $160, the payoff is Max[0, 160-140] = $20. To replicate this payoff, we need 1.25 calls: 
1.25 * Max[0, 160-140] = $20

Therefore, we would need to buy 1.25 calls along with the risk-free asset to replicate the stock.

You Are Evaluating a Call Option with an Exercise Price