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 using the call option and the risk-free asset, we need to find the delta of the option, which is the ratio of the change in the option's price to the change in the stock's price. If the stock price goes up to $160, the call option's value (with an exercise price of $140) will be $20 ($160 - $140). If the stock price goes down to $135, the call option will be worthless ($0). The change in the option's price is $20 - $0 = $20, and the change in the stock's price is $160 - $135 = $25. Therefore, the delta (Δ) is $20 / $25 = 0.8. To replicate the stock, you would need to buy 1 / Δ = 1 / 0.8 = 1.25 calls.

You Are Evaluating a Call Option with an Exercise Price