The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. Which of the following hedges the position?
A) Buy 0.6 shares for each call option sold
B) Buy 0.4 shares for each call option sold
C) Short 0.6 shares for each call option sold
D) Short 0.4 shares for each call option sold

Question

Quizplus · Accepted Answer

The hedge ratio (delta) is calculated as (C_u - C_d) / (S_u - S_d), where C_u and C_d are the call option values at the up and down states, and S_u and S_d are the stock prices at the up and down states. Here, delta = (4 - 0) / (36 - 26) = 0.4. Thus, buying 0.4 shares for each call option sold hedges the position.

The Current Price of a Non-Dividend-Paying Stock Is $30