A share of stock is currently priced at $20 and will change with equal likelihood to either $50 or $10.A call option with a $25 exercise price is available on the stock.How many shares of stock must be purchased to replicate the payoff from owning one call option?
A)$.50 shares
B)$.75 shares
C)$.63 shares
D)$1.25 shares

Question

Quizplus · Accepted Answer

We can use a combination of buying and selling shares to replicate the payoff from owning one call option. 
If the stock price goes up to $50, the call option will be exercised and we will buy shares at the exercise price of $25. 
If the stock price goes down to $10, the call option will expire worthless and we will not buy any shares. 
To replicate this, we can buy some fraction x of a share at $20 and sell some fraction y of a share at $10. 
If the stock price goes up to $50, the value of our position will be 25x - 10y. We want this to equal $25, so 25x - 10y = 25. 
If the stock price goes down to $10, the value of our position will be -10y. We want this to equal $0, so -10y = 0. 
Solving these equations, we get x = 0.63 and y = 1.58. Therefore, we need to buy 0.63 shares to replicate the payoff from owning one call option.

A Share of Stock Is Currently Priced at $20 and Will