Question

Show that Black-Scholes call option hedge ratios also increase as the stock price increases. Consider a 1-year option with exercise price $50, on a stock with annual standard deviation 20%. The T-bill rate is 3% per year. Find N(d1) for stock prices $45, $50, and $55.

Answer 1

Check explanation.

Step-by-step explanation:

A call option hedge ratio shows how an option price with respect to price changes in the underlying stock. A call option hedge ratio is used in determining the number of shares of stocks to hedge an option position.

We have Call option with the following characteristics:

X = 50; T=1 year; standard deviation = 20%; T-bill rate = 3%.

Hedge ratio = N(d1) from the Black-Scholes equation

For S=$45, d1 = -0.0268 and N(d1) =0.489309.

For S = $50, d1 = 0.5 and N(d1) = 0.6915.

If S = $55, d1 = 0.97655 and N(d1) = 0.8356.

From the above values obtained, it means that the price of the call option becomes more sensitive to changes in the price of the stock at higher stock prices.