Question

Show that Black-Scholes call option hedge ratios increase as the stock price increases. Consider a one-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.

Short answer

With the increase in stock prices N (d₁) too increases.

Step-by-step solution

Given information’

Exercise price = X = 50

Rate = r = 3%

Standard deviation= σ= 20%

Time = T = 1

Formula for (d₁) = In (S₀ / X) + (r -δ+σ² /2)T / σ√2

Calculation of (d1) and black Scholes hedge ratio

S.	d1	N(d1)
a.	- 0.2768	0.3910
b.	0.2500	0.5987
c.	0.7266	0.7662
		= normdist(d1)

This is evident that with the increase in stock prices N(d₁) too increases.