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Found in: Page 553

### Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

# 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.

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

See the step by step solution

## Step 1: 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

## Step 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.