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Essentials Of Investments
Found in: Page 553
Essentials Of Investments

Essentials Of Investments

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

Short Answer

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 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.

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