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Q16I

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Essentials Of Investments
Found in: Page 554
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

Use the Black-Scholes formula to find the value of a call option on the following stock:

Time to expiration = 6 months

Standard deviation = 50% per year

Exercise price = $50

Stock price = $50

Interest rate = 3%

$7.34

See the step by step solution

Step by Step Solution

Step 1: Given information’

So = $50 = stock price

X = 50 = exercise price

r = 3% = rate

σ = 50% = standard deviation

T = 6 months = time

Step 2: Calculation of the value of call options

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

d1 = In( 50 / 50) + (.03 – δ+ (.52 / 2) x .5 / .5 √2

= 0.2192

N(d1) = 0.5868

d2 = d1 - σ√T = -0.1344

N(d2) = 0.4466

C = S0 e-rtN(d1) – Xe-rt N(d2)

= $7.34

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