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Expert-verified Found in: Page 554 ### Essentials Of Investments

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

# Use the Black-Scholes formula to find the value of a call option on the following stock:Time to expiration = 6 monthsStandard deviation = 50% per yearExercise price = $50Stock price =$50Interest 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 ### Want to see more solutions like these? 