Q16I

Expert-verifiedFound in: Page 554

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 months**

**Standard deviation = 50% per year**

**Exercise price = $50**

**Stock price = $50**

**Interest rate = 3%**

$7.34

S_{o }= $50 = stock price

X = 50 = exercise price

r = 3% = rate

σ = 50% = standard deviation

T = 6 months = time

Formula for (d_{1}) = In (S_{0} / X) + (r -δ+ σ^{2} /2)T / σ√2

d_{1 }= In( 50 / 50) + (.03 – δ+ (.5^{2 }/ 2) x .5 / .5 √2

= 0.2192

N(d_{1}) = 0.5868

d_{2 }= d1 - σ√T = -0.1344

N(d_{2}) = 0.4466

C = S_{0 }e^{-rt}N(d_{1}) – Xe^{-rt} N(d_{2})

= $7.34

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