Question

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%

Short answer

$7.34

Step-by-step solution

Given information’

S_o= $50 = stock price

X = 50 = exercise price

r = 3% = rate

σ= 50% = standard deviation

T = 6 months = time

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 = S₀e^-rtN(d₁) – Xe^-rt N(d₂)

= $7.34