Question

An analyst is interested in using the Black-Scholes model to value call options on the stock of Ledbetter Inc. The analyst has accumulated the following information: The price of the stock is $30. The strike price is $22. The option matures in 4 months. The standard deviation of the stock’s returns is 0.40. The risk-free rate is 4%. Using the Black-Scholes model, what is the value of the call option?

Answer 1

·         S₀ = 30

S_X = 22

r = 4%

s = 4% = 0.04

T = 4/12 = 0.33

d₁ = (ln(S₀/S_X) + (?²/2 + r)T)/?

d₁ = (ln(30/22) + (0.04²/2 + 0.04)*4/12)/0.04 *        

d₁ = (0.31015 + 0.0136)/ 0.02309

d₁ = 14.0189

d₂ = d₁ – ?

d₂ = 14.0189 – 0.02309= 13.9959

N(d₁) = N(14.0189) = 1

N(d₂) = N(13.9959) = 1

C₀ = S₀ N(d₁) - S_X N(d₂)e^-rT

C₀ = 30 * 1 – (22 * 1 * e^{-0.04 * 4/12})

C₀ = 30 – 21.7086 = 8.2914

The price of call option is 8.2914