Question

What are the prices of a call option and a put option with the following characteristics? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Stock price	=	$77
Exercise price	=	$75
Risk-free rate	=	3.40% per year, compounded continuously
Maturity	=	5 months
Standard deviation	=	59% per year

Answer 1

BSM formula for a call and a put option pricing.

Where, S_o = $77, K = $75, r = 3.40% , =59%, , T = 5/12 = 0.42

d₁ = 0.2973, d₂ = -0.0851

So, N(d₁) = 0.6169, N(d₂) = 0.4661 and N(-d₁) = 0.3831, N(-d₂) = 0.5339

Using call option pricing formula (given above)

Call Option Price, c= 47.5013 - 34.4618

Call Option Price, c= $13.0395

Put Option Price, p=39.4747 - 29.4987

Put Option Price, p = $9.9760