Question

Question 3:

Ramadan & Travis LLC has recruited you as their fresh derivatives pricing analyst. As part of your first task, the CFO James Blair provides you the following information:

Stock price	$25
Volatility	15%
Risk free rate	10% per annum
Exercise price	$32
Time to maturity of option	6 months

(a) Determine the price of a European call option. Clearly show all your workings.  

(b) Using the put-call parity model, estimate the price of the put option.

Answer 1

a) Using Black & Scholes Model, Price of Call option (P) is calculated by following formula

P = Spot Price * N(d1) - Exercise Price * e-rt * N(d2)

d1 = [ln(Current Market Price / Exercise Price) + (r + 0.5σ2) * t] / (σ * t0.5)

d2 = d1 - (σ * t0.5)

Therefore,

d1 = [ln(25/32) + (0.10 + 0.5*0.152) * 0.5] / (0.15*0.50.5)

= ln(0.78) + (0.11125 * 0.5) / 0.10607

= (-0.24846 + 0.05563) / 0.10607

= -1.82

d2 = -1.82 - (0.15*0.50.5)

= -1.93

N(d1) = 0.034379

N(d2) = 0.026803

Value of Call Option = $25 * 0.034379 - $32 * e-0.1*0.5 * 0.026803

= $0.04

b) Using Put call Parity Theory, Value of Put Option

(Exercise Price * e-rt) + OP of Call = Current Market Price + OP of Put

OP of Put = (Exercise Price * e-rt) + OP of Call - Current Market Price

= ($32*0.95123) + $0.04 - $25

= $5.48