Question

Use the following information to answer the next two questions.

A stock currently trades for $110 per share. Call options on the stock are available with a strike price of $115. The options expire in 20 days. The annual risk free rate is 4% and the expected standard deviation is 0.40.

Find the value of a call option using the Black-Scholes option pricing model (Assume 365 days per year)

Use the Black-Scholes option pricing model to find the value of a put option written on the same stock that matures in 20 days and has a strike price of 115. (Assume 365 days per year).

Answer 1

HI

Here S=110,

X=115,

r=4%=0.04,

=0.4,

time to maturity t =20/365=0.0548 years

Call Value C= SN(d₁) – Xe^-rtN(d₂)

q = 0

d1 = (ln(110/115) + 0.0548*(0.04+(0.4)^2/2))/0.4*sqrt(0.0548)

d₁=-0.4045

d2 = d1 - std dev*sqrt(t) =

d₂=-0.4981

N(d₁)=0.3429

N(d₂)=0.3092

Value of Call C = 110*0.3429 - 115*e^(-0.04*20/365)*0.3092

Value of Call C = $2.24

Value of Put P = Xe ^–r(t) [1-N(d₂)] – S [1-N(d₁)]

P = 114.748*(1-0.3092) -110*(1-0.3429)

P = $6.99

Thanks