Question

1. Calculate the European put price using the BSMOPM. The current stock price is 50 and the exercise price is 55. The continuously compounded risk-free rate is 5%. The option expires in 25 days and volatility is 75%.

Round to 4 decimals – You must solve this by hand clearly show the answer for each part

Answer 1

As per BSMOPM or Black sholes Model,

Value of the Put Option =

E = exercise price = 55

Vs = current stock price =50

e = 2.7182818

r = risk free rate = 5% or 0.05

t= time= 25/365

=standard deviation or volatility= 75% or 0.75

Ln = natural Log

N = Cumulative standard normal distribution function

hence

Ln 50/55 = -0.09531017979

N(d1) = N(-0.370) = 0.35569

N(-d1) = 1-N(d1) = 1-0.35569 = 0.64431

N(d2) = N(-0.566) = 0.28570

N(-d2) = 1-N(d2) = 1- 0.28570=0.71430

Hence

Value of the Put Option =

hence  European put option price = $6.94