# Option Pricing-Black Scholes, Put Call Parity

A. Use the Black-scholes formula to find the price of a three-month European call option on a non-dividend-paying stock with a current price of $50. Assume the exercise price is $51, the continuously compounded riskless interest rate is 8% per year, and standard deviation is .4.

b. What is the composition of the initial replicating portfolio for this call option?

c. Use the put-call parity relation to find the Black-Scholes formula for the price of the corresponding put option.

Â© BrainMass Inc. brainmass.com March 4, 2021, 9:37 pm ad1c9bdddfhttps://brainmass.com/business/black-scholes-model/option-pricing-black-scholes-put-call-parity-259556

#### Solution Preview

Please see the attached file

a. use the Black-scholes formula to find the price of a three-month European call option on a non-dividend-paying stock with a current price of $50. Assume the exercise price is $51, the continuously compounded riskless interest rate is 8% per year, and s is .4.

Note: * refers to multiplication and ^ to raised to the power of

We will use Black Scholes Pricing Formula

Value of call= S N(d1) - X * e -r(T-t) * N(d2)

We therefore need to calculate the values of d1 and d2

d1= {ln (S/X) + ( r + Â½ s2 ) x (T-t)}/ (s x square root of (T-t))

d2= {ln (S/X) + ( r - Â½ s2 ) x (T-t)}/ (s x square root of (T-t)) =d1-s x square root of (T-t)

Inputs

Stock Price= ...

#### Solution Summary

Uses the Black-scholes formula to find the price of a three-month European call option on a non-dividend-paying stock. Uses the put-call parity relation to find the Black-Scholes formula for the price of the corresponding put option.