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Option Pricing-Black Scholes, Put Call Parity

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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.

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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.

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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 + ½ s2 ) x (T-t)}/ (s x square root of (T-t))
d2= {ln (S/X) + ( r - ½ s2 ) x (T-t)}/ (s x square root of (T-t)) =d1-s x square root of (T-t)

Inputs

Stock Price= ...

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