Explore BrainMass

Explore BrainMass

    Option Pricing-Black Scholes, Put Call Parity

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com June 3, 2020, 11:01 pm ad1c9bdddf
    https://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 + 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= ...

    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.

    $2.19

    ADVERTISEMENT