Consider the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that it has the same value as a European call option with the same strike price and maturity as the European put option. Deduce that a European put option has the same value as a European call option with the same strike price and maturity when the strike price for both options is the forward price.

International Financial Management
14th Edition
ISBN:9780357130698
Author:Madura
Publisher:Madura
Chapter5: Currency Derivatives
Section: Chapter Questions
Problem 4BIC
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Consider the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that it has the same value as a European call option with the same strike price and maturity as the European put option. Deduce that a European put option has the same value as a European call option with the same strike price and maturity when the strike price for both options is the forward price.

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Given Information:

Terminal value is the portfolio defined as the present value of future cash flows at some point in time with constant growth rate expectation

A forward contract is a contracting state that buyer the buyer or the seller of the security has to lock in buying and selling price of the asset., and the transaction cost will occur in future 

a forward contract is a contract in which the buyer or seller is under the obligation to buy or sell the given asset at a predetermined price and date in the future, forward contracts are settled on delivery

A put option gives the option holder the right to sell the assets at a certain fixed price

A call option gives the option holders the right to purchase the security at a certain fixed price.

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