Question

Suppose there are call options and forward contracts available on coal, but no put options. Show how a financial engineer could synthesize a put option using the available contracts. What does your answer tell you about the general relationship among puts, calls and forwards?

Answer 1

Forward is an agreement where the person has the right & obligation to deliver the asset at expiry at the predetermined price.Call option gives the right but not obligation to purchse the asset at expiry at predetermined price. put option is a right to sell the asset at expiry at predetermined price.

A call option gives payoff if the asset pricei is higher than the exercise price and a person who is long the forward will get the payoff if the asset price is higher than the forward rate and person has to pay if the asset price is lesser than the forward rate.

a person who is long the put will pay money if the asset price is lower than the exercise price

So synthetic put option can be created by Selling the forward and buying the call option on coal where the forward rate is equal to the strike price of the call option

This strategy pays off similar to put option. If the price exceeds the strike price the loss from the forward option will set off from gain from call option and if asset price is lower than the exercise price than forward will payoff and call option will be useless.