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

A put option is a option contract that allows the buyer of the option the right to sell (not obligation) an underlying stock at a specific price. If the price goes down after purchasing the contract, the buyer can exercise the option else if the price is going up he can let the option expire.

A syntetic put can be created by shorting a forward contract and buying an at the money call option for the same stock and same expiry. By doing so, the combined contract behave in such a way that of a put option. ie: If price goes up, the due to the short position in forward and long position in call, he wont have any loss or profit and is equivalent to letting the put option expire. Similarly if the price goes down, he can let the call option expire and get a positive profit from forward contract due to his short position which is similar to a put option.

The relation shows us about the principles of put call parity which says that a price of a put option at a strike price is related to the price of a call option of the same strike price.