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Derivatives Crash Course for Dummies: What is wrong with the payoff profile of the synthetic forward?

In our Derivatives Crash Course for Dummies, Master Class: Options and Derivatives Crash Course: Session Five: Synthetics we had discussed how we can synthetically create a derivative product by combining two vanilla contracts. We had presented the payoff profile of a synthetic long forward contract created by combining a long call and a short put as follows:

Derivative

The composite result of the two individual payoff profiles results in a payoff profile that resembles the payoff profile for a long forward contract.

Derivative 1

However, if you look closely at the first diagram given above you will notice that there is something wrong with it. What is wrong with this diagram?

In order to answer this question let us once again review the pay off profiles of a long call option (where you have bought the contract) and a short put option (where you have written the option).

A long call

long call

A short put

short put

For a more detailed review of these options you may like to go over this post first: Master Class: Options and Derivatives Crash Course: Session Four: Payoff profiles – Options, Calls and Puts.

Getting back to the topic, if you were to combine these two payoffs, the resulting graph would show a gap between the payoff profiles of the long call and the short put, and the diagonal lines would not intersect as given in the first diagram above.

The net result of the payoffs, i.e. payoff of Call (including call premium) – payoff of Put (including put premium), however, would result in a straight line that resembled the payoff of a forward contract. This is illustrated below:

payoff

In the figure above, both the call and put options have a strike price of 5.1 and a premium of 0.25. The net result from selling the put and buying the call would be the same as the payoff profile had you purchased a forward contract where you agree to buy the underlying at the pre-determined price of 5.1 at a future date.

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