## [PGP-I FM] Payoff diagrams

Payoff diagrams are simply diagrammatic representation of payoffs at termination/expiration of a contract w.r.t value of the underlying .

For example, for a baker’s forward contract (long forward) it is a plot of its payoff () at expiration () w.r.t the wheat’s spot price . Let’s recap the payoffs for some of the contract we have already talked about, and then some:

- Long Forward:
- Short Forward:
- Long Call:
- Short Call:
- Long Put:
- Short Put:

With this idea in place, we can also talk about the payoff diagram of an underlying itself w.r.t itself. This is of course trivial, because a stock is a stock is a stock, so if we buy a stock, that stock’s value is just the value of the stock.

Another easy one is that for a zero-coupon bond. A zero-coupon bond always return the face value at ‘expiration’ (maturity). It is often convenient in the context of options to talk about about a zero-coupon bond with face value and expiration , i.e coinciding with that implicit in the forward contracts/options.

Let’s draw some pictures now. Since they are all basically plots of very simple functions as , I take it that you recall enough of drawing functions of the kind from your school days to not spend time explaining how you would draw these. Here we go.

*Long Forward and Short Forward*

*Long Call and Short Call*

*Long Put and Short Put*

*Stock (underlying) and Zero-coupon Bond*

Note that all upward sloping lines have a slope of +1 and downward sloping lines have a slope of -1 (why?).

Written by Vineet

October 28, 2016 at 7:07 pm

Posted in Teaching: FM

Tagged with Derivatives, FM-2016, Options, Payoff Diagrams

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