Finding Payoff Functions for Common Options

Summary

The document points readers seeking payoff formulas for non-path-dependent options toward standard references. For plain vanilla options, it recommends learning the payoff diagrams for long and short calls and puts, then combining those building blocks to understand more complex strategies. A textbook on option pricing formulas is suggested as a broad reference, while another derivatives text is cited for vanilla payoff diagrams.

It also notes that digital or binary options can be treated as very narrow call spreads for practical pricing and hedging. More elaborate named structures, including seagull and wedding cake options, illustrate how varied combinations can become. The discussion offers resource suggestions and intuition rather than listing formulas or evaluating strategies, and it does not provide quantitative examples or evidence comparing the references.

Key ideas

• Long and short calls and puts are basic building blocks for constructing vanilla option strategies.
• Payoff diagrams help explain the behavior of combinations of calls and puts.
• Digital options can be approximated in practice by narrow call spreads for pricing and hedging.
• Standard options textbooks are suggested as references for payoff functions.

Tags

# List of Option Payoffs


# List of Option Payoffs












Does anyone know of a good resource which lists all commonly used options together with their payoff functions? I'm specifically interested in non-path-dependent options.

## Answer by Dimitri Vulis (score 4, accepted)

https://quant.stackexchange.com/a/63918

Take a look at Espen Gaarder Haug. The Complete Guide to Option Pricing Formulas Hardcover, 2nd edition (2007).

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/63917

There is an abundance of different strategies and option types. If you are only looking at vanilla strategies, i.e. combinations of puts and calls, then I'd suggest looking at the payoff charts here. Some of the intuition behind these payoffs is useful as well. You can even come up with more fancy strategies and names such as seagull options or wedding cake options.

If you want to include light exotics you could include digital/binary options in your list. These are nothing other than very tight call spreads and are in practice priced and hedged as such.

As you can see, as long you understand the payoff diagram of a long/short call/put you can combine them in many ways.

## Answer by Felix (score 0)

https://quant.stackexchange.com/a/63912

For plain-vanilla options I would generally recommend Hull, J. C. (2012) Options, futures, and other derivatives.

For example, in the 7ths edition it's on page 183.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.