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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.

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

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    $\begingroup$ Thank you, this is everything I was looking for and more! $\endgroup$
    – R. Rayl
    May 11 '21 at 20:37
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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.

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    $\begingroup$ "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." +1: a good professor would explain it as such and you won't ever forget it again. $\endgroup$
    – simsalabim
    May 12 '21 at 7:27
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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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