Embed Interactive Demonstration New! Files require Wolfram CDF Player or Mathematica. This Demonstration illustrates the price and "greeks" for chooser options in comparison to those for regular put and call options.

What's the pricing formula for Chooser Option - Actuarial Outpost

Chooser options are a type of exotic option that, at some pre-specified time in the future, can be converted into either a put or call option with expiry and strike. The price of a chooser option, , thus tends to be higher than that of the corresponding call or put, or.

The amount of extra value depends on and: As tends to , tends to. It can be shown using general put-call parity considerations that, for , a chooser option is equivalent to a portfolio comprising a call option with strike and expiry together with a put option with strike and expiry assuming a constant interest rate. Within the Black—Scholes model, chooser options can therefore be priced using the solutions for call and put options.

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In this Demonstration, the price of chooser options is explored, as well as the derivative of the value function with respect to the various input parameters the "greeks": For convenience, we assume zero dividends. This is because at , the chooser option will become either a put or call option, which will have roughly opposite deltas at the money.

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Therefore, the delta of the chooser option will tend to change very quickly around , and hence gamma is large. Hull, Options, Futures, and Other Derivatives , New Jersey: Haug , The Complete Guide to Option Pricing Formulas , 2nd ed.

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