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# Chooser option

In finance, a chooser option is a special type of option contract. It gives the purchaser a fixed period to decide whether the derivative will be a European call or put option.

In more detail, a chooser option has a specified decision time ${\displaystyle t_{1}}$, where the buyer has to make the decision described above. Finally, at the expiration time ${\displaystyle t_{2}}$ the option expires. If the buyer has chosen that it should be a call option, the payout is ${\displaystyle \max(S-K,0)}$. For the choice of a put option, the payout is ${\displaystyle \max(K-S,0)}$. Here ${\displaystyle K}$ is the strike price of the option and ${\displaystyle S}$ is the stock price at expiry.

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## Replication

For stocks without dividend, the chooser option can be replicated using one call option with strike price ${\displaystyle K}$ and expiration time ${\displaystyle t_{2}}$, and one put option with strike price ${\displaystyle Ke^{-r(t_{2}-t_{1})}}$ and expiration time ${\displaystyle t_{1}}$;.[1]

## References

1. ^ Yue-Kuen Kwok, Compound options

## Bibliography

• Yue-Kuen Kwok, Compound options (from Derivatives Week and Encyclopedia of Financial Engineering and Risk Management) [1]