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

## Replication

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

