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 $$ K e^{-r(t_2-t_1)} $$ and expiration time $$ t_1 $$;.