Integral of a Gaussian function

In finance, a chooser option is a special type of option contract. It gives the purchaser a fixed period of time 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 $t_1$;.

Bibliography

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