Chooser option

The holder chooses at a specified time between a European call option and a European put option with the same later maturity and strike. Put-call parity makes its value equal to a call of the original maturity plus a put of the choice-time maturity with appropriately discounted strike.

At its choice time this claim permits purchase of either of two later-expiring European options for an exercise cost $K$, or abandonment. Its payoff is $\max (p-K,c-K,0)$. For common strike $K_3$ and remaining time $\tau$, put-call parity places the branch crossing at $D=K_3{e}^{-r\tau }$. In the Black-Scholes model, both branch values there equal $D[2\Phi (\sigma \sqrt{\tau }/2)-1]$. An exercise cost above this minimum creates a central interval in which neither choice is worth exercising.