With numerical examples, how can the payoff of a chooser option be replicated with European call and put options?
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Consider a European chooser option which allows you to choose at time $\tau$ if you want to receive a put option and call option with maturity $T>\tau$.
At time $\tau$, using the put-call parity, the payoff is $$\max\{C,P\}=\max\{C,C-S+Ke^{-r(T-\tau)}\}=C+\max\{Ke^{-r(T-\tau)}-S,0\}.$$
Thus, owning the chooser option is identical to owning a call option with strike price $K$ and maturity $T$ and a put option with strike price $Ke^{-r(T-\tau)}$ and maturity $\tau$.
You can now use any option pricing model (eg Black-Scholes option) to determine the value of these two option and the combined value will be the value of the chooser option.
Interestingly, if $\tau=T$, then $\max\{C,P\}=C+P$. Note that one of the options will be worthless though (expire OTM).
