Chooser Options

Ordinary options force you to commit upfront to buying a call or a put. A chooser option relaxes that: the buyer pays one premium today, and at a specified choice date in the future — before final expiry — gets to look at where the underlying is trading and simply pick whether the position becomes a call or a put from that point onward. It's useful whenever you're confident volatility is coming but genuinely unsure of the direction — around an earnings release or a binary regulatory decision, say — and want the flexibility priced in rather than betting on a direction now.

The simplest version, a simple chooser, has both the call and the put share the same strike $K$ and the same final expiry $T$; only the choice date $t_1 < T$ differs from expiry. This special case has a clean pricing trick: at the choice date, choosing the more valuable of a call and a put with the same strike and maturity is mathematically equivalent to holding a call with strike $K$ expiring at $T$ plus a put with a shifted strike expiring at $t_1$, via put-call parity — which is why a simple chooser can be priced with a closed-form Black-Scholes-style formula rather than needing a full simulation.

As a sense of the number: a simple chooser is always worth at least as much as a straddle (a call and put both bought today with the same strike and maturity) struck at the same terms, because the chooser lets you defer the direction bet to a later, more informed date — that extra flexibility has value, so the chooser's premium sits above the straddle's, with the gap widening the longer the deferral period before the choice date.