How does a chooser option work, and when is the optimal time to decide between a call and a put?

A chooser option (also called an as-you-like-it option) gives the holder the right to declare the option as either a call or a put at a specified choice date before expiration. This flexibility comes at a premium but is cheaper than buying both a call and a put outright.\n\nStructure:\n\nAt the choice date t_c, the holder selects:\n- Call if: C(S, K, T - t_c) >= P(S, K, T - t_c)\n- Put if: P(S, K, T - t_c) > C(S, K, T - t_c)\n\nThe payoff at choice date is: max(C, P) where both options share the same strike K and remaining time T - t_c.\n\nSimple Chooser Pricing via Put-Call Parity:\n\nFor a European chooser (same strike and maturity for both call and put):\n\nmax(C, P) = C + max(0, P - C)\n\nUsing put-call parity, P - C = K x e^{-r(T-t_c)} - S x e^{-q(T-t_c)}\n\nSo: Chooser = C(S, K, T) + P(S, K x e^{-r(T-t_c)}, t_c)\n\nThis decomposes the chooser into a longer-dated call plus a shorter-dated put with adjusted strike.\n\nWorked Example:\nHarborview Fund purchases a chooser on Pinnacle Dynamics stock. Current price: $100, strike: $100, choice date: 3 months, expiration: 9 months, r = 5%, q = 2%, vol = 28%.\n\nUsing the decomposition:\n- Component 1: 9-month call with K = $100 → $11.85 (BSM)\n- Component 2: 3-month put with adjusted K = $100 x e^{-0.05 x 0.5} = $97.53 → $3.40 (BSM)\n- Chooser value: $11.85 + $3.40 = $15.25\n\nFor comparison:\n- Vanilla 9-month call alone: $11.85\n- Vanilla 9-month put alone: $9.60\n- Straddle (call + put): $21.45\n\nThe chooser at $15.25 is cheaper than the straddle ($21.45) because the holder must commit at month 3, giving up optionality for the remaining 6 months.\n\nComplex Choosers:\nComplex choosers allow different strikes and/or maturities for the call and put components. These cannot be decomposed via put-call parity and require numerical pricing (binomial trees or Monte Carlo).\n\nWhen Choosers Are Useful:\n- Ahead of major binary events (earnings, regulatory decisions) where direction is uncertain but a position is desired\n- When a hedger anticipates either buying or selling an asset but the decision depends on future information\n- As a cheaper alternative to a straddle when direction clarity arrives before expiration\n\nStudy complex option strategies in our FRM course materials.