Chooser Option Pricing Lab (Rubinstein 1991)

1. The Rubinstein (1991) Chooser Option Framework

A chooser option grants the buyer the right to determine at time $t$ whether the option will be a European call or European put expiring at $T \ge t$. At choice date $t$, a rational investor selects the contract with the greater market value:

By put-call parity at time $t$, $C_t - P_t = S_t e^{-q(T-t)} - K e^{-r(T-t)}$. Rewriting the max operator:

Discounting this expectation back to $t=0$ yields Mark Rubinstein's seminal closed-form solution:

2. Critical Stock Price Hurdle ($S^*$)

The investor chooses a call if $S_t > S^*$ and a put if $S_t < S^*$, where $S^*$ solves $C(S^*, K, T-t) = P(S^*, K, T-t)$. For a simple chooser, this critical boundary simplifies to:

When interest rates exceed dividend yields ($r > q$), $S^* < K$, meaning calls become more valuable even at slightly out-of-the-money spot prices due to the cost of carry.

3. Boundary Properties & Straddle Comparison

A chooser option is bounded tightly between vanilla options and full straddles:

• Zero Choice Horizon ($t \to 0$): The investor must choose immediately, collapsing the contract value to $\max(C_0, P_0)$.
• Terminal Choice Horizon ($t \to T$): The investor delays the choice until final maturity $T$, meaning $\max(C_T, P_T) = \max(\max(S-K, 0), \max(K-S, 0)) = |S_T - K|$, which is an exact straddle.
• Cost Efficiency: For intermediate dates $0 < t < T$, the chooser gives broad bidirectional volatility protection at a 15% to 35% discount compared to purchasing both legs of a straddle.

4. Industry Applications & Event Risk Hedging

Corporate Earnings Catalysts: Fund managers purchase chooser options ahead of high-uncertainty quarterly earnings reports where explosive moves are anticipated but direction is unknown.

Biopharma FDA Approvals: Binary clinical readout results (approval vs rejection) cause massive price bifurcation; chooser options allow investors to capture post-announcement trends.

Macroeconomic / Geopolitical Events: Central bank interest rate decisions, elections, and commodity trade policy shifts create regime uncertainty well-suited for chooser structures.