One-Factor Based Exercise Strategies for American Options in Multi-Factor Models

Pricing American equity options in a multi-factor setting is so cumbersome that the typical approach is based on, reduced, one-factor exercise strategies. Practitioners and academics calibrate the model to the European counterpart, but the early-exercise premium is derived from a barrier option or from Black-Scholes, depending only on the stock price. Conventional wisdom dictates that the associated losses are insignificant, a few basis points (bps), but there is no rationale behind it. We challenge this view. We factorize the associated losses in the product of four terms and properly distinguish between a barrier option, which implies a suboptimal exercise policy, and the case of Black-Scholes model, which introduces a misspecified model (but produces lower pricing errors which go either way). Pricing errors are significant (i.e., two-digits bps) only for in-the-money and mid-/long-term American options, in highly skewed models and with larger interest-rate dividend-yield spreads. In-the-money and long-term American options are a "tough call." Skewed models are associated to stochastic volatility. And the interest-rate dividend spread relates to the early-exercise-premium.