One factor based exercise strategies for American options in multi-factor models

Pricing and exercising American equity options in a multi-factor setting is so cumbersome that the typical approach in practice is based on simple, i.e., reduced, one-factor exercise strategies. Practitioners calibrate the model to the European counterpart, but the early-exercise premium is derived from Black-Scholes or from a barrier option, depending only on the stock price. Conventional wisdom dictates that the associated losses are insignificant, a few basis points, but there is not rational behind it. We challenge this view and, in the case of a barrier option, which implies a suboptimal exercise policy, we factorize the associated losses in the product of four terms: moneyness, interest rate minus dividend yield, elasticity of the exercise boundary or maturity, and the state variables dispersion. In the case of Black-Scholes, which introduces model risk, but produces lower pricing errors (which can go either way), we also explain this difference. An extensive numerical exercise confirms these two theoretical results and shows that for in-the-money and mid-/long-term American options, the errors can be significative, challenging the market practice.