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

Pricing and exercising American equity options in a multi-factor setting is so cumbersome that the 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 part 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 four terms (moneyness, dividend yield minus interest rates, 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, these errors depend on the curvature of the boundary. The numerical exercise confirms these two theoretical results and shows significative errors for in-the-money and longer term options, challenging the market practice.