An Approximation of an Equivalent European Payoff for the American Put Option

We develop a numerical procedure, in the Black-Scholes model, to approximate the payoff of a European type option generating prices that are equal to the prices of the American put option in the continuation region. This... [ view full abstract ]

We develop a numerical procedure, in the Black-Scholes model, to approximate the payoff of a European type option generating prices that are equal to the prices of the American put option in the continuation region. This equivalent European payoff is a sum of power payoffs and the price and the hedging indicators can be computed in closed form. For a given set of model parameters the computation of the equivalent European payoff reduces to solving a linear optimization problem. We conduct a numerical experiment and the method produces American prices with relative RMSE less than 0.01% compared to a benchmark.