Abstract:
We propose an approach for computing the arbitrage-free interval
for the price of an American option in discrete incomplete market
models via linear programming. The main idea is built replicating
strategies that use both the basic asset and some European derivatives
available on the market for trading. This method goes under the name
of calibrated option pricing and it has given significant results for
European options. Here we extend the analysis to American options
showing that the arbitrage-free interval can be characterized in terms
of martingale measures and that it gets significantly reduced with
respect to the non calibrated case.
Keywords: American option; incomplete market; arbitrage-free interval;
calibrated option pricing; dual theory; martingale measures.