Analytic valuation of American path-dependent options

Abstract

American options are type of options that can be exercised anytime during their life. Therefore, the valuation of such options is usually classified as optimal stopping problems or free boundary problems. I derive the analytic pricing formulas and integral equations of American chained options, Russian options with finite time horizon, American floating strike lookback options, and American maximum quanto options. To verify the derived pricing formula and the integral equation satisfied by the free boundary are correct, we numerically solve the derived integral equations using recursive integration method or simple iterative method.