Analytic properties of American option prices under a modified Black-Scholes equation with spatial fractional derivatives

摘要

This paper investigates analytic properties of American option prices underthe finite moment log-stable (FMLS) model. Under this model the price ofAmerican options is characterised by the free boundary problem of a fractionalpartial differential equation (FPDE) system. Using the technique ofapproximation we prove that the American put price under the FMLS model isconvex with respect the underlying price, and specify the impact of the tailindex on option prices.