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

Authors

Wenting Chen, Jiangnan UniversityFollow
Kai Du, University of WollongongFollow
Xinzi Qiu, University of WollongongFollow

RIS ID

117127

Publication Details

Chen, W., Du, K. & Qiu, X. (2018). Analytic properties of American option prices under a modified Black-Scholes equation with spatial fractional derivatives. Physica A: Statistical Mechanics and its Applications, 491 37-44.

Abstract

This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterized by a nonlinear fractional partial differential equation (FPDE) system. Using the technique of approximation, we prove that the American put price under the FMLS model is convex with respect to the underlying price, and specify the impact of the tail index on option prices. We also show numerical examples to support our analytic results.