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

TL;DR

This paper studies American option prices within a fractional PDE framework under the FMLS model, revealing convexity properties and the influence of tail index on pricing.

Contribution

It introduces a fractional PDE approach to analyze American options under the FMLS model, highlighting convexity and tail index effects.

Findings

American put prices are convex with respect to the underlying price.

The tail index significantly impacts option prices.

The fractional PDE approach provides new insights into option valuation.

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 characterised by the free boundary problem of a 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 the underlying price, and specify the impact of the tail index on option prices.