Recovering a time-homogeneous stock price process from perpetual option prices

TL;DR

This paper addresses the inverse problem of constructing a time-homogeneous stock price model from given perpetual American option prices, extending the understanding of model calibration in financial mathematics.

Contribution

It introduces a method to recover the underlying stock process from perpetual American option prices, providing a new approach to model calibration.

Findings

A constructive procedure for model recovery from option prices

Demonstration of the method's effectiveness with theoretical examples

Extension of existing models to inverse problem setting

Abstract

It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes, we show how to construct a time-homogeneous stock price model which reproduces the given option prices.