Convergence of Estimated Option Price in a Regime switching Market

TL;DR

This paper studies the convergence of estimated option prices in a regime-switching market modeled by a semi-Markov process, proposing smooth approximations and verifying convergence and solution existence with numerical validation.

Contribution

It introduces a method for approximating transition rate estimators to ensure the existence of classical solutions for option pricing equations in regime-switching markets.

Findings

Uniform convergence of transition rate estimators

Existence of classical solutions for the modified price equation

Numerical experiments confirming theoretical results

Abstract

In an observed generalized semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition rate, to meet the existence of classical solution of the modified price equation, the estimator is approximated in the class of smooth functions and furthermore, the convergence is established. Later, the existence of the solution of the modified price equation is verified and the point-wise convergence of such approximation of option price is proved to answer the tractability of its application in Finance. To demonstrate the consistency in result a numerical experiment has been reported.