Asian option as a fixed-point

TL;DR

This paper models Asian option pricing as a fixed-point problem within a regime-switching framework, providing an iterative method for valuation that accounts for economic regime changes affecting asset dynamics.

Contribution

It introduces a fixed-point characterization of Asian options under regime-switching models and proposes an iterative solution method with proven convergence.

Findings

The fixed-point approach accurately prices Asian options in regime-switching models.

The iterative method converges geometrically to the true option value.

The model captures economic regime changes affecting asset prices.

Abstract

We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sudden exogenous events in the economy. Asian options are particularly interesting because the payoff depends on the integrated asset price. We study the case of both floating- and fixed-strike Asian call options with arithmetic averaging when the asset follows a regime-switching geometric Brownian motion with coefficients that depend on a Markov chain. The typical approach to finding the value of a financial option is to solve an associated system of coupled partial differential equations. Alternatively, we propose an iterative procedure that converges to the value of this contract with geometric rate using a classical fixed-point theorem.