Asymptotic behavior of prices of path dependent options

TL;DR

This paper introduces a numerical method leveraging the Markov property to price long-term, path-dependent options by approximating them with vanilla options, applicable to assets modeled by Levy processes.

Contribution

It presents a novel numerical approach for pricing long maturity, path-dependent options using Markov property-based approximation with vanilla options.

Findings

Effective approximation of path-dependent options using vanilla options.

Applicable to assets following Levy processes.

Provides specific payoff functions for approximation.

Abstract

In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain vanillas. We give some examples whose underlying assets behave as some popular Levy processes. Moreover, we give some payoffs and functions used to approximate them.