On "A General Framework for Pricing Asian Options Under Markov Processes"

TL;DR

This paper advances the pricing of Asian options under Markov processes by deriving explicit Laplace transforms in a continuous-time Markov chain setting, enhancing computational efficiency.

Contribution

It explicitly computes inverse Z- and Laplace transforms for Asian options under CTMC, improving previous theoretical results and numerical methods.

Findings

Explicit single Laplace transforms are derived for Asian options.

Numerical studies show improved computational efficiency.

The framework extends previous models to continuous-time Markov chains.

Abstract

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In this note, under the setting of continuous-time Markov chain (CTMC), we explicitly carry out the inverse Z-transform and the inverse Laplace transform respectively for the discretely and the continuously monitored cases. The resulting explicit single Laplace transforms improve their Theorem 2, p.543, and numerical studies demonstrate the gain in efficiency.