Multilevel Monte Carlo and its Applications in Financial Engineering

TL;DR

This paper reviews recent advances in Multilevel Monte Carlo algorithms, focusing on their applications in financial engineering for option pricing and risk management, highlighting hybrid methods and adaptive sampling techniques.

Contribution

It provides a comprehensive overview of recent developments, including hybrid algorithms combining importance sampling with MLMC and adaptive sampling for efficient risk measure estimation.

Findings

Hybrid MLMC algorithms reduce variance in option pricing.

Adaptive sampling improves efficiency in estimating VaR and CVaR.

The reviewed methods enhance computational efficiency in financial risk analysis.

Abstract

In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two subareas, namely, option pricing and financial risk management. For the former, the discussion involves incorporation of the importance sampling algorithm, in conjunction with the MLMC estimator, thereby constructing a hybrid algorithm in order to achieve reduction for the overall variance of the estimator. In case of the latter, we discuss the studies carried out in order to construct an efficient algorithm in order to estimate the risk measures of Value-at-Risk (VaR) and Conditional Var (CVaR), in an efficient manner. In this regard, we briefly discuss the motivation and the construction of an adaptive sampling algorithm with an aim to efficiently estimate the nested expectation, which, in general is computationally expensive.