2022/09/29 by Devang Sinha, Sinha, Devang, Siddhartha P. Chakrabarty +1
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2209.14549
openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.