Pricing and Risk Analysis in Hyperbolic Local Volatility Model with Quasi Monte Carlo

2021/06/15 by Julien Hok, Hok, Julien, Sergei Kucherenko +1
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Stochastic processes and financial applications #q-fin.CP

paper · pdf · doi:10.48550/arxiv.2106.08421

arxiv created 2021/06/15 · openalex publication_date 2021/06/15 · arxiv updated 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Local volatility models usually capture the surface of implied volatilities more accurately than other approaches, such as stochastic volatility models. We present the results of application of Monte Carlo (MC) and Quasi Monte Carlo (QMC) methods for derivative pricing and risk analysis based on Hyperbolic Local Volatility Model. In high-dimensional integration QMC shows a superior performance over MC if the effective dimension of an integrand is not too large. In application to derivative pricing and computation of Greeks effective dimensions depend on path discretization algorithms. The results presented for the Asian option show the superior performance of the Quasi Monte Carlo methods especially for the Brownian Bridge discretization scheme.

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