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

TL;DR

This paper evaluates the effectiveness of Quasi Monte Carlo methods over traditional Monte Carlo in pricing derivatives and analyzing risk within the Hyperbolic Local Volatility Model, highlighting improved accuracy especially with Brownian Bridge discretization.

Contribution

It demonstrates the superior performance of Quasi Monte Carlo methods in high-dimensional derivative pricing using the Hyperbolic Local Volatility Model, emphasizing the impact of discretization schemes.

Findings

QMC outperforms MC in high-dimensional integration tasks.

Brownian Bridge discretization enhances QMC performance.

QMC provides more accurate Greeks estimation for Asian options.

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.