Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models

2004 ◽  
Vol 4 (5) ◽  
pp. 597-606 ◽  
Author(s):  
Jean-Pierre Fouque ◽  
Chuan-Hsiang Han
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Monte Carlo Methods ◽  
Variance Reduction ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Volatility Models

Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

2021 ◽  
Vol 53 (1) ◽  
pp. 220-250
Author(s):  
Zorana Grbac ◽  
David Krief ◽  
Peter Tankov
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Variance Reduction ◽  
Large Deviation ◽  
Heston Model ◽  
Stochastic Volatility Models ◽  
Monte Carlo Computation ◽  
Volatility Models ◽  
Long Time ◽  
Path Dependent

AbstractWe establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

scholarly journals A note on calculating expected shortfall for discrete time stochastic volatility models

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Michael Grabchak ◽  
Eliana Christou
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Monte Carlo Methods ◽  
Expected Shortfall ◽  
Leverage Effect ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Empirical Analyses

AbstractIn this paper we consider the problem of estimating expected shortfall (ES) for discrete time stochastic volatility (SV) models. Specifically, we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV models. This includes both models where the innovations are independent of the volatility and where there is dependence. This dependence aims to capture the well-known leverage effect. The performance of our Monte Carlo methods is analyzed through simulations and empirical analyses of four major US indices.

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