Variance reduction of Monte Carlo and randomized quasi-Monte Carlo estimators for stochastic volatility models in finance

1999 ◽  
Author(s):  
Hatem Ben Ameur ◽  
Pierre L'Ecuyer ◽  
Christiane Lemieux
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Variance Reduction ◽  
Stochastic Volatility Models ◽  
Quasi Monte Carlo ◽  
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 stochastic volatility model estimation

2019 ◽  
Vol 17 (4) ◽  
pp. 22
Author(s):  
Omar Abbara ◽  
Mauricio Zevallos
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Parameter Estimates ◽  
Model Estimation ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Monte Carlo Evaluation

<p>The paper assesses the method proposed by Shumway and Stoffer (2006, Chapter 6, Section 10) to estimate the parameters and volatility of stochastic volatility models. First, the paper presents a Monte Carlo evaluation of the parameter estimates considering several distributions for the perturbations in the observation equation. Second, the method is assessed empirically, through backtesting evaluation of VaR forecasts of the S&amp;P 500 time series returns. In both analyses, the paper also evaluates the convenience of using the Fuller transformation.</p>

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