Short Communication: Pricing Path-Dependent Derivatives under Multiscale Stochastic Volatility Models: A Malliavin Representation

2020 ◽  
Vol 11 (3) ◽  
pp. SC-14-SC-25
Author(s):  
Yuri F. Saporito
Keyword(s):  
Stochastic Volatility ◽  
Short Communication ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Path Dependent

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.

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