Efficient Simulation of Generalized SABR and Stochastic Local Volatility Models

Friday, June 15, 2018 - 9:30am - 10:00am
Lind 305
Duy Nguyen (Marist College)
In this talk, we consider the efficient simulation of asset prices for general stochastic local
volatility models, which include the Heston stochastic volatility model and the stochastic alpha
beta rho (SABR) model as special cases. Our simulation algorithm is constructed based on a novel
application of a continuous-time Markov chain (CTMC) approximation to the latent stochastic
variance process. Compared with traditional time discretization approaches, our method exhibits
several advantages, including a second order convergence rate in the space of the approximating
CTMC under suitable regularity conditions. Replacing the stochastic variance process with a
discrete-state approximation greatly simplifyies the direct sampling of the integrated variance, thus
enabling a highly efficient semi-exact simulation scheme. Extensive numerical examples illustrate
the efficiency of our estimator, which compares favorably to existing biased or unbiased simulation
estimators in the literature. This new approach to simulation has the potential for numerous
applications which involve the estimation of path-dependent functionals of a diffusion process. (Joint with Zhenyu Cui and J. Lars Kirkby)
MSC Code: 
91G80, 93E11, 93E20