Simulation of conditional expectations under fast mean-reverting stochastic volatility models

@inproceedings{Cozma2020SimulationOC,
  title={Simulation of conditional expectations under fast mean-reverting stochastic volatility models},
  author={Andrei Cozma and Christoph Reisinger},
  booktitle={MCQMC},
  year={2020}
}
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of financial entities. We then seek an efficient estimator for the probability of a default, indicated by a firm value below a certain threshold, conditional on common factors. We first analyse the convergence of the Euler--Maruyama scheme applied to the fast… 

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References

SHOWING 1-10 OF 19 REFERENCES
Stochastic Evolution Equations for Large Portfolios of Stochastic Volatility Models
TLDR
This work considers a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary and establishes good regularity properties for solutions, however uniqueness remains an open problem.
MEAN-REVERTING STOCHASTIC VOLATILITY
We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis
Multiscale Stochastic Volatility Asymptotics
In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process
Stochastic PDEs for large portfolios with general mean-reverting volatility processes
In this article we consider a large structural market model of defaultable assets, where the asset value processes are modelled by using stochastic volatility models with default upon hitting a lower
Multiple Time Scales and the Exponential Ornstein-Uhlenbeck Stochastic Volatility Model
We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage
Numerical valuation of basket credit derivatives in structural jump-diffusion models
We consider a model where each company’s asset value follows a jump-diusion process, and is connected with other companies via global factors. Motivated by ideas in Bush et al. (2011), where the
Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives
We consider N Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the
Stochastic Evolution Equations in Portfolio Credit Modelling
TLDR
A structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor is considered and the existence and uniqueness for the solution taking values in a suitable function space are established.
Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results
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