Abstract
In 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.
Highlights
Empirical studies consistently show that financial returns do not have a constant volatility and instead exhibit volatility clustering
In this paper we considered the problem of estimating expected shortfall (ES) for stochastic volatility (SV) models
We introduced two Monte Carlo methods, which are easy to implement in many common situations and can be used in both the case where the volatility is independent of the innovation and where there is dependence
Summary
Empirical studies consistently show that financial returns do not have a constant volatility and instead exhibit volatility clustering. We again perform a small simulation study to compare the performance of M1(τ , σ ) and M2(τ , σ ) For these simulations we assume that δt and ηt are independent standard normal random variables, or equivalently that (ηt , ǫt ) ∼ N (0, ) , where is given by (11). If we evaluate Z for several models, the one where Z has the smallest absolute value is considered to be the best An issue with this method is that it is sensitive to the estimate of VaR. As in the previous case, the method where V has the smallest absolute value is considered to be the best
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