VIX Computation Based on Affine Stochastic Volatility Models in Discrete Time

2017 ◽  
pp. 141-164
Author(s):  
A. Hitaj ◽  
L. Mercuri ◽  
E. Rroji
Keyword(s):  
Stochastic Volatility ◽  
Discrete Time ◽  
Stochastic Volatility Models ◽  
Volatility Models

scholarly journals Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 35
Author(s):  
Moawia Alghalith ◽  
Christos Floros ◽  
Konstantinos Gkillas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Simulation Analysis ◽  
Stochastic Volatility Models ◽  
Nonparametric Estimators ◽  
Volatility Models ◽  
Equity Index ◽  
Over Time

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasonably accurate. Such evidence implies that the stochastic volatility models proposed in the literature with constant volatility of volatility may fail to approximate the discrete-time short rate dynamics.

DISCRETE-TIME VARIANCE-OPTIMAL HEDGING IN AFFINE STOCHASTIC VOLATILITY MODELS

2010 ◽  
pp. 375-393 ◽  
Author(s):  
JAN KALLSEN ◽  
JOHANNES MUHLE-KARBE ◽  
NATALIA SHENKMAN ◽  
RICHARD VIERTHAUER
Keyword(s):  
Stochastic Volatility ◽  
Discrete Time ◽  
Stochastic Volatility Models ◽  
Time Variance ◽  
Optimal Hedging ◽  
Volatility Models

scholarly journals A note on calculating expected shortfall for discrete time stochastic volatility models

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Michael Grabchak ◽  
Eliana Christou
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Monte Carlo Methods ◽  
Expected Shortfall ◽  
Leverage Effect ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Empirical Analyses

AbstractIn 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.

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