Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

Moawia Alghalith,Konstantinos Gkillas,Christos Floros

doi:10.3390/risks8020035

Moawia Alghalith, Konstantinos Gkillas + Show 1 more

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https://doi.org/10.3390/risks8020035

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Abstract

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.

Highlights

Financial market volatility is a key factor for many issues in finance, ranging from asset management to risk management (Poon and Granger 2003)
We proceeded in a Monte Carlo simulation analysis and found that our estimates are reasonably accurate
We relax the assumption of a constant volatility of volatility and we allow the volatility of volatility to vary over time

Summary

Introduction

Financial market volatility is a key factor for many issues in finance, ranging from asset management to risk management (Poon and Granger 2003). Since volatility can be used in investment decisions, derivative pricing and financial market regulation, several approaches have been proposed in the existing literature with regard to its estimation. A key assumption is that that volatility can change over time, many changes in volatility can be modeled stochastically. There is evidence that stochastic volatility models outperform constant volatility models Stochastic volatility models resolve the shortcoming of the Black and Scholes model that the volatility is constant over time and is unaffected by the changes in the price level of the underlying asset. Volatility can be estimated by parametric, semi-parametric and nonparametric estimators (see Asai et al 2006; Maasoumi and McAleer 2008; Asai and McAleer 2011; Caporin and McAleer 2012 for a detailed discussion on this topic), statistical inferences for stochastic volatility models are mainly parametric. Cox et al (1985) and Heston (1993) offered some indicative examples of parametric estimation. Alghalith (2012)

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