Article2005

Estimation of integrated volatility in stochastic volatility models

50 citations0/0 files storedApplied Stochastic Models in Business and Industry

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Complex Systems and Time Series Analysis

Abstract

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log-returns). We derive consistency and distributional results for the estimators given high-frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1987The Pricing of Options on Assets with Stochastic Volatilities 1998Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts 1993A long memory property of stock market returns and a new model 2001The distribution of realized stock return volatility 2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models 2001The Distribution of Realized Exchange Rate Volatility 2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics

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2012Asymptotic Theory of Range-Based Multipower Variation 2007Inference in Lévy-type stochastic volatility models 2011Estimation of the instantaneous volatility 2009Bipower Variation for Gaussian Processes with Stationary Increments

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