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Stochastic Volatility

  • Reference work entry
Complex Systems in Finance and Econometrics

Article Outline

Glossary

Definition of the Subject

Introduction

Model Specification

Realized Volatility

Applications

Estimation Methods

Future Directions

Acknowledgments

Bibliography

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Notes

  1. 1.

    Discrete-time SV models go father back in time, at least to the easly paper by Rosenberg [232] recently reprinted in Shephard [240].

Abbreviations

Implied volatility :

The value of asset return volatility which equates a model‐implied derivative price to the observed market price. Most notably, the term is used to identify the volatility implied by the Black and Scholes [63] option pricing formula.

Quadratic return variation :

The ex-post sample‐path return variation over a fixed time interval.

Realized volatility :

The sum of finely sampled squared asset return realizations over a fixed time interval. It is an estimate of the quadratic return variation over such time interval.

Stochastic volatility :

A process in which the return variation dynamics include an unobservable shock which cannot be predicted using current available information.

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Acknowledgments

We are grateful to Olena Chyruk, Bruce Mizrach (the Section Editor) and Neil Shephard for helpful comments and suggestions. Of course, all errors remain our sole responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System. The work of Andersen is supported by a grant from the NSF to the NBER and support from CREATES funded by the Danish National Research Foundation.

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  1. Kellogg School of Management, Northwestern University, Evanston, USA

    Torben G. Andersen

  2. NBER, Cambridge, USA

    Torben G. Andersen

  3. CREATES, Aarhus, Denmark

    Torben G. Andersen

  4. Federal Reserve Bank of Chicago, Chicago, USA

    Luca Benzoni

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Andersen, T.G., Benzoni, L. (2009). Stochastic Volatility. In: Meyers, R. (eds) Complex Systems in Finance and Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7701-4_38

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