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Erschienen in:

2015 | OriginalPaper | Buchkapitel

15. Stochastic Volatility

verfasst von : Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

Erschienen in: Derivative Security Pricing

Verlag: Springer Berlin Heidelberg

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Abstract

Empirical studies show that the volatility of asset returns are not constant and the returns are more peaked around the mean and have fatter tails than implied by the normal distribution. These empirical observations have led to models in which the volatility of returns follows a diffusion process. In this chapter, we introduce some stochastic volatility models and consider option prices under stochastic volatility. In particular, we consider the solutions of the option pricing when volatility follows a mean-reverting diffusion process. We also introduce the Heston model, one of the most popular stochastic volatility models.

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Vorheriges Kapitel Partial Differential Equation Approach Under Geometric Jump-Diffusion Process

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Of course in recent years there has been the growth of the so-called VIX options. There are options on the so-called VIX implied volatility index. Within this framework volatility has become a traded factor. We shall discuss VIX option in a later section.

See Appendix 15.1.

In deriving this result we are relying essentially on the result (8.13), appropriately modified to take account of the different interval of integration.

This amounts to taking the double Fourier transform.

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Titel: Stochastic Volatility
verfasst von: Carl Chiarella
Xue-Zhong He
Christina Sklibosios Nikitopoulos
Verlag: Springer Berlin Heidelberg
Buch: Derivative Security Pricing
Print ISBN: 978-3-662-45905-8

Electronic ISBN: 978-3-662-45906-5

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-662-45906-5_15