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Option Pricing with Long Memory Stochastic Volatility Models

Zhigang Tong

ISBN 10: 3659346276 / ISBN 13: 9783659346279
Published by LAP Lambert Academic Publishing
New Condition: New Soft cover
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184 pages. Dimensions: 8.7in. x 5.9in. x 0.4in.It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9783659346279

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Bibliographic Details

Title: Option Pricing with Long Memory Stochastic ...

Publisher: LAP Lambert Academic Publishing

Binding: Paperback

Book Condition:New

Book Type: Paperback

About this title

Synopsis:

It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.

About the Author:

Zhigang Tong currently is a doctoral student at Department of Mathematics and Statistics in University of Ottawa, Canada. He is interested in probabilistic and statistical properties of fractional (so called long memory) processes and their modifications, with particular emphasis on applications of those models in finance.

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