Long memory in continuous‐time stochastic volatility models

Long memory in continuous‐time stochastic volatility models This paper studies a classical extension of the Black and Scholes model for option pricing, often known as the Hull and White model. Our specification is that the volatility process is assumed not only to be stochastic, but also to have long‐memory features and properties. We study here the implications of this continuous‐time long‐memory model, both for the volatility process itself as well as for the global asset price process. We also compare our model with some discrete time approximations. Then the issue of option pricing is addressed by looking at theoretical formulas and properties of the implicit volatilities as well as statistical inference tractability. Lastly, we provide a few simulation experiments to illustrate our results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

Long memory in continuous‐time stochastic volatility models

Mathematical Finance, Volume 8 (4) – Oct 1, 1998

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Publisher
Wiley
Copyright
Blackwell Publishers Inc 1998
ISSN
0960-1627
eISSN
1467-9965
D.O.I.
10.1111/1467-9965.00057
Publisher site
See Article on Publisher Site

Abstract

This paper studies a classical extension of the Black and Scholes model for option pricing, often known as the Hull and White model. Our specification is that the volatility process is assumed not only to be stochastic, but also to have long‐memory features and properties. We study here the implications of this continuous‐time long‐memory model, both for the volatility process itself as well as for the global asset price process. We also compare our model with some discrete time approximations. Then the issue of option pricing is addressed by looking at theoretical formulas and properties of the implicit volatilities as well as statistical inference tractability. Lastly, we provide a few simulation experiments to illustrate our results.

Journal

Mathematical FinanceWiley

Published: Oct 1, 1998

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