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Long memory in continuous‐time stochastic volatility models

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  • Fabienne Comte
  • Eric Renault

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.

Suggested Citation

  • Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    • Handle: RePEc:bla:mathfi:v:8:y:1998:i:4:p:291-323
    DOI: 10.1111/1467-9965.00057
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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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