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ARCH Models and Option Pricing: the Continuous-Time Connection

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Listed:
  • Antonio Mele

    () (THEMA)

  • Fabio Fornari

    () (Bank of Italy)

Abstract

To implement continuous time option pricing models in which ARCH models can be used as direct or indirect approximators of stochastic volatility, we construct continuous time economies exhibiting equilibrium dynamics to which most asymmetric ARCH models converge in distribution as the sample frequency becomes indefinitely large. In the candidate economies, volatility is a diffusion that allows for the "leverage effect," and has a variance that is proportional to the square of the volatility itself. Such characteristics introduce non-linearities in the resulting pricing models; models of the term structure of interest rates, for instance, are not affine, and are treated following two approaches. The first uses a variant of the Crank-Nicholson scheme numerically to integrate the pde followed by the equilibrium price of a bond. We also implement a second, less traditional approach that is based on a method of iterated approximations. In all cases, we provide parameter estimates that are based on indirect inference procedures in which the previous convergence results are used to exploit ARCH as auxiliary models. The convergence foundations of the pricing models considered here are based on a class of ARCH models that is large enough to make these pricing models incorporate realistic patterns of volatility of the Markovian type.

Suggested Citation

  • Antonio Mele & Fabio Fornari, 1999. "ARCH Models and Option Pricing: the Continuous-Time Connection," Computing in Economics and Finance 1999 113, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:113
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    References listed on IDEAS

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    Cited by:

    1. Fornari, F. & Mele, A., 1998. "ARCH Models and Option Pricing: The Continuous Time Connection," Papers 9830, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    2. Antonio Mele & Fabio Fornari, 1999. "Stochastic Volatility and the Informational Content of Option Prices: Empirical Analysis," Computing in Economics and Finance 1999 912, Society for Computational Economics.

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    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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