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Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models

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Author Info

  • Dennis Kristensen

    ()
    (Columbia University and CREATES)

  • Antonio Mele

    ()
    (London School of Economics)

Abstract

This paper develops a new systematic approach to implement approximate solutions to asset pricing models within multi-factor diffusion environments. For any model lacking a closed- form solution, we provide a solution obtained by expanding the analytically intractable model around a known auxiliary pricing function. We derive power series expansions, which provide increasingly improved refinements to the initial mispricing arising from the use of the auxiliary model. In practice, the expansions can be truncated to include only a few terms to generate extremely accurate approximations. We illustrate our methodology in a variety of contexts, including option pricing with stochastic volatility, volatility contracts and the term-structure of interest rates.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-14.

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Length: 33
Date of creation: 05 Apr 2009
Date of revision:
Handle: RePEc:aah:create:2009-14

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Asset pricing; stochastic volatility; the term-structure of interest rates; closed-form approximations;

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References

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Cited by:
  1. Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
  2. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, Elsevier, vol. 176(2), pages 93-111.
  3. Azusa Takeyama & Nick Constantinou & Dmitri Vinogradov, 2012. "A Framework for Extracting the Probability of Default from Stock Option Prices," IMES Discussion Paper Series, Institute for Monetary and Economic Studies, Bank of Japan 12-E-14, Institute for Monetary and Economic Studies, Bank of Japan.
  4. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, Elsevier, vol. 179(2), pages 158-177.

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