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The Journal of Derivatives

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Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities

Luca Capriotti and Ruggero Vaia
The Journal of Derivatives Winter 2020, jod.2020.1.107; DOI: https://doi.org/10.3905/jod.2020.1.107
Luca Capriotti
is a managing director at Credit Suisse, and an adjunct faculty member at New York University in Brooklyn, New York and at University College London in London, UK
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Ruggero Vaia
is a senior scientist of the Consiglio Nazionale delle Ricerche with expertise in quantum statistical mechanics of low-dimensional systems. He works at the Istituto dei Sistemi Complessi in Sesto Fiorentino (FI), Italy, and is associated to the Istituto Nazionale di Fisica Nucleare
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Abstract

The authors show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semi-analytical approximation of transition probabilities and Arrow-Debreu densities for arbitrary diffusions. The authors illustrate the accuracy of the method by presenting results for the Black-Karasinski and the GARCH linear models, for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility, and for multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of derivatives pricing applications.

TOPICS: Derivatives, options, credit default swaps

Key Findings

  • • The connection between Feynman’s path-integrals and the formalism of derivatives pricing provides powerful computational tools for financial applications.

  • • An ‘effective potential’ path-integral formalism of quantum statistical mechanics, employed over the years for the study of a number quantum systems, can be employed to develop semi-analytical approximations of transition probabilities and Arrow-Debreu prices for non-linear diffusion.

  • • The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of derivatives pricing applications.

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The Journal of Derivatives: 29 (5)
The Journal of Derivatives
Vol. 29, Issue 5
Summer 2022
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Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities
Luca Capriotti, Ruggero Vaia
The Journal of Derivatives Apr 2020, jod.2020.1.107; DOI: 10.3905/jod.2020.1.107

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Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities
Luca Capriotti, Ruggero Vaia
The Journal of Derivatives Apr 2020, jod.2020.1.107; DOI: 10.3905/jod.2020.1.107
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  • Article
    • Abstract
    • EFFECTIVE POTENTIAL APPROXIMATION IN QUANTUM STATISTICAL MECHANICS
    • PATH-INTEGRAL FORMULATION OF STOCHASTIC CALCULUS
    • NUMERICAL RESULTS
    • CONCLUSIONS
    • ACKNOWLEDGMENTS
    • ADDITIONAL READING
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