Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities
| Autor: | Luca Capriotti, Ruggero Vaia |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Derivative pricing
GARCH Economics and Econometrics Arrow–Debreu model Inhomogeneous Brownian Motion Autoregressive conditional heteroskedasticity Computational Finance (q-fin.CP) Path integrals 01 natural sciences FOS: Economics and business symbols.namesake Quantitative Finance - Computational Finance Stochastic processes 0502 economics and business 0103 physical sciences Arrow-Debreu pricing Feynman diagram Applied mathematics 010306 general physics Quantum statistical mechanics Quantum thermodynamics Quantum 050208 finance 05 social sciences Linear model Zero-coupon bonds Black-Karasinski model Semi-classical methods Path integral formulation symbols Finance |
| Zdroj: | The Journal of derivatives 28 (2020): 8–25. doi:10.3905/jod.2020.1.107 info:cnr-pdr/source/autori:Luca Capriotti, Ruggero Vaia/titolo:Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities/doi:10.3905%2Fjod.2020.1.107/rivista:The Journal of derivatives/anno:2020/pagina_da:8/pagina_a:25/intervallo_pagine:8–25/volume:28 |
| ISSN: | 2168-8524 1074-1240 |
| DOI: | 10.3905/jod.2020.1.107 |
| Popis: | We 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. We 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. Comment: 12 pages, 4 figures |
| Databáze: | OpenAIRE |
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