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Applications of δ-function perturbation to the pricing of derivative securities

Author

Listed:
  • Decamps, Marc
  • De Schepper, Ann
  • Goovaerts, Marc
Abstract
In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ-function perturbations. First, we show that results about infinitely repulsive δ-function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with δ-function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable.

Suggested Citation

  • Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:3:p:677-692
    DOI: 10.1016/j.physa.2004.05.035
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    References listed on IDEAS

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    1. Kleinert, Hagen, 2002. "Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 217-242.
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    6. Carl Chiarella, Nadima El-Hassan, & Adam Kucera, "undated". "Option Pricing in a Path Integral Framework Using Fourier-Hermite Series Expansions," Computing in Economics and Finance 1997 132, Society for Computational Economics.
    7. Montagna, Guido & Morelli, Marco & Nicrosini, Oreste & Amato, Paolo & Farina, Marco, 2003. "Pricing derivatives by path integral and neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 189-195.
    8. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    9. GOOVAERTS, Marc & DE SCHEPPER, Ann & DECAMPS, Marc, 2002. "Transition probabilities for diffusion equations by means of path integrals," Working Papers 2002026, University of Antwerp, Faculty of Business and Economics.
    10. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "An empirical model of volatility of returns and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 178-198.
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    Cited by:

    1. Antoine Lejay & Paolo Pigato, 2017. "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data," Working Papers hal-01669082, HAL.
    2. Alexander Gairat & Vadim Shcherbakov, 2014. "Density of Skew Brownian motion and its functionals with application in finance," Papers 1407.1715, arXiv.org, revised Mar 2015.
    3. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    4. Xiaoyang Zhuo & Olivier Menoukeu-Pamen, 2017. "Efficient Piecewise Trees For The Generalized Skew Vasicek Model With Discontinuous Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-34, June.
    5. Tian, Yingxu & Zhang, Haoyan, 2018. "Skew CIR process, conditional characteristic function, moments and bond pricing," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 230-238.
    6. Song, Shiyu & Wang, Suxin & Wang, Yongjin, 2016. "On some properties of reflected skew Brownian motions and applications to dispersion in heterogeneous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 90-105.
    7. Antoine Lejay & Paolo Pigato, 2019. "A Threshold Model For Local Volatility: Evidence Of Leverage And Mean Reversion Effects On Historical Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-24, June.

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