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Quantifying risks with exact analytical solutions of derivative pricing distribution

Author

Listed:
  • Zhang, Kun
  • Liu, Jing
  • Wang, Erkang
  • Wang, Jin

Abstract

Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.

Suggested Citation

  • Zhang, Kun & Liu, Jing & Wang, Erkang & Wang, Jin, 2017. "Quantifying risks with exact analytical solutions of derivative pricing distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 757-766.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:757-766
    DOI: 10.1016/j.physa.2016.12.044
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Raphael Douady, 1999. "Closed Form Formulas For Exotic Options And Their Lifetime Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 6, pages 177-202, World Scientific Publishing Co. Pte. Ltd..
    3. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    4. Matthias Otto, 1998. "Using path integrals to price interest rate derivatives," Papers cond-mat/9812318, arXiv.org, revised Jun 1999.
    5. Linetsky, Vadim, 1998. "The Path Integral Approach to Financial Modeling and Options Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 129-163, April.
    6. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    7. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    10. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    12. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    13. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
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    Cited by:

    1. Hyong-Chol O & Tae-Song Kim & Tae-Song Choe, 2021. "Solution Representations of Solving Problems for the Black-Scholes equations and Application to the Pricing Options on Bond with Credit Risk," Papers 2109.10818, arXiv.org, revised Nov 2021.
    2. Hyong Chol O & Tae Song Kim, 2020. "Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach," Papers 2007.01511, arXiv.org.
    3. Hyong Chol O & Dae Song Choe & Gyong-Dok Rim, 2022. "Analytical Pricing of 2 Factor Structural PDE model for a Puttable Bond with Credit Risk," Papers 2203.05719, arXiv.org.
    4. Khalique, Chaudry Masood & Motsepa, Tanki, 2018. "Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 871-879.

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