IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1908.04959.html
   My bibliography  Save this paper

Computational method for probability distribution on recursive relationships in financial applications

Author

Listed:
  • Jong Jun Park
  • Kyungsub Lee

Abstract

In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging error, the Asian option, and statistical hypothesis testing. We propose a method to calculate such a distribution, utilizing a recursive method, and examine it using various examples. The results of the numerical experiment show that our proposed method has high accuracy.

Suggested Citation

  • Jong Jun Park & Kyungsub Lee, 2019. "Computational method for probability distribution on recursive relationships in financial applications," Papers 1908.04959, arXiv.org.
    • Handle: RePEc:arx:papers:1908.04959
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1908.04959
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Artur Sepp, 2012. "An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1119-1141, May.
    3. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    4. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    7. Kyungsub Lee, 2014. "Recursive Formula for Arithmetic Asian Option Prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(3), pages 220-234, March.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    10. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    11. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    12. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    15. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    16. Geon Ho Choe & Kyungsub Lee, 2014. "High Moment Variations and Their Application," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(11), pages 1040-1061, November.
    17. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    18. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prosper Dovonon, 2013. "Conditionally Heteroskedastic Factor Models With Skewness And Leverage Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1110-1137, November.
    2. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    3. Kyungsub Lee, 2013. "Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data," Papers 1311.5036, arXiv.org, revised Jul 2015.
    4. Kyungsub Lee & Byoung Ki Seo, 2017. "Performance of Tail Hedged Portfolio with Third Moment Variation Swap," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 447-471, October.
    5. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    6. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    8. Steven Heston & Saikat Nandi, 1997. "A closed-form GARCH option pricing model," FRB Atlanta Working Paper 97-9, Federal Reserve Bank of Atlanta.
    9. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, Department of Economics and Business Economics, Aarhus University.
    10. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    11. Diep Duong & Norman R. Swanson, 2011. "Volatility in Discrete and Continuous Time Models: A Survey with New Evidence on Large and Small Jumps," Departmental Working Papers 201117, Rutgers University, Department of Economics.
    12. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Oxford University Press, vol. 7(1), pages 2-42.
    13. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    14. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    15. Campbell, John Y. & Giglio, Stefano & Polk, Christopher & Turley, Robert, 2018. "An intertemporal CAPM with stochastic volatility," Journal of Financial Economics, Elsevier, vol. 128(2), pages 207-233.
    16. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    17. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    18. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.
    19. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    20. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1908.04959. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.