[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2251-d465383.html
   My bibliography  Save this article

Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading

Author

Listed:
  • Chih-Chen Hsu

    (Department of Business Administration, Soochow University, Taipei 100006, Taiwan)

  • Chung-Gee Lin

    (Department of Financial Engineering and Actuarial Mathematics, Soochow University, Taipei 100006, Taiwan
    Taiwan/Pervasive Artificial Intelligence Research (PAIR) Labs, Taipei 106031, Taiwan)

  • Tsung-Jung Kuo

    (Department of Financial Engineering and Actuarial Mathematics, Soochow University, Taipei 100006, Taiwan)

Abstract
This research extended the model developed by Hull and White by integrating Taylor-series expansion into the model for deriving approximate analytical solutions for stochastic volatility forward-starting Asian options. Numerical experiments were performed to compare the proposed model with the Monte Carlo model over numerous simulations and demonstrated that the developed model has a pricing accuracy greater than 99%. Furthermore, the computation time was approximately 10 −5 s for each simulation. The model’s outstanding computational performance demonstrates its capability to address the challenges of high-frequency trading.

Suggested Citation

  • Chih-Chen Hsu & Chung-Gee Lin & Tsung-Jung Kuo, 2020. "Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading," Mathematics, MDPI, vol. 8(12), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2251-:d:465383
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2251/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2251/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bernales, Alejandro, 2019. "Make-take decisions under high-frequency trading competition," Journal of Financial Markets, Elsevier, vol. 45(C), pages 1-18.
    2. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282, April.
    3. J. K. Hoogland & C. D. D. Neumann, 2001. "Local Scale Invariance And Contingent Claim Pricing Ii: Path-Dependent Contingent Claims," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 23-43.
    4. Jianqiang Sun & Langnan Chen & Shiyin Li, 2013. "A Quasi‐Analytical Pricing Model for Arithmetic Asian Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(12), pages 1143-1166, December.
    5. Michael A. Kouritzin, 2016. "Explicit Heston Solutions and Stochastic Approximation for Path-dependent Option Pricing," Papers 1608.02028, arXiv.org, revised Apr 2018.
    6. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    7. Xingchun Wang, 2020. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(3), pages 410-429, March.
    8. Aprahamian, Hrayer & Maddah, Bacel, 2015. "Pricing Asian options via compound gamma and orthogonal polynomials," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 21-43.
    9. Moshe Arye Milevsky & Steven E. Posner, 1999. "Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma 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 7, pages 203-218, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. 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.
    12. Sander Willems, 2019. "Asian option pricing with orthogonal polynomials," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 605-618, April.
    13. Markus Baldauf & Joshua Mollner, 2020. "High‐Frequency Trading and Market Performance," Journal of Finance, American Finance Association, vol. 75(3), pages 1495-1526, June.
    14. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    15. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    16. Chueh‐Yung Tsao & Chuang‐Chang Chang & Chung‐Gee Lin, 2003. "Analytic approximation formulae for pricing forward‐starting Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(5), pages 487-516, May.
    17. 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.
    18. Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing," Finance 9907002, University Library of Munich, Germany.
    19. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
    20. Alain P. Chaboud & Benjamin Chiquoine & Erik Hjalmarsson & Clara Vega, 2014. "Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 69(5), pages 2045-2084, October.
    21. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    22. Shafi, Khuram & Latif, Natasha & Shad, Shafqat Ali & Idrees, Zahra, 2019. "High-frequency trading: Inverse relationship of the financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    23. Michael A. Kouritzin, 2018. "Explicit Heston Solutions And Stochastic Approximation For Path-Dependent Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-45, February.
    24. J. K. Hoogland & C. D. D. Neumann, 2001. "Local Scale Invariance And Contingent Claim Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-21.
    25. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    26. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yue Qi & Yue Wang, 2023. "Innovating and Pricing Carbon-Offset Options of Asian Styles on the Basis of Jump Diffusions and Fractal Brownian Motions," Mathematics, MDPI, vol. 11(16), pages 1-22, August.

    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. Bara Kim & In-Suk Wee, 2014. "Pricing of geometric Asian options under Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1795-1809, October.
    2. Yanhong Zhong & Guohe Deng, 2019. "Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate," Complexity, Hindawi, vol. 2019, pages 1-13, January.
    3. Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    4. Yijuan Liang & Xiuchuan Xu, 2019. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities," Sustainability, MDPI, vol. 11(3), pages 1-21, February.
    5. Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org, revised Sep 2018.
    6. Hideharu Funahashi & Masaaki Kijima, 2013. "An Extension of the Chaos Expansion Approximation for the Pricing of Exotic Basket Options　," KIER Working Papers 857, Kyoto University, Institute of Economic Research.
    7. Weinan Zhang & Pingping Zeng, 2023. "A transform-based method for pricing Asian options under general two-dimensional models," Quantitative Finance, Taylor & Francis Journals, vol. 23(11), pages 1677-1697, November.
    8. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    9. Ballestra, Luca Vincenzo & Pacelli, Graziella & Zirilli, Francesco, 2007. "A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3420-3437, November.
    10. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    11. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    12. 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.
    13. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    14. Chueh-Yung Tsao & Chao-Ching Liu, 2012. "Asian Options with Credit Risks: Pricing and Sensitivity Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 48(S3), pages 96-115, September.
    15. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    16. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    17. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    18. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    19. Matthew Lorig, 2011. "Pricing Derivatives on Multiscale Diffusions: an Eigenfunction Expansion Approach," Papers 1109.0738, arXiv.org, revised Apr 2012.
    20. Michael A. Kouritzin & Anne Mackay, 2020. "Branching Particle Pricers With Heston Examples," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-29, February.

    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:gam:jmathe:v:8:y:2020:i:12:p:2251-:d:465383. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.