[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v4y2004i3p301-314.html
   My bibliography  Save this article

Geometric Asian options: valuation and calibration with stochastic volatility

Author

Listed:
  • Hoi Ying Wong
  • Ying Lok Cheung
Abstract
This paper studies continuously sampled geometric Asian options (GAO) in a stochastic volatility economy. The underlying asset price is assumed to follow a geometric Brownian motion with stochastic volatility driven by a mean-reverting process. Semi-analytical pricing formulae for GAO are derived in a fast mean-reverting stochastic volatility economy by the means of a perturbation method. The effects of stochastic volatility on averaging type options are examined. A unified regression approach is proposed to capture smiles of some geometric Asian options and European options in one shot.

Suggested Citation

  • Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 301-314.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:3:p:301-314
    DOI: 10.1088/1469-7688/4/3/006
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1088/1469-7688/4/3/006
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1088/1469-7688/4/3/006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Min Dai, 2003. "One-state variable binomial models for European-/American-style geometric Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 288-295.
    2. 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.
    3. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    4. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    5. Yue-Kuen Kwok & Hoi-Ying Wong, 2000. "Currency-Translated Foreign Equity Options With Path Dependent Features And Their Multi-Asset Extensions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 257-278.
    6. John E. Angus, 1999. "A note on pricing Asian derivatives with continuous geometric averaging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 845-858, October.
    7. 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.
    8. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    9. Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
    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. Jilong Chen & Christian Ewald, 2017. "On the Performance of the Comonotonicity Approach for Pricing Asian Options in Some Benchmark Models from Equities and Commodities," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-32, March.
    2. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    3. Mohamed Amine Kacef & Kamal Boukhetala, 2021. "A closed-form approximation for pricing geometric Istanbul options," Papers 2103.07440, arXiv.org.
    4. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou, 2016. "Jumps and stochastic volatility in crude oil prices and advances in average option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1859-1873, December.
    5. Wong, Hoi Ying & Chan, Chun Man, 2007. "Lookback options and dynamic fund protection under multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 357-385, May.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2009. "Pricing Average Options on Commodities," CARF F-Series CARF-F-177, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2012.
    7. 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.
    8. 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.
    9. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    10. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    11. Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    12. Hoi Ying Wong & Chun Man Chan, 2008. "Turbo warrants under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 739-751.
    13. Rupak Chatterjee & Zhenyu Cui & Jiacheng Fan & Mingzhe Liu, 2018. "An efficient and stable method for short maturity Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1470-1486, December.
    14. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "Analytical valuation for geometric Asian options in illiquid markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 175-191.
    15. Gifty Malhotra & R. Srivastava & H. C. Taneja, 2019. "Pricing of the Geometric Asian Options Under a Multifactor Stochastic Volatility Model," Papers 1912.10640, arXiv.org.
    16. Kenichiro Shiraya & Akihiko Takahashi, 2010. "Pricing Average Options on Commodities," CIRJE F-Series CIRJE-F-747, CIRJE, Faculty of Economics, University of Tokyo.
    17. Lee, Min-Ku, 2016. "Asymptotic approach to the pricing of geometric asian options under the CEV model," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 544-548.
    18. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.

    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. Keng‐Hsin Lo & Kehluh Wang & Ming‐Feng Hsu, 2008. "Pricing European Asian options with skewness and kurtosis in the underlying distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(6), pages 598-616, June.
    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. 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.
    4. Rongwen Wu & Michael C. Fu, 2003. "Optimal Exercise Policies and Simulation-Based Valuation for American-Asian Options," Operations Research, INFORMS, vol. 51(1), pages 52-66, February.
    5. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    6. 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.
    7. Jinke Zhou & Xiaolu Wang, 2008. "Accurate closed‐form approximation for pricing Asian and basket options," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(4), pages 343-358, July.
    8. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 449-473, June.
    9. Kyungsub Lee, 2013. "Recursive formula for arithmetic Asian option prices," Papers 1311.4969, arXiv.org.
    10. Ping Wu & Robert J. Elliott, 2017. "A simple efficient approximation to price basket stock options with volatility smile," Annals of Finance, Springer, vol. 13(1), pages 1-29, February.
    11. Noorani, Idin & Mehrdoust, Farshid & Nasroallah, Abdelaziz, 2021. "A generalized antithetic variates Monte-Carlo simulation method for pricing of Asian option in a Markov regime-switching model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 1-15.
    12. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    13. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    14. 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.
    15. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.
    16. 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.
    17. Xueping Wu & Jin Zhang, 1999. "Options on the minimum or the maximum of two average prices," Review of Derivatives Research, Springer, vol. 3(2), pages 183-204, May.
    18. Tak Siu, 2006. "Option Pricing Under Autoregressive Random Variance Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 62-75.
    19. Ziming Dong & Dan Tang & Xingchun Wang, 2023. "Pricing vulnerable basket spread options with liquidity risk," Review of Derivatives Research, Springer, vol. 26(1), pages 23-50, April.
    20. Kenji Hamatani & Masao Fukushima, 2011. "Pricing American options with uncertain volatility through stochastic linear complementarity models," Computational Optimization and Applications, Springer, vol. 50(2), pages 263-286, October.

    More about this item

    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:taf:quantf:v:4:y:2004:i:3:p:301-314. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.