IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v37y2013i8p2702-2713.html
   My bibliography  Save this article

Pricing discrete path-dependent options under a double exponential jump–diffusion model

Author

Listed:
  • Fuh, Cheng-Der
  • Luo, Sheng-Feng
  • Yen, Ju-Fang

Abstract

We provide methodologies to price discretely monitored exotic options when the underlying evolves according to a double exponential jump diffusion process. We show that discrete barrier or lookback options can be approximately priced by their continuous counterparts’ pricing formulae with a simple continuity correction. The correction is justified theoretically via extending the corrected diffusion method of Siegmund (1985). We also discuss the jump effects on the performance of this continuity correction method. Numerical results show that this continuity correction performs very well especially when the proportion of jump volatility to total volatility is small. Therefore, our method is sufficiently of use for most of time.

Suggested Citation

  • Fuh, Cheng-Der & Luo, Sheng-Feng & Yen, Ju-Fang, 2013. "Pricing discrete path-dependent options under a double exponential jump–diffusion model," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2702-2713.
    • Handle: RePEc:eee:jbfina:v:37:y:2013:i:8:p:2702-2713
    DOI: 10.1016/j.jbankfin.2013.03.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426613001660
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2013.03.023?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. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    3. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    4. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Kubilius Kestutis & Platen Eckhard, 2002. "Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps," Monte Carlo Methods and Applications, De Gruyter, vol. 8(1), pages 83-96, December.
    7. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    8. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    10. 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.
    11. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, 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. Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    2. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    3. Chen, Rongda & Zhou, Hanxian & Yu, Lean & Jin, Chenglu & Zhang, Shuonan, 2021. "An efficient method for pricing foreign currency options," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    4. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
    5. Lee, Hangsuck & Lee, Gaeun & Song, Seongjoo, 2023. "Min–max multi-step barrier options and their variants," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    6. Lee, Hangsuck & Choi, Yang Ho & Lee, Gaeun, 2022. "Multi-step barrier products and static hedging," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    7. Carlos Esparcia & Elena Ibañez & Francisco Jareño, 2020. "Volatility Timing: Pricing Barrier Options on DAX XETRA Index," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    8. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    9. Xie, Fei & He, Zhijian & Wang, Xiaoqun, 2019. "An importance sampling-based smoothing approach for quasi-Monte Carlo simulation of discrete barrier options," European Journal of Operational Research, Elsevier, vol. 274(2), pages 759-772.
    10. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    11. Carole Bernard & Junsen Tang, 2016. "Simplified Hedge For Path-Dependent Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-32, November.
    12. Sheng-Feng Luo & Hsin-Chieh Wong, 2023. "Continuity correction: on the pricing of discrete double barrier options," Review of Derivatives Research, Springer, vol. 26(1), pages 51-90, April.
    13. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    14. Jinzhi Li, 2021. "Bayesian estimation of the stochastic volatility model with double exponential jumps," Review of Derivatives Research, Springer, vol. 24(2), pages 157-172, July.

    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. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    2. Liming Feng & Vadim Linetsky, 2008. "Pricing Options in Jump-Diffusion Models: An Extrapolation Approach," Operations Research, INFORMS, vol. 56(2), pages 304-325, April.
    3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    4. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    5. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.
    6. 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.
    7. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    8. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    9. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    10. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
    11. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    12. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.
    13. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    14. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    15. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    16. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    17. 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.
    18. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    19. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    20. Helin Zhu & Fan Ye & Enlu Zhou, 2015. "Fast estimation of true bounds on Bermudan option prices under jump-diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1885-1900, November.

    More about this item

    Keywords

    Barrier options; Lookback options; Jump diffusion models; Continuity correction; Laplace transform;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    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:eee:jbfina:v:37:y:2013:i:8:p:2702-2713. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbf .

    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.