IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v43y2018icp30-53.html
   My bibliography  Save this article

Compound option pricing under a double exponential Jump-diffusion model

Author

Listed:
  • Liu, Yu-hong
  • Jiang, I-Ming
  • Hsu, Wei-tze

Abstract

A compound option, an option on another option, plays an important role in financial field since it can be used to price American option and corporate debt with discrete coupons. In the real options literature, compound options are most suitable to be employed to investment problems involving sequential decision making. Most compound option and real options formulae are based on log-normal distribution while the empirical evidence shows that the return distribution in real market exhibits asymmetric leptokurtic feature, higher peak and two heavier tails. This paper introduces the jump-diffusion process into pricing compound options and derives the related valuation formulas. We assume that the dynamic of the underlying asset return process consists of a drift component, a continuous Wiener process and discontinuous jump-diffusion processes which have jump times that follow the compound Poisson process and the logarithm of jump size follows the double exponential distribution proposed by Kou (2002). Numerical results indicate that the advantage of combining the double exponential distribution and normal distribution is that it can capture the phenomena of both the asymmetric leptokurtic features and the volatility smile. Furthermore, the compound options under the double exponential jump diffusion model which we derived are more generalized than those proposed by Gukhal (2004) and Geske (1979), and thus have wider application.

Suggested Citation

  • Liu, Yu-hong & Jiang, I-Ming & Hsu, Wei-tze, 2018. "Compound option pricing under a double exponential Jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 43(C), pages 30-53.
    • Handle: RePEc:eee:ecofin:v:43:y:2018:i:c:p:30-53
    DOI: 10.1016/j.najef.2017.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940816301681
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2017.10.002?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. Geske, Robert & Johnson, H. E., 1984. "The Valuation of Corporate Liabilities as Compound Options: A Correction," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(2), pages 231-232, June.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    4. Ben-Ameur, Hatem & Breton, Michele & Francois, Pascal, 2006. "A dynamic programming approach to price installment options," European Journal of Operational Research, Elsevier, vol. 169(2), pages 667-676, March.
    5. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    6. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    7. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    8. repec:bla:jfinan:v:43:y:1988:i:5:p:1235-56 is not listed on IDEAS
    9. Cassimon, D. & Engelen, P. J. & Thomassen, L. & Van Wouwe, M., 2004. "The valuation of a NDA using a 6-fold compound option," Research Policy, Elsevier, vol. 33(1), pages 41-51, January.
    10. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    11. Trigeorgis, Lenos, 1993. "The Nature of Option Interactions and the Valuation of Investments with Multiple Real Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 1-20, March.
    12. Cortazar, Gonzalo & Schwartz, Eduardo S, 1993. "A Compound Option Model of Production and Intermediate Inventories," The Journal of Business, University of Chicago Press, vol. 66(4), pages 517-540, October.
    13. Chang-Wen Duan & William T. Lin & Cheng Few Lee, 2003. "Sequential Capital Budgeting as Real Options: The Case of a New DRAM Chipmaker in Taiwan," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 87-112.
    14. Lin, William T, 2002. "Computing a Multivariate Normal Integral for Valuing Compound Real Options," Review of Quantitative Finance and Accounting, Springer, vol. 18(2), pages 185-209, March.
    15. 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.
    16. Whaley, Robert E., 1981. "On the valuation of American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 9(2), pages 207-211, June.
    17. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    18. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    19. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
    20. Robert H. Keeley & Sanjeev Punjabi & Lassaad Turki, 1996. "Valuation of Early-Stage Ventures: Option Valuation Models vs. Traditional Approaches," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 5(2), pages 115-138, Summer.
    21. Jiang, I-Ming & Yang, Sheng-Yung & Liu, Yu-Hong & Wang, Alan T., 2013. "Valuation of double trigger catastrophe options with counterparty risk," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 226-242.
    22. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    23. M. H. A. Davis & W. Schachermayer & R. G. Tompkins, 2001. "Pricing, no-arbitrage bounds and robust hedging of instalment options," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 597-610.
    24. Fischer, Stanley, 1978. "Call Option Pricing when the Exercise Price Is Uncertain, and the Valuation of Index Bonds," Journal of Finance, American Finance Association, vol. 33(1), pages 169-176, March.
    25. Artur Sepp, 2004. "Analytical Pricing Of Double-Barrier Options Under A Double-Exponential Jump Diffusion Process: Applications Of Laplace Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 151-175.
    26. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    27. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
    28. Longstaff, Francis A, 1990. "Pricing Options with Extendible Maturities: Analysis and Applications," Journal of Finance, American Finance Association, vol. 45(3), pages 935-957, July.
    29. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
    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. Feng, Jiqiang & Li, Yongcai & Zhang, Yingfang & Xu, Chen, 2023. "Stabilization of multi-link delayed neutral-type complex networks with jump diffusion via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    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. Lee, Meng-Yu & Yeh, Fang-Bo & Chen, An-Pin, 2008. "The generalized sequential compound options pricing and sensitivity analysis," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 38-54, January.
    2. 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.
    3. repec:dau:papers:123456789/9845 is not listed on IDEAS
    4. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    5. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    6. Gukhal, C.R.Chandrasekhar Reddy, 2004. "The compound option approach to American options on jump-diffusions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2055-2074, September.
    7. Yepes Rodri­guez, Ramón, 2008. "Real option valuation of free destination in long-term liquefied natural gas supplies," Energy Economics, Elsevier, vol. 30(4), pages 1909-1932, July.
    8. Spiros H. Martzoukos & Nayia Pospori & Lenos Trigeorgis, 2024. "Corporate investment decisions with switch flexibility, constraints, and path-dependency," Review of Quantitative Finance and Accounting, Springer, vol. 62(3), pages 1223-1250, April.
    9. repec:dau:papers:123456789/1046 is not listed on IDEAS
    10. Kung, James J. & Lee, Lung-Sheng, 2009. "Option pricing under the Merton model of the short rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 378-386.
    11. Chi-Yo Huang & Hong-Ling Hsieh & Hueiling Chen, 2020. "Evaluating the Investment Projects of Spinal Medical Device Firms Using the Real Option and DANP-mV Based MCDM Methods," IJERPH, MDPI, vol. 17(9), pages 1-41, May.
    12. Minqiang Li & Kyuseok Lee, 2011. "An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1245-1269.
    13. Gong, Pu & He, Zhiwei & Zhu, Song-Ping, 2006. "Pricing convertible bonds based on a multi-stage compound-option model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 449-462.
    14. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    15. 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.
    16. Lander, Diane M. & Pinches, George E., 1998. "Challenges to the Practical Implementation of Modeling and Valuing Real Options," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 537-567.
    17. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    18. Foad Shokrollahi, 2017. "Pricing compound and extendible options under mixed fractional Brownian motion with jumps," Papers 1708.04829, arXiv.org.
    19. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    20. Agliardi, Rossella, 2006. "Options to expand: Some remarks," Finance Research Letters, Elsevier, vol. 3(1), pages 65-72, March.
    21. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    22. Chung, Y. Peter & Johnson, Herb, 2011. "Extendible options: The general case," Finance Research Letters, Elsevier, vol. 8(1), pages 15-20, March.

    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:ecofin:v:43:y:2018:i:c:p:30-53. 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/inca/620163 .

    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.