IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v151y2011i3d10.1007_s10957-011-9899-y.html
   My bibliography  Save this article

Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures

Author

Listed:
  • Jun-ya Gotoh

    (Chuo University)

  • Yoshitsugu Yamamoto

    (University of Tsukuba)

  • Weifeng Yao

    (China Universal Asset Management Co., Ltd)

Abstract

We generalize the notion of arbitrage based on the coherent risk measure, and investigate a mathematical optimization approach for tightening the lower and upper bounds of the price of contingent claims in incomplete markets. Due to the dual representation of coherent risk measures, the lower and upper bounds of price are located by solving a pair of semi-infinite linear optimization problems, which further reduce to linear optimization when conditional value-at-risk (CVaR) is used as risk measure. We also show that the hedging portfolio problem is viewed as a robust optimization problem. Tuning the parameter of the risk measure, we demonstrate by numerical examples that the two bounds approach to each other and converge to a price that is fair in the sense that seller and buyer face the same amount of risk.

Suggested Citation

  • Jun-ya Gotoh & Yoshitsugu Yamamoto & Weifeng Yao, 2011. "Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 613-632, December.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9899-y
    DOI: 10.1007/s10957-011-9899-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9899-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-011-9899-y?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. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    2. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    3. Peter Ritchken & Shyanjaw Kuo, 1989. "On Stochastic Dominance and Decreasing Absolute Risk Averse Option Pricing Bounds," Management Science, INFORMS, vol. 35(1), pages 51-59, January.
    4. 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.
    5. Jun-ya Gotoh & Hiroshi Konno, 2002. "Bounding Option Prices by Semidefinite Programming: A Cutting Plane Algorithm," Management Science, INFORMS, vol. 48(5), pages 665-678, May.
    6. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. Yumiharu Nakano, 2003. "Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 163-181.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    10. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
    11. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    12. Antonella Basso & Paolo Pianca, 1997. "Decreasing Absolute Risk Aversion and Option Pricing Bounds," Management Science, INFORMS, vol. 43(2), pages 206-216, February.
    13. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
    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. 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.
    2. Roy H. Kwon & Jonathan Y. Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    3. Roy Kwon & Jonathan Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    4. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2012. "Non-parametric method for European option bounds," Review of Quantitative Finance and Accounting, Springer, vol. 38(1), pages 109-129, January.
    5. Jun-ya Gotoh & Hiroshi Konno, 2002. "Bounding Option Prices by Semidefinite Programming: A Cutting Plane Algorithm," Management Science, INFORMS, vol. 48(5), pages 665-678, May.
    6. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    7. repec:dau:papers:123456789/30 is not listed on IDEAS
    8. Ryan, Peter J., 2003. "Progressive option bounds from the sequence of concurrently expiring options," European Journal of Operational Research, Elsevier, vol. 151(1), pages 193-223, November.
    9. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    10. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    11. Patrick Bei{ss}ner, 2012. "Coherent Price Systems and Uncertainty-Neutral Valuation," Papers 1202.6632, arXiv.org.
    12. Chatterjee, Somnath & Jobst, Andreas, 2019. "Market-implied systemic risk and shadow capital adequacy," Bank of England working papers 823, Bank of England.
    13. 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.
    14. Saeed Marzban & Erick Delage & Jonathan Yumeng Li, 2020. "Equal Risk Pricing and Hedging of Financial Derivatives with Convex Risk Measures," Papers 2002.02876, arXiv.org, revised Sep 2020.
    15. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    16. Cinfrignini, Andrea & Petturiti, Davide & Vantaggi, Barbara, 2023. "Dynamic bid–ask pricing under Dempster-Shafer uncertainty," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    17. Basso, A. & Pianca, P., 2001. "Option pricing bounds with standard risk aversion preferences," European Journal of Operational Research, Elsevier, vol. 134(2), pages 249-260, October.
    18. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    19. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    20. Li Chen & Simai He & Shuzhong Zhang, 2011. "Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection," Operations Research, INFORMS, vol. 59(4), pages 847-865, August.
    21. Donald Aingworth & Sanjiv Das & Rajeev Motwani, 2006. "A simple approach for pricing equity options with Markov switching state variables," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 95-105.

    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:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9899-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.