IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v16y2013i07ns0219024913500337.html
   My bibliography  Save this article

Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging

Author

Listed:
  • IGOR HALPERIN

    (JPMorgan Chase, 270 Park Avenue, New York, NY 10172, USA;
    Polytechnic Institute of New York University, 6 Metro Tech Center, RH 517E, Brooklyn NY 11201, USA)

  • ANDREY ITKIN

    (Numerix LLC, 150 East 42nd Street, 15th Floor, New York, NY 10017, USA;
    Polytechnic Institute of New York University, 6 Metro Tech Center, RH 517E, Brooklyn NY 11201, USA)

Abstract

We study the problem of the optimal pricing and hedging of a European option written on an illiquid asset Z using a set of proxies: a liquid asset S, and N liquid European options Pi, each written on a liquid asset Yi, i = 1, N. We assume that the S-hedge is dynamic while the multi-name Y-hedge is static. Using the indifference pricing approach with an exponential utility, we derive an HJB equation for the value function, and build an efficient numerical algorithm. The latter is based on several changes of variables, a splitting scheme, and a set of fast Gauss Transforms (FGT), and turns out to be more efficient in terms of complexity and lower local space error than a finite-difference method. While in this paper we apply our framework to an incomplete market version of the credit-equity Merton model, the same approach can be used for other asset classes (equities, commodities, foreign exchange, and so on), for example, for pricing and hedging options with illiquid strikes or illiquid exotic options.

Suggested Citation

  • Igor Halperin & Andrey Itkin, 2013. "Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:07:n:s0219024913500337
    DOI: 10.1142/S0219024913500337
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024913500337
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024913500337?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    2. Igor Halperin & Andrey Itkin, 2013. "Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17.
    3. Igor Halperin & Andrey Itkin, 2014. "Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 427-442, March.
    4. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    5. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
    6. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
    7. S. Narayan, 2009. "India," Chapters, in: Peter Draper & Philip Alves & Razeen Sally (ed.), The Political Economy of Trade Reform in Emerging Markets, chapter 7, Edward Elgar Publishing.
    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. Igor Halperin & Andrey Itkin, 2013. "Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17.

    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. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    2. Azoumah, Y. & Yamegueu, D. & Ginies, P. & Coulibaly, Y. & Girard, P., 2011. "Sustainable electricity generation for rural and peri-urban populations of sub-Saharan Africa: The "flexy-energy" concept," Energy Policy, Elsevier, vol. 39(1), pages 131-141, January.
    3. Findlater, K.M. & Kandlikar, M., 2011. "Land use and second-generation biofuel feedstocks: The unconsidered impacts of Jatropha biodiesel in Rajasthan, India," Energy Policy, Elsevier, vol. 39(6), pages 3404-3413, June.
    4. Maria Ludovica Drudi & Giulio Carlo Venturi, 2023. "Assessing the liquidity premium in the Italian bond market," Questioni di Economia e Finanza (Occasional Papers) 795, Bank of Italy, Economic Research and International Relations Area.
    5. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    6. Elizabeth Kaletski & Nishith Prakash, 2017. "Can Elected Minority Representatives Affect Health Worker Visits? Evidence from India," Review of Development Economics, Wiley Blackwell, vol. 21(1), pages 67-102, February.
    7. Damir Filipovi'c & Martin Larsson & Francesco Statti, 2017. "Unspanned Stochastic Volatility in the Multi-factor CIR Model," Papers 1705.02789, arXiv.org, revised Apr 2018.
    8. Mitrut, Andreea & Wolff, François-Charles, 2011. "The impact of legalized abortion on child health outcomes and abandonment. Evidence from Romania," Journal of Health Economics, Elsevier, vol. 30(6), pages 1219-1231.
    9. Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2015. "Commodity derivatives pricing with cointegration and stochastic covariances," European Journal of Operational Research, Elsevier, vol. 246(2), pages 476-486.
    10. Gao, Lin & Hitzemann, Steffen & Shaliastovich, Ivan & Xu, Lai, 2022. "Oil volatility risk," Journal of Financial Economics, Elsevier, vol. 144(2), pages 456-491.
    11. L. A. Bordag & I. P. Yamshchikov & D. Zhelezov, 2015. "Portfolio optimization in the case of an asset with a given liquidation time distribution," Post-Print hal-01186961, HAL.
    12. Mattoo, Aaditya & Subramanian, Arvind, 2012. "Equity in Climate Change: An Analytical Review," World Development, Elsevier, vol. 40(6), pages 1083-1097.
    13. Varun & Prakash, Ravi & Bhat, I.K., 2010. "A figure of merit for evaluating sustainability of renewable energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(6), pages 1640-1643, August.
    14. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819, arXiv.org, revised Jul 2018.
    15. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    16. Gomes, Francisco & Fugazza, Carolina & Campanale, Claudio, 2015. "Life-Cycle Portfolio choice with Liquid and Illiquid Assets," CEPR Discussion Papers 10369, C.E.P.R. Discussion Papers.
    17. Eiji Yamamura, 2012. "Groups and information disclosure: evidence on the Olson and Putnam hypotheses in Japan," International Journal of Social Economics, Emerald Group Publishing Limited, vol. 39(6), pages 423-439, May.
    18. Susan K Christoffersen & Donald B Keim & David K Musto & Aleksandra Rzeźnik, 2022. "Passive-Aggressive Trading: The Supply and Demand of Liquidity by Mutual Funds [Does motivation matter when assessing trade performance? An analysis of mutual funds]," Review of Finance, European Finance Association, vol. 26(5), pages 1145-1177.
    19. Tan, Raymond R. & Aviso, Kathleen B. & Barilea, Ivan U. & Culaba, Alvin B. & Cruz, Jose B., 2012. "A fuzzy multi-regional input–output optimization model for biomass production and trade under resource and footprint constraints," Applied Energy, Elsevier, vol. 90(1), pages 154-160.
    20. Kathuria, Vinish & Seethamma Natarajan, Rajesh Raj & Sen, Kunal, 2010. "State business relations and manufacturing productivity growth in India," MPRA Paper 20314, University Library of Munich, Germany.

    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:wsi:ijtafx:v:16:y:2013:i:07:n:s0219024913500337. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.