IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1511.06032.html
   My bibliography  Save this paper

The Entropic Measure Transform

Author

Listed:
  • Renjie Wang
  • Cody Hyndman
  • Anastasis Kratsios

Abstract

We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a semimartingale BSDE under general conditions. The EMT is used to reinterpret the conditional entropic risk-measure and to obtain a convenient formula for the conditional expectation of a process which admits an affine representation under a related measure. The entropic measure transform is then used provide a new characterization of defaultable bond prices, forward prices, and futures prices when the asset is driven by a jump diffusion. The characterization of these pricing problems in terms of the EMT provides economic interpretations as a maximization of returns subject to a penalty for removing financial risk as expressed through the aggregate relative entropy. The EMT is shown to extend the optimal stochastic control characterization of default-free bond prices of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013). These methods are illustrated numerically with an example in the defaultable bond setting.

Suggested Citation

  • Renjie Wang & Cody Hyndman & Anastasis Kratsios, 2015. "The Entropic Measure Transform," Papers 1511.06032, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1511.06032
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1511.06032
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:bla:ecnote:v:33:y:2004:i:2:p:183-208 is not listed on IDEAS
    2. Hyndman, Cody Blaine, 2007. "Forward-backward SDEs and the CIR model," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1676-1682, November.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    6. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    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. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    2. 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.
    3. Liu, Jun & Longstaff, Francis A. & Mandell, Ravit E., 2000. "The Market Price of Credit Risk: An Empirical Analysis of Interest Rate Swap Spreads," University of California at Los Angeles, Anderson Graduate School of Management qt0zw4f9w6, Anderson Graduate School of Management, UCLA.
    4. 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.
    5. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," 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 20, pages 1207-1246, Elsevier.
    6. repec:wyi:journl:002109 is not listed on IDEAS
    7. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    8. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    9. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    10. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    11. Cheikh Mbaye & Frédéric Vrins, 2022. "Affine term structure models: A time‐change approach with perfect fit to market curves," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 678-724, April.
    12. Robert J. Elliott & Tak Kuen Siu, 2016. "Pricing regime-switching risk in an HJM interest rate environment," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1791-1800, December.
    13. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    14. Pierre Collin‐Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, August.
    15. Jun Liu & Francis A. Longstaff & Ravit E. Mandell, 2006. "The Market Price of Risk in Interest Rate Swaps: The Roles of Default and Liquidity Risks," The Journal of Business, University of Chicago Press, vol. 79(5), pages 2337-2360, September.
    16. Dong Heon Kim, 2004. "Nonlinearity in the Term Structure," Econometric Society 2004 Far Eastern Meetings 440, Econometric Society.
    17. D H Kim, 2005. "Nonlinearity in the Term Structure," Centre for Growth and Business Cycle Research Discussion Paper Series 51, Economics, The University of Manchester.
    18. Saa-Requejo, Jesus & Santa-Clara, Pedro, 1997. "Bond Pricing with Default Risk," University of California at Los Angeles, Anderson Graduate School of Management qt3w71g2ch, Anderson Graduate School of Management, UCLA.
    19. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    20. Kris Jacobs & Xiaofei Li, 2008. "Modeling the Dynamics of Credit Spreads with Stochastic Volatility," Management Science, INFORMS, vol. 54(6), pages 1176-1188, June.
    21. Mari, Carlo & Reno, Roberto, 2005. "Credit risk analysis of mortgage loans: An application to the Italian market," European Journal of Operational Research, Elsevier, vol. 163(1), pages 83-93, May.

    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:arx:papers:1511.06032. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.