Advanced Search
MyIDEAS: Login

Saddlepoint approximations for affine jump-diffusion models

Contents:

Author Info

  • Glasserman, Paul
  • Kim, Kyoung-Kuk
Registered author(s):

    Abstract

    Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuous-time asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms that have an exponential-affine form; these transforms have been characterized in great generality by Duffie et al. [2000. Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343-1376]. Calculating model prices requires inversion of these transforms, and this has limited the application of AJD models to the comparatively small subclass for which the transforms are available in closed form. This article seeks to widen the scope of AJD models amenable to practical application through approximate transform inversion techniques. More specifically, we develop the use of saddlepoint approximations for AJD models. These approximations facilitate the calculation of prices in AJD models whose transforms are not available explicitly. We derive and test several alternative saddlepoint approximations and find that they produce accurate prices over a wide range of parameters.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/B6V85-4SH6B7X-3/2/9ec6133ec14ee10687ef64be1054c76d
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 33 (2009)
    Issue (Month): 1 (January)
    Pages: 15-36

    as in new window
    Handle: RePEc:eee:dyncon:v:33:y:2009:i:1:p:15-36

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Transform inversion Characteristic function Option prices Numerical approximations;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
    2. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA.
    3. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    4. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
    7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    8. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    10. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    11. Mattias Jonsson & K. Ronnie Sircar, 2002. "Partial Hedging In A Stochastic Volatility Environment," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 375-409.
    12. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
    13. Wang, Suojin, 1992. "General saddlepoint approximations in the bootstrap," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 61-66, January.
    14. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    15. Amir Dembo & Jean-Deominique Deuschel & Darrell Duffie, 2002. "Large Portfolio Losses," NBER Working Papers 9177, National Bureau of Economic Research, Inc.
    16. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    17. Chernov, Mikhail, 2003. "Empirical reverse engineering of the pricing kernel," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 329-364.
    18. Lieberman, Offer, 1994. "On the Approximation of Saddlepoint Expansions in Statistics," Econometric Theory, Cambridge University Press, vol. 10(05), pages 900-916, December.
    19. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    20. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
    21. Gordy, Michael B., 2002. "Saddlepoint approximation of CreditRisk+," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1335-1353, July.
    22. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    23. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
    24. Peng Cheng & Olivier Scaillet, 2007. "Linear-Quadratic Jump-Diffusion Modeling," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 575-598.
    25. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    26. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    27. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
    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 in new window

    Cited by:
    1. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:33:y:2009:i:1:p:15-36. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.