Density approximations for multivariate affine jump-diffusion processes
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in option pricing, credit risk, and likelihood inference highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.
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.
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.
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.:
- 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.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
- 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.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- 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.
- Osnat Stramer & Matthew Bognar & Paul Schneider, 2010. "Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 450-480, Fall.
- Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-91, April.
- Pierre Collin-Dufresne & Robert S. Goldstein & Christopher S. Jones, 2008. "Identification of Maximal Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 63(2), pages 743-795, 04.
- Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
- Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
- Michael Sørensen & Julie Lyng Forman, 2007.
"The Pearson diffusions: A class of statistically tractable diffusion processes,"
CREATES Research Papers
2007-28, Department of Economics and Business Economics, Aarhus University.
- Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465.
- Dennis Kristensen & Antonio Mele, 2009.
"Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models,"
CREATES Research Papers
2009-14, Department of Economics and Business Economics, Aarhus University.
- Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
- Küchler, Uwe & Tappe, Stefan, 2008. "On the shapes of bilateral Gamma densities," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2478-2484, October.
- Hui Chen & Scott Joslin, 2011.
"Generalized Transform Analysis of Affine Processes and Applications in Finance,"
NBER Working Papers
16906, National Bureau of Economic Research, Inc.
- Hui Chen & Scott Joslin, 2012. "Generalized Transform Analysis of Affine Processes and Applications in Finance," Review of Financial Studies, Society for Financial Studies, vol. 25(7), pages 2225-2256.
- Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
- Aït-Sahalia, Yacine & Kimmel, Robert L., 2010.
"Estimating affine multifactor term structure models using closed-form likelihood expansions,"
Journal of Financial Economics,
Elsevier, vol. 98(1), pages 113-144, October.
- Yacine Aït-Sahalia & Robert Kimmel, 2002. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," NBER Technical Working Papers 0286, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Kimmel, Robert L., 2008. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," Working Paper Series 2008-19, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
- Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001.
"Likelihood Inference for Discretely Observed Nonlinear Diffusions,"
Econometric Society, vol. 69(4), pages 959-93, July.
- Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard & Ola Elerian & Siddhartha Chib, 1998. "Likelihood inference for discretely observed non-linear diffusions," Economics Series Working Papers 1998-W10, University of Oxford, Department of Economics.
- Ola Elerian & Siddhartha Chib & Neil Shephard, 2000. "Likelihood inference for discretely observed non-linear diffusions," OFRC Working Papers Series 2000mf02, Oxford Financial Research Centre.
- 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.
- Küchler, Uwe & Tappe, Stefan, 2008. "Bilateral gamma distributions and processes in financial mathematics," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 261-283, February.
- JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
- Christa Cuchiero & Martin Keller-Ressel & Josef Teichmann, 2012. "Polynomial processes and their applications to mathematical finance," Finance and Stochastics, Springer, vol. 16(4), pages 711-740, October.
- 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.
- David S. Bates, 2006. "Maximum Likelihood Estimation of Latent Affine Processes," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 909-965.
- 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.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:176:y:2013:i:2:p:93-111. 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.