Basic affine jump diffusion

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In probability theory, a basic affine jump diffusion (basic AJD) is a stochastic process Z of the form

where is a standard Brownian motion, and is an independent compound Poisson process with constant jump intensity and independent exponentially distributed jumps with mean . For the process to be well defined, it is necessary that and . A basic AJD is a special case of an affine process and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD.

Basic AJDs are attractive for modeling default times in credit risk applications,[1][2][3][4] since both the moment generating function

and the characteristic function

are known in closed form.[3]

The characteristic function allows one to calculate the density of an integrated basic AJD

by Fourier inversion, which can be done efficiently using the FFT.

References[edit]

  1. ^ Darrell Duffie, Nicolae Gârleanu (2001). "Risk and Valuation of Collateralized Debt Obligations". Financial Analysts Journal. 57: 41–59. doi:10.2469/faj.v57.n1.2418.  Preprint
  2. ^ Allan Mortensen (2006). "Semi-Analytical Valuation of Basket Credit Derivatives in Intensity-Based Models". Journal of Derivatives. 13: 8–26. doi:10.3905/jod.2006.635417.  Preprint
  3. ^ a b Andreas Ecker (2009). "Computational Techniques for basic Affine Models of Portfolio Credit Risk". Journal of Computational Finance. 13: 63–97.  Cite error: Invalid <ref> tag; name "Eck09" defined multiple times with different content (see the help page). Cite error: Invalid <ref> tag; name "Eck09" defined multiple times with different content (see the help page).
  4. ^ Peter Feldhütter, Mads Stenbo Nielsen (2010). "Systematic and idiosyncratic default risk in synthetic credit markets".  Preprint