“Basic affine jump diffusion”的意思、由来-开放百科全书

词条

Basic affine jump diffusion

释义

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, since both the moment generating function

and the characteristic function

are known in closed form.

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.

1. ^¹{{cite journal | author = Allan Mortensen | year = 2006 | title = Semi-Analytical Valuation of Basket Credit Derivatives in Intensity-Based Models | journal = Journal of Derivatives | volume = 13 | pages = 8–26 | doi=10.3905/jod.2006.635417}} Preprint
2. ^¹²{{cite journal | author = Andreas Ecker | year = 2009 | title = Computational Techniques for basic Affine Models of Portfolio Credit Risk | journal = Journal of Computational Finance | volume = 13 | pages = 63–97 | doi=10.21314/JCF.2009.200}} Preprint
3. ^¹{{cite journal | author = Peter Feldhütter, Mads Stenbo Nielsen | year = 2010 | title = Systematic and idiosyncratic default risk in synthetic credit markets}} Preprint

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1 : Stochastic processes

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