basicAffineProcess: basicAffineProcess: A package of tools for the Basic Affine...
In michaelgordy/basicAffineProcess: Basic Affine Processes

Description Details Laplace transform functions Simulation functions

The basicAffineProcess package provides Laplace transforms and random number generators for the basic affine process and the important special case of the Cox-Ingersoll-Ross (CIR) process (i.e., square-root diffusion).

A basic affine process (BAP) follows stochastic differential equation

dX[t] = (μ-κ X[t]) dt + σ X[t]^{1/2} dW[t] + dJ[t]

where W[t] is a Brownian motion and J[t] is a compound Poisson process with arrival rate λ and jump sizes distributed exponential with mean ζ.

We have separate routines for two special cases:

λ=0: X[t] is a CIR process.
σ=0: X[t] is a mean-reverting compound Poisson (MRCP) process.

Let Y[t] be the time-integral of X[s] over s=(0,t). Notation X[t] and Y[t] and parameters (μ,κ,σ,λ,ζ) are used throughout the documentation of this package.

The extended transform is

ψ(t;u,w,X0) = E[exp(wY[t]+uX[t])| X0]

Given a vector of times tt, the Laplace transform returns a list (tt, A0, B0, A1, B1), all vectors of the same length. The returns are defined by ψ(t;0,w,X0)=exp(A0+B0*X0) and

ψ'(t;0,w,X0)=exp(A0+B0*X0)(A1+B1*X0)

where ψ' is the derivative with respect to time. The extended transforms are provided by Duffie (J. of Banking & Finance, 2005, Appendix D.4).

The simulation functions ...

michaelgordy/basicAffineProcess documentation built on May 22, 2019, 9:50 p.m.