In finance the CIR processes are used to model short term interest rate,stochastic volatility and credit *** current exact simulation methods are too slow and the numerical approximation methods usually have big *** t...
In finance the CIR processes are used to model short term interest rate,stochastic volatility and credit *** current exact simulation methods are too slow and the numerical approximation methods usually have big *** this paper,we present an easy,fast and exact simulation method for the CIR *** new method is much faster than the Poisson method,which involves in sampling from a gamma distribution with a shape parameter having Poisson *** new method is also faster than most of the existing discretization schemes when they require more discrete time points to reduce their discretization *** Poisson method is exact but unacceptably slow when the Poisson mean is large,which occurs frequently during the simulation of the CIR processes on lots of discrete time *** discretization schemes can be *** their discretization errors converge to zero very slowly when the process is close to zero,due to the non- Lipschitzian diffusion coefficient function near *** method is exact and has no such troubles caused by the square-root function as those in the discretization *** comparisons with the QE algorithm for the CIR model and the Heston Model are given through Monte Carlo simulations.
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