Saddlepoint Approximations for Extended Poisson Process Models
نویسنده
چکیده
The saddlepoint approximation to the probabilities of a general time-homogenous birth process, as derived by Daniels 6 , is revisited. Of interest is the accuracy of the approximation for extended Poisson process models constructed from state-dependent birth processes. Numerical calculations are used to examine the accuracy of the probability approximation for a range of state-dependent models, and an alternative derivation of the approximation is given. This alternative derivation suggests an adjustment for when the distribution is close to Poisson.
منابع مشابه
Saddlepoint Approximations for Expectations and an Application to CDO Pricing
We derive two types of saddlepoint approximations for expectations in the form of E[(X − K)], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the i.i.d. case. The approximations are further extended to cover the case of lattice variables. An application of the saddlepoint approximations to C...
متن کاملEstimating Greeks in Simulating Lévy-Driven Models
We develop methods for estimating price sensitivities by simulation for Lévy-driven models. The methods combine pathwise derivatives and likelihood ratio method estimators with alternative approaches to approximating and simulating Lévy processes. We develop estimators based on exact sampling of increments, time-change representations of Lévy processes, saddlepoint approximations to the score f...
متن کاملSaddlepoint Approximations for Affine Jump-Diffusion Models
Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuoustime asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms that have an exponential-affine form; these transforms have been characterized in great generality by Du...
متن کاملImplementation of Saddlepoint Approximations to BootstrapDistributions .
In many situations, saddlepoint approximations can be used to replace Monte Carlo simulations to nd the boot-strap distribution of a statistic. We explain how boot-strap and permutation distributions can be expressed as conditional distributions and how methods for linear programming and for tting generalized linear models can be used to nd the saddlepoint approximations. If the statistic of in...
متن کاملDiscrete Small Sample Asymptotics
(ABSTRACT) Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Pois-son approximations may be substantially improved by tilting, expansion, and other related methods. This work will develop and examine the use of these methods, as well as present examples where such methods may be n...
متن کامل