Author: Dmitry SmelovPublisher:
ISBN:
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Languages : en
Pages :
Book Description
This thesis treats the problems of exact simulation and parameter inference for jump-diffusion processes. It has two parts. The first part develops a method for the exact simulation of a skeleton, a hitting time and other functionals of a one-dimensional jump-diffusion with state-dependent drift, volatility, jump intensity and jump size. The method requires the drift function to be C1, the volatility function to be C2, and the jump intensity function to be locally bounded. No further structure is imposed on these functions. The method leads to unbiased simulation estimators of security prices, transition densities, hitting probabilities, and other quantities. Numerical results illustrate its features. The second part develops and analyzes likelihood estimators for the parameters of a discretely-observed jump diffusion. We consider the case when the transition density of the process admits an expansion in terms of an infinite series. A randomization technique leads to an unbiased Monte Carlo estimator of the transition density and the likelihood function. We provide conditions under which resulting likelihood estimators are consistent and asymptotically normal. The method avoids the second-order bias of conventional discretization-based estimators. Unlike the estimators based directly on the density expansion, we do not require high-frequency observations. Numerical results confirm the method's properties.