This paper develops, analyzes, and tests computational procedures for the numerical solution of LIBOR market models with jumps. We consider, in particular, a class of models in which jumps are driven by marked point processes with intensities that depend on the LIBOR rates themselves. While this formulation offers some attractive modeling features, it presents a challenge for computational work...

We introduce nonparametric estimators of the coefficients of a univariate jump-diffusion process when observations are recorded discretely. We allow the drift, diffusion and intensity function to be level dependent. We also show that the estimator of the diffusion coefficient is consistent even if the jump process has infinite activity. Our results rely on the fact that it is possible to disent...

A new Bayesian significance test is adjusted for jump detection in a diffusion process. This is an advantageous procedure for temporal data having extreme valued outliers, like financial data, pluvial or tectonic forces records and others.

We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion linear quadratic jump-diffusion processes (Duffie, Pan and Singleton [13], Cheng and Scaillet [10]) so that the pr...

The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level. In thi...

exchange rate prediction, as one of the main variables in macroeconomics, has been one of the aims of the economic research for a long time. for modeling and predicting exchange rate we apply stochastic differential equation, specifically we use geometric brownian motion (gbm) and jump-diffusion process (mjdp) attributed to merton. we show that the result of simulation based on gbm and mjdp out...