Related papers: On a positivity preserving numerical scheme for ju…
In this article, we present a method to construct a positivity-preserving numerical scheme for a jump-extended CEV (Constant Elasticity of Variance) process, whose jumps are governed by a spectrally positive $\alpha$-stable process with…
We consider mean-reverting CIR/CEV processes with delay and jumps used as models on the financial markets. These processes are solutions of stochastic differential equations with jumps, which have no explicit solutions. We prove the…
We consider a pure-jump stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) process driven by a non-symmetric stable L{\'e}vy process with jump activity $\alpha$ $\in$ (1, 2) and we address the joint estimation of drift, scaling and jump…
In this paper, we introduce a linear stochastic volatility model driven by $\alpha$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its…
We study in this article the strong rate of convergence of the Euler-Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik. We obtain the strong rate of convergence under similar assumptions for strong…
In this paper, we consider a fixed delay Cox-Ingersoll-Ross process (CIR process) on the regime where it does not hit zero, the aim is to determine a positive preserving implicit Euler Scheme. On a time grid with constant stepsize our…
We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable L\'evy process with jump activity $\alpha…
In this work, we propose the balanced implicit method (BIM) to approximate the solution of the delay Cox-Ingersoll-Ross (CIR) model with jump which often gives rise to model an asset price and stochastic volatility . We show that this…
We introduce a class of interest rate models, called the $\alpha$-CIR model, which gives a natural extension of the standard CIR model by adopting the $\alpha$-stable L{\'e}vy process and preserving the branching property. This model allows…
In this paper we generalize an explicit numerical scheme for the CIR process that we have proposed before. The advantage of the new proposed scheme is that preserves positivity and is well posed for a (little bit) broader set of parameters…
Credit Valuation Adjustment (CVA) pricing models need to be both flexible and tractable. The survival probability has to be known in closed form (for calibration purposes), the model should be able to fit any valid Credit Default Swap (CDS)…
We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of…
We consider a Cox--Ingersoll--Ross (CIR) type short rate model driven by a mixed fractional Brownian motion. Let $M=B+B^H$ be a one-dimensional mixed fractional Brownian motion with Hurst index $H>1/2$, and let…
The stochastic logistic model with regime switching is an important model in the ecosystem. While analytic solution to this model is positive, current numerical methods are unable to preserve such boundaries in the approximation. So,…
In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the numerical solutions are positive. Under some reasonable…
We study an extension of the Cox-Ingersoll-Ross (CIR) process that incorporates jumps at deterministic dates, referred to as stochastic discontinuities. Our main motivation stems from short-rate modelling in the context of overnight rates,…
We study the jump-diffusion CIR process, which is an extension of the Cox-Ingersoll-Ross model and whose jumps are introduced by a subordinator. We provide sufficient conditions on the L\'evy measure of the subordinator under which the…
We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases:…
This paper considers a general stochastic SIR epidemic model driven by a multidimensional Levy jump process with heavy tailed increments and possible correlation between noise components. In this framework, we derive new sufficient…
We discuss a Markov jump process regarded as a variant of the CIR (Cox-Ingersoll-Ross) model and its infinite-dimensional extension. These models belong to a class of measure-valued branching processes with immigration, whose jump…