Related papers: Polynomial Jump-Diffusion Models
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the…
We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for affine jump-diffusions with a canonical state…
We present an analytic solution of a differential-difference equation that appears when one solves an optimal stopping time problem with state process following a jump-diffusion process. This equation occurs in the context of real options…
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of…
For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte…
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…
We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…
This article presents a finite element method (FEM) for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled by an exponential Levy process. We provide a variational formulation…
In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching L\'{e}vy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit…
We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a…
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively,…
It is generally accepted that the asset price processes contain jumps. In fact, pure jump models have been widely used to model asset prices and/or stochastic volatilities. The question is: is there any statistical evidence from the…