The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a B...

This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, si...

In this paper, we present two efficient algorithms for pricing credit default swaps based on a structural default model. In our model, the value of the firm is assumed to be the exponential of a jump-diffusion process. Our first algorithm to price a credit default swap within this framework is an efficient and unbiased Monte Carlo simulation. An excellent performance is obtained by first simula...

There is strong evidence that structural models of credit risk significantly underestimate both credit yield spreads and the probability of default if the value of corporate assets follows a diffusion process. Adding a jump component to the firm value process is a potential remedy for the underestimation. However, there are very few empirical studies of jump-diffusion (or Levy) structural model...

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general function...

The primary goal of this paper is to price European options in the Merton’s framework with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes a...

In this survey we shall focus on the following issues related to jump-diffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a risk-neutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as...

Owing to the fluctuation of financial markets from time to time, some parameters, such as the interest rate, volatility, cannot be precisely described. Under the assumption that the risk-free rate, the volatility, and the average jump intensity are fuzzy numbers, this paper presents the jump-diffusion approach to price vulnerable options in fuzzy environments. We also provide the crisp possibil...

Diffusion of molecules is simulated stochastically by letting them jump between voxels in a Cartesian mesh. The jump coefficients are first derived using finite difference, finite element, and finite volume approximations of the Laplacian on the mesh. An alternative is to let the first exit time for a molecule in random walk in a voxel define the jump coefficient. Such coefficients have the adv...