This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard fini...

The need of considering price dynamics alternative to the classical Black-Scholes model for derivatives pricing is widely known. The stochastic variability of market parameters and in particular the empirical evidence of non constant surfaces of implied volatility in real markets require more realistic models for the assets dynamics. Many approaches are available to obtain a better fitting of m...

Fast pricing of American-style options has been a difficult problem since it was first introduced to the financial markets in 1970s, especially when the underlying stocks’ prices follow some jump-diffusion processes. In this paper, we extend the “true martingale algorithm” proposed by Belomestny et al. (2009) for the pure-diffusion models to the jump-diffusion models, to fast compute true tight...

We investigate the pricing of swing options in a model where the logarithm of the spot price is the sum of a deterministic seasonal trend and an Ornstein-Uhlenbeck process driven by a jump diffusion. First we calibrate the model to Nord Pool electricity market data. Second, the existence of an optimal exercise strategy is proved, and we present a numerical algorithm for computation of the swing...

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump...

We consider a savings plan, where the paid capital is guaranteed at time of retirement, in the German market available as Riester-Rente and supported by federal cash payments and tax benefits. We generalize several capital guarantee mechanisms to payment plans and compare their distribution: the return distribution of a classical insurance strategy with investments in the actuarial reserve fund...

This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are selfand cross-exciting, and facilitate the description of complex event dependence structures. Ordinary differential equations characterize the transform of an affine point process and the probab...

We study a mean field game problem arising from the production control for multiple firms with price stickiness in commodity market. The dynamics each firm is described as (controlled) jump-diffusion process mean-field interaction. Each aims to maximize her expectation of cumulative net profit coupled other through processes. By solving limiting and fixed-point problem, we construct an explicit...

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...