This paper treats the risk-averse optimal portfolio problem with consumption in continuous time for a stochastic-jump-volatility, jump-diffusion (SJVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SJVJD model with logtruncated-double-exponential jump-amplitude distribution in returns and exponential jumpamplitude distribution in volatility for...

Computational methods for a jump-diffusion portfolio optimization application using a loguniform jump distribution are considered. In contrast to the usual geometric Brownian motion problem based upon two parameters, mean appreciation and diffusive volatility, the jumpdiffusion model will have at least five, since jump process needs at least a rate, a mean and a variance, depending on the jump-...

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 main goal of this paper is to study market volatility risk premia. I develop a multifactor model by proposing a pricing kernel, where the market return, the diffusion volatility and the jump volatility are fundamental factors that change the investment opportunity set. Based on estimates of the diffusion and jump volatility factors using an enriched dataset including S&P500 index returns, i...

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 consider the hedging problem in a jump-diffusion market with correlated assets. For this purpose, we employ the locally risk-minimizing approach and obtain the hedging portfolio as a solution of a multidimensional system of linear equations. ‎This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk-minimizing portfolio. ‎...

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...