We consider the stochastic solution to a Cauchy problem corresponding to a nonnegative diffusion with zero drift, which represents a price process under some risk-neutral measure. When the diffusion coefficient is locally Holder continuous with some exponent in (0,1], the stochastic solution is...

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...

We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying...

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of minimizing the out-of-sample variance. Its asymptotic...

This paper investigates the effects of the "uptick rule" (a short selling regulation formally known as rule 10a-1) by means of a simple stock market model, based on the ARED (adaptive rational equilibrium dynamics) modeling framework, where heterogeneous and adaptive beliefs on the future prices...

Small Medium-sized Enterprises (SMEs) face many obstacles when they try to access credit market. These obstacles are increased if the SMEs are innovative. In this case, financial data are insufficient or even not reliable. Thus, when building a judgemental rating model, mainly based on...

This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process...

Market confidence is essential for successful investing. By incorporating multi-market into the evolutionary minority game, we investigate the effects of investor beliefs on the evolution of collective behaviors and asset prices. When there exists another investment opportunity, market...

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under...

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if...