Related papers: Volatility Smile as Relativistic Effect

We show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as exp(-c|y|), where c is a positive…

We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine theorem and L\'evian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and…

In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian…

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…

The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…

The analysis of observed conditional distributions of both lagged and simultaneous intraday price increments of a basket of stocks reveals phenomena of dependence - induced volatility smile and kurtosis reduction. A model based on…

This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and…

The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…

Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…

In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and…

It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular…

We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…

The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…

We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric…

Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample…

In the Vasicek credit portfolio model, tail risk is driven primarily by the asset-correlation parameter, yet empirically is subject to correlation risk. We propose a stochastic correlation extension of the Vasicek framework in which the…

The paper deals with the asymptotic laws of functional of standard random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in the Weibull domain…

We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale…

We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the…