This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE...

This paper describes expectations and Buy-Sell transactions of assets as ground for modeling trading volume and price fluctuations. We study simple model of mutual relations between transactions and expectations and derive economic equations that describe disturbances of asset prices, trading...

The tick structure of the financial markets entails that price changes observed at very high frequency are discrete. Departing from this empirical evidence we develop a new model to describe the dynamic properties of multivariate time-series of high frequency price changes, including the high...

The Middle East and North Africa region is one of the most politically volatile and food insecure areas on earth. The sum of political upheavals and endemic food-security constraints has reduced many MENA nations to the equivalent of small, import-dependent countries. Such countries are...

In this paper, we study stationary states and mean first passage times (MFPT) of the square root process of Feller, the GARCH diffusion model. Asymptotic expansions of MFPT around the starting position and the boundary points of each process as well as the sensitivity analysis of FPT in a change...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

We construct a state-and-time discrete martingale which is calibrated globally to a set of given input option prices which may exhibit arbitrage. We also provide an method to take small steps, fully consistent with the transition kernels of the large steps Its robustness vs. arbitrage violations...

In this paper we use the method of images to derive the closed-form formula for the first passage time density of a timed-dependent Ornstein-Uhlenbeck process to a parametric class of moving boundaries. The results are then applied to develop a simple, efficient and systematic approximation...

We construct a state-and-time discrete martingale which is calibrated globally to a set of given input option prices which may exhibit arbitrage. We also provide a method to take small steps, fully consistent with the transition kernels of the large steps. The method's robustness vs. arbitrage...

We recall some fundamentals on Levy processes. Then the Gamma distribution, the Variance Gamma process and option pricing for this process are considered in detail. To implement the Variance Gamma model for option pricing, we use the fast Fourier transform, time change and discuss error bounds