Increments in financial markets have anomalous statistical properties including fat-tailed distributions and volatility clustering (i.e., the autocorrelation functions of return increments decay quickly but those of the squared increments decay slowly). One of the central questions in financial...

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time τ⩾0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a...

Recently, a new approach in the fine analysis of sample paths of stochastic processes has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved...

The solution Xn to a nonlinear stochastic differential equation of the form dXn(t)+An(t)Xn(t)dt−12∑j=1N(Bjn(t))2Xn(t)dt=∑j=1NBjn(t)Xn(t)dβjn(t)+fn(t)dt, Xn(0)=x, where βjn is a regular approximation of a Brownian motion βj, Bjn(t) is a family of linear continuous operators from V to H...

We study a family of quadratic, possibly degenerate, stochastic differential equations in the plane, motivated by applications to turbulent transport of heavy particles. Using Lyapunov functions, Hörmander’s hypoellipticity theorem, and geometric control theory, we find a critical parameter...

Simple sufficient conditions for the existence of a unique equivalent martingale measure are provided. Furthermore, these conditions give us a handle on situations where an equivalent martingale measure cannot exist. The existence of a unique equivalent martingale measure is of relevance to...

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an...

The paper developes a VAR macrofinance model of the Czech economy. It shows that yield misalignments from the yields implied by the macrofinance model partially determine subsequent yield changes over three to nine months. These yield misalignments tend to persist for a number of months. This...

This paper analyses the main drivers of sovereign bond spreads in a globalised world. Specifically, we account for international spillovers of bond spreads by adding an additional driver, namely, financial markets, and allowing interactions across countries and markets. We contribute to the VAR...