This note addresses the properties of mean-reverting stochastic processes of the Black-Karasinski type with additional stochastic jumps. For these processes, which are well suited for many financial applications such as the modelling of commodity prices and credit spreads, one would usually like...

This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our...

The Poisson distribution, in general remains sensitive to small departure of frequencies especially at the right tail of the distribution. In many situations it may happen that the Generalized Poisson Distribution (GPD) or a compound distribution provides a closer fit to a frequency distribution...

This paper develops a difference-in-semielasticities (DIS) interpretation for the coefficients of dichotomous variable interaction terms in nonlinear models with exponential conditional mean functions, including but not limited to Poisson, Negative Binomial, and log linear models. We show why...

The recent analytical closed-form result ('http://ssrn.com/abstract=2549033' http://ssrn.com/abstract=2549033) discovered by Market Memory Trading L.L.C. (“MMT”) for the probability density function of the European style options with stochastic volatility, considered within the Heston model,...

The first ever explicit formulation of the concept of the option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True...