Today there are many equity derivatives that are traded on organized and over-the-counter markets. The models that allow market participants to value them and manage the associated risks on a daily basis are numerous. The idea of this study is, for vanilla equity options, to understand the Black...

An "explosion moment" is a large movement in the market that can be caused by fundamental changes or the normal dynamic of some assets. These movements can be difficult to navigate and can lead to poor investment decisions. There are two types of events that can cause explosion moments:...

This study presents a set of closed-form exact solutions for pricing discretely sampled variance swaps and volatility swaps, based on the Heston stochastic volatility model with regime switching. In comparison with all the previous studies in the literature, this research, which obtains...

In 2007, the SAVI was launched as an index designed to measure the market's expectation of the 3-month market volatility. The SAVI soon became the benchmark for measuring the market sentiment, and in this light can be thought of as a market “fear” index.Two years later, in 2009 the...

We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is...

We investigate PDEs of the form u_t = 1/2 σ^2 (t, x)u_{xx} − g(x)u which are associated with the calculation of expectations for a large class of local volatility models. We find nontrivial symmetry groups that can be used to obtain standard integral transforms of fundamental solutions of the...

Alexander Izmailov, Ph.D (theoretical physics) and Brian Shay, Ph.D (mathematics), of Market Memory Trading, L.L.C., present in a series of nine (9) white papers, aspects of a revolutionary advance in uncovering hidden dependencies via filtering noise from correlation matrices developed by the...

In this paper, we propose an innovative VIX model which takes future market information available to the traders into account. The future information is modeled by an initially enlarged filtration in our setup. We derive an explicit representation for the anticipative VIX process and obtain the...

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process,...

Stock market variance-return or price relations are sometimes negative and sometimes positive. We explain these puzzling findings using a model with two ("bad" and "good") variances. In the model, conditional equity premium depends positively on bad variance and negatively on good variance....