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...

The first ever explicit formulation of the concept of an 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 Value-at-Risk...

• The first ever explicit formulation of the concept of an 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...

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate...

We present an embarrassingly simple method for supervised learning of SABR model's European option price function based on lookup table or rote machine learning. Performance in time domain is comparable to generally used analytic approximations utilized in financial industry. However, unlike the...

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression error as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity....

In this paper we introduce the Smooth Permanent Surge [SPS] model. The model is an integrated non lineal moving average process with possibly unit roots in the moving average coefficients. The process nests the Stochastic Permanent Break [STOPBREAK] process by Engle and Smith (1999) and in a...

Maximum likelihood estimation (MLE) of stochastic differential equations (SDEs) is difficult because in general the transition density function of these processes is not known in closed form, and has to be approximated somehow. An approximation based on efficient importance sampling (EIS) is...