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...

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...

A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the...

The paper proposes a simple test for the hypothesis of strong cycles and as a by-product a test for weak dependence for linear processes. We show that the limit distribution of the test is the maximum of a (semi)Gaussian process G(amp;#964;), amp;#964; amp;#8712; [0; 1]. Because the covariance structure of...

Stationarity testing for time series which include a smooth trend with unknown parameters is considered in this paper. A pseudo-Lagrange Multiplier stationarity test is proposed and its asymptotic null distribution is obtained. The distribution depends on the unknown parameters of the model....