NEW COMPUTATIONAL ALGORITHM FOR STOCHASTIC MODELS SUBJECTED TO RANDOM FIELDS OF NON-FINITE VARIANCES

A new algorithm is developed to compute a stochastic model subjected to random fields of non-finite variances. Developing this algorithm motives from an informal test in which representing stochastic models following the Lévy distribution is tried. The first step of current algorithm is deriving moving least square reproducing kernel (MLSRK) approximations of stochastic models. These MLSRK approximations are derived over local support domains in the probability space. Thus, equating it is still possible, even if the variance of studied stochastic model is not finite. The second step is computing the studied stochastic model versus discrete samples computed by the resulting MLSRK approximations in the first step. The third step is computing statistical parameters of the studied stochastic model using the results in the second step. Testing the succeeding algorithm finds that it doesn't require many samples and any empirical coefficient to represent accurately stochastic models following Lévy, Cauchy, and multivariate Cauchy distributions. It also provides accurate computation of means and variances of the option price with the stochastic volatility following two empirical Pareto- Lévy and non-stable Lévy distributions. Except for MLSRK approximations of the option price and stochastic volatility, such computation is completed by a deterministic meshless collocation formulation of the Black-Scholes equation.