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Multiple Streams of Random Numbers Pierre L'Ecuyer's latest generator.

Simulation of Heston's model (Implements a second order scheme)

4 files are included in the package: (1) fs01.m - the 1st-order local linear approximation (LLA) very similar to algorithm by Farmer and Sidorowich (1987). Uses constrained linear least squares (lsqlin) and (2) ts1.m - to reconstruct the vectors of the state space. (3) Example.m - runs fs01 and ts1 to predict (4) composite.txt - synthetic time series of decadal average sunspot number.

Key Benefits of the OptionCity Calculator Flexible models with stochastic volatility and stock price jumps Option prices with Greeks (sensitivity to parameters) Realistic Smile charts Fast evaluations Self-validating results. (You validate calculations by selecting a different numerical method: Lattice, Series, or Monte Carlo)

Computes numerically VaR and Expected shortfall under Generalized Student t distribution.

fast and accurate state-of-the-art bivariate kernel density estimator with diagonal bandwidth matrix. The kernel is assumed to be Gaussian. The two bandwidth parameters are chosen optimally without ever using/assuming a parametric model for the data or any "rules of thumb".

stable distributions are a better model for equity returns. There are different numerical methods that can be used to estimates the parameters of the stable distribution. The goodness of estimation depends of two things : the model that is used to estimate the parameters, and, of course, the number of observations. The choice of the estimation model is a compromise between the quality of the estimates, and the speed of the algorithm. Even if stable distributions seem to better model asset returns, it seems that this model overestimates occurences of extreme events. You will find below the modified versions that have been used for this work. stabrnd is used to generate numbers following a stable distribution, stabfit estimates the parameters of a stable distribution given a data sample, stabmlefit estimates the parameters (very slowly) with the maximum-likelihood method and dstable calculates the density of a given stable distribution.

Directory Description Arithmetic programs Evaluation of Bessel Functions. Roots in the Complex Domain Differential equations Functional approximations by Iteration & Recursion Geometry programs Graphic programs (manual scaling) Graphic programs (automatic scaling) Graphic programs (signal processing) Least squares approximation. Linear Programming Algorithms concerning matrices Programs concerning Mechanics NEW Operations on Polynomials Roots of real functions. Series approximation techniques Signal processing Sorting Statistics

consistent with the nomenclature in John Nolan's Stable Distributions: Models for Heavy Tailed Data.

Asymmetric Power Distribution (APD) family of densities extends the Generalized Power Distribution to cases where the data exhibits asymmetry. It contains the asymmetric Gaussian and Laplace densities as special cases. In the paper entitled "Asymmetric Power Distribution: Theory and Applications to Risk Measurement", I provide a detailed description of the properties of an APD random variable, such as its quantiles and expected shortfalls.

Mathematic notebook of an algorithm to construct primitive polynomials construct multi-dimensional Sobol sequences.

A lot of people (and some software providers) are not aware of this simple trick to avoid oscillation in binomial trees. Oscillation might become dangerous when calculating Greeks via numerical differentiation. Here's the trick. E.g., for American options, we just replace the last step in the binomial tree with the closed-form Black-Scholes formula. To run the program, please also download a European Black Scholes matlab file bsval at the Author's website.