Log-Normal Stochastic Volatility Model: Moment Generating Function and Pricing of Vanilla Options

% Implementation of the analytical approach for valuation of vanilla options under the log-normal stochastic volatility model
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%Key functionality:
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% 1) LogNormalBetaSVPricingMain for computing option prices and comparision to MC simulations
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% 2) LogNormalBetaSVCalibrationMain for model calibration to market implied volatilities
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% Implemented functionality in this file LogNormalBetaSVPricingMain:
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% [1] Compute option prices in the lognormal beta SV model
% using Fourier inversion formulas with the moment generating function (MGF)
% computed by solving the system of ODE-s using:
% 1 - 4th order Runge-Kutta method (see the paper for analytical details) - preferable default method
% 2 - Rosenbrock stiff method
% 3 - Using Matlab ODE solver - slow and innacurate
% [2] Compute options prices by Monte-Carlo simulation of the log-normal SV model
% [3] Compare option prices between the analytic approach and MC simulation, and also implied volatilities from this prices
% [4] Supported are options on the equity and quadratic variance (QV)
% [5] Implemented jump size distributions: deterministic jumps in log-return and volatility
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% Based on the paper:
% Sepp, A. (2016), Log-Normal Stochastic Volatility Model: Affine Decomposition of Moment Generating Function and Pricing of Vanilla Options
% Working paper available at SSRN: http://ssrn.com/abstract=2522425
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% by Artur Sepp
% artursepp@gmail.com
% http://kodu.ut.ee/~spartak/
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% Last Update: March 7, 2016
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% This code is distributed via the mathworks file-exchange and it is covered by the BSD license
% This code is being provided solely for information and general illustrative purposes.
% The author will not be responsible for numbers produced from using the code.