Code covered by the BSD License

### Highlights fromReview of Discrete and Continuous Processes in Finance

from Review of Discrete and Continuous Processes in Finance by Attilio Meucci
discrete-time and continuous-time processes for finance, theory and empirical examples

S_LevyProcesses.m
```% this file generates paths from four types of Levy processes:
% Merton's jump-diffusion, normal-inverse-gamma, variance-gamma, Kou's jump-diffusion

% see A. Meucci (2009)
% "Review of Discrete and Continuous Processes in Finance - Theory and Applications"
% available at ssrn.com

% Code by A. Meucci, April 2009
% Most recent version available at www.symmys.com > Teaching > MATLAB

close all; clc; clear;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% inputs
ChooseProcess=2; % 1=Merton, 2=normal-inverse-Gaussian, 3=variance-gamma, 4=double-exponential
ts=[1/252 : 1/252 : 1]; % grid of time values at which the process is evaluated ("0" will be added, too)
J=3; % number of simulations

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% simulate processes

if ChooseProcess==1 %Merton
mu=.00;     % deterministic drift
sig=.20; % Gaussian component

l=3.45; % Poisson process arrival rate
a=0; % drift of log-jump
D=.2; % st.dev of log-jump

X=JumpDiffusionMerton(mu,sig,l,a,D,ts,J);

figure
plot([0 ts],X');
title('Merton jump-diffusion')
end

if ChooseProcess==2 % normal-inverse-Gaussian
% (Schoutens notation)
al=2.1;
be=0;
de=1;
% convert parameters to Cont-Tankov notation
[th,k,s]=Schout2ConTank(al,be,de);

X=NIG(th,k,s,ts,J);

figure
plot([0 ts],X');
title('normal-inverse-Gaussian')
end

if ChooseProcess==3 % variance-gamma
mu=.1;     % deterministic drift in subordinated Brownian motion
kappa=1;   %
sig=.2;    % s.dev in subordinated Brownian motion

X=VG(mu,sig,kappa,ts,J);

figure
plot([0 ts],X');
title('variance gamma')
end

if ChooseProcess==4 % Kou
mu=.0; % deterministic drift
l=4.25; % Poisson process arrival rate
p=.5; % prob. of up-jump
e1=.2; % parameter of up-jump
e2=.3; % parameter of down-jump
sig=.2; % Gaussian component

X=JumpDiffusionKou(mu,sig,l,p,e1,e2,ts,J);

figure
plot([0 ts],X');
title('double exponential')

end```

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