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runEurepeanOption.m
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% runEuropeanOption
% pricing Eurepean
clc; close all; clear variables;
rng(1192) % set the seed
T = 1;S0 = 30;r = 0.1;K = 30;
Nsim = 1e5; Nstep = 40;N = 200; M = 100;
epsilon = 0.01;
model = 'BS';
optionType = 'Call';
theta = 0.5;
NumMethod = 'explicit';
switch optionType
case 'Call'
switch model
case 'BS'
param = 0.6;
% 1) closed formula
PriceExact = blsprice(S0,K,r,T,param);
% 2) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 3) FFT
[ priceFFT, check_marting ] = FFT(K, S0, T, r, model, param);
% 4) PDE LogPrice implementation short
[pricePDELogPrice] = FDLogPrice1( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 5) LogPrice implementation full
[pricePDELogPrice2] = FDLogPrice2( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 6) PDE Price implementation short
[pricePDEPrice] = FDPrice1( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 7) FEM LogPrice implementation short
[pricePDE_FEM_LogPrice1] = FEMLogPrice1( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 8) FEM LogPrice implementation full
[pricePDE_FEM_LogPrice2] = FEMLogPrice2( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 9) Upwind method
[priceUW] = FDLogPriceUpWind( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
case 'Merton'
param = [0.5;0.6;0.1;0.1];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 2) FFT
[ priceFFT, check_marting ] = FFT(K, S0, T, r, model, param);
% 3) PIDE logmoneyness
[pricePIDElogmon] = FDLevyLogMoneyness1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
% 4) PIDE logprice
[pricePIDElogprice] = FDLevyLogPrice1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
% 5) PIDE Price
[pricePIDEprice] = FDLevyPrice1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
case 'Kou'
param = [0.6;0.01;9;6;0.3];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 3) FFT
[ priceFFT,check_marting] = FFT(K, S0, T, r, model, param);
% 4) PIDE
[pricePIDElogmon] = FDLevyLogMoneyness1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
% 4) PIDE logprice
[pricePIDElogprice] = FDLevyLogPrice1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
% 5) PIDE Price
[pricePIDEprice] = FDLevyPrice1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
case 'VG'
% theta_VG, sigma_VG, kappa
param = [0.03;0.12;0.2;0.2];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 2) FFT
[ priceFFT, check_marting ] = FFT(K, S0, T, r, model, param);
% 3) PIDE logmonyness
[pricePDElogmoneyness] = FDLevyLogMoneyness1AI( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta,...
epsilon);
% 4) PIDE logprice forward price
[pricePDElogpricefwdprice] = FDLevyLogpriceFwdprice1AI( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta,...
epsilon);
case 'VG2'
param = [0.16;0.0694;0.0166];
% 4) PIDE logmonyness
[pricePDElogmoneyness] = FDLevyLogMoneyness1AI( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta,...
epsilon);
case 'NIG'
param = [0.2;0.8];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 3) FFT
[ priceFFT, check_marting ] = FFT(K, S0, T, r, model, param);
% 4) PIDE
otherwise
end
case 'Put'
switch model
case 'BS'
param = 0.6;
% 1) closed formula
[~, PriceExact] = blsprice(S0,K,r,T,param);
% 2) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 3) FFT
% call put parity
% 4) PDE short implementation
[pricePDELogPrice] = FDLogPrice1( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 5) PDE Price implementation short
[pricePDEPrice] = FDPrice1( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
% 7) FEM LogPrice implementation short
[pricePDE_FEM_LogPrice] = FEMLogPrice1( S0,K,r,T,N,M,param,optionType,NumMethod,theta);
case 'Merton'
param = [0.5;0.6;0.1;0.1];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 2) PIDE
[pricePIDE] = FDLevyLogMoneyness1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
% 4) PIDE logprice
[pricePIDElogprice] = FDLevyLogPrice1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
case 'Kou'
param = [0.6;0.01;9;6;0.3];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 2) PIDE
[pricePIDE] = FDLevyLogMoneyness1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
% 4) PIDE logprice
[pricePIDElogprice] = FDLevyLogPrice1( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta);
case 'VG'
% theta_VG, sigma_VG, kappa
param = [0.03;0.12;0.2;0];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
% 2) PIDE logmoneyness
[pricePDElogmoneyness] = FDLevyLogMoneyness1AI( S0,K,r,T,N,M,param,model,optionType,NumMethod,theta,...
epsilon);
case 'NIG'
param = [0.2; 0.8];
% 1) MC
[PriceMC, check, IC] = PricingOptionMC( S0,r,T,K,param,Nsim,Nstep,...
model,optionType);
otherwise
end
otherwise
end