rec.rar_rec

%% Classic Monte Carlo simualtion % Vincent Leclercq, The MathWorks, 2007, vincent.leclercq@mathworks.fr % clear all; close all; NbTrials = 10000; %RunMode = 'LogNomrality'; RunMode = 'OptionPricing'; %% Load Data (retrieved originally from Thomson Datastream) load Equities.mat PastDate = today()-1 * 365; %% Retrieve the dates in a numeric format Dates = cellfun(@(x)(datenum(x,'yyyy-mm-ddTHH:MM:SS')),Equities.DATE); AssetPrices = cellfun(@(x) (str2double(x)),Equities.P ); %% Plot the Series plot(Dates,AssetPrices);set(gcf,'WindowStyle','Docked'); legend(Equities.DISPNAME); datetick('x','mmmyy'); xlim([PastDate, today()]); grid on; %% Compute the returns % We can compute the returns for one or many stocks at the same time using % matrix computation and matlab easy syntax Suez_Returns = tick2ret(AssetPrices); DailyVol = std(Suez_Returns); AnnualVol = DailyVol * sqrt(252); SpotPrice = AssetPrices(end); InterestRate = 0.0375; %% Portfolio simulation (Monte Carlo) using the Financial toolbox function % For help, one can use the doc portsim function % We call the portfolio simulation using Financial toolbox to % simulate 10000 scenarios. Of course, correlation are preserved % We assume an horizon of 6 * 22 trading days, ie 6 month maturity %% Using Annual statistics SimulatedRetsAnnual = portsim(InterestRate,AnnualVol^2, 12, 1/12, NbTrials,'Expected'); % NbStep * TimeStep = 1 (in years !!!) %% Using Daily statistics NumberOfSimulationSteps = 12; SimulatedRetsDaily = portsim(InterestRate./252, DailyVol^2, 12, 252./12, NbTrials,'Expected');% NbStep * TimeStep = 252 (in days!!!) %% Generate the Prices and plot them SimulatedPricesAnnual = ret2tick(squeeze(SimulatedRetsAnnual) ,SpotPrice); SimulatedPricesDaily = ret2tick(squeeze(SimulatedRetsDaily) ,SpotPrice ); figure;hist(SimulatedPricesAnnual(end,:),40);title('Prices, annual timestep used');set(gcf,'WindowStyle','Docked'); figure;hist(SimulatedPricesDaily(end,:),40);title('Prices, daily timestep used');set(gcf,'WindowStyle','Docked'); %% Check For LogNormality of the Price series ExpectedVariance = (SpotPrice^2) * (exp(AnnualVol^2) - 1)* exp(2*InterestRate); disp(['Mean Price (Annual Parameters) -> ', num2str(mean(SimulatedPricesAnnual(end,:))) ' , Theoric value (Hull) :' num2str(SpotPrice * exp(InterestRate))]); disp(['Mean Price (Daily Parameters) -> ', num2str(mean(SimulatedPricesDaily(end,:))) ' , Theoric value (Hull) :' num2str(SpotPrice * exp(InterestRate))]); disp(['Expected Variance (Annual Parameters) -> ', num2str(var(SimulatedPricesAnnual(end,:))) ' , Theoric value (Hull) :' num2str(ExpectedVariance)]); disp(['Expected Variance (Daily Parameters) -> ', num2str(var(SimulatedPricesDaily(end,:))) ' , Theoric value (Hull) :' num2str(ExpectedVariance)]); %% Parameter sweep % Now that we have done this, we can ccompute the same thing for different % Exercise prices if strcmp(RunMode,'OptionPricing') k = 1; NumberOfSteps = 400; ExercisePrices= linspace(0.8 * SpotPrice,1.2 * SpotPrice,NumberOfSteps); VanillaPriceAnnual = zeros(NumberOfSteps,1); VanillaPriceDaily = zeros(NumberOfSteps,1); ProbabilityITMAnnual = zeros(NumberOfSteps,1); ProbabilityITMDaily = zeros(NumberOfSteps,1); CIAnnual = zeros(NumberOfSteps,2); CIDaily = zeros(NumberOfSteps,2); BLSPrices = zeros(NumberOfSteps,1); %% TimeInYear = 1; for i = 1 : NumberOfSteps [BLSPrices(i),dummy] = blsprice(SpotPrice, ExercisePrices(i), InterestRate, TimeInYear, AnnualVol, 0); [VanillaPriceAnnual(i), ProbabilityITMAnnual(i) ,CIAnnual(i,:)] = GetOptionPrice(SimulatedPricesAnnual,ExercisePrices(i),TimeInYear,InterestRate,'Vanilla'); [VanillaPriceDaily(i), ProbabilityITMDaily(i) , CIDaily(i,:)] = GetOptionPrice(SimulatedPricesDaily,ExercisePrices(i),TimeInYear,InterestRate,'Vanilla'); end; %% h = figure; [AX,H1,H2] = plotyy(ExercisePrices,[VanillaPriceAnnual BLSPrices CIAnnual] , ExercisePrices,ProbabilityITMAnnual); xlabel('Exercise Price'); title('Option prices for a Vanilla option using a 1 year - Annual volatility'); Axes_YLabels = get(AX,'Ylabel'); set(Axes_YLabels{1},'String','Option Price') ; set(H1(1),'LineStyle','-'); set(H1(1),'Color','r'); set(H1(1),'LineWidth',2); set(H1(2),'LineStyle','-'); set(H1(2),'Color','b'); set(H1(2),'LineWidth',2); set(H1(3),'LineStyle','--'); set(H1(3),'Color','r'); set(H1(3),'LineWidth',1); set(H1(4),'LineStyle',':'); set(H1(4),'Color','r'); set(H1(4),'LineWidth',1); set(H2,'LineStyle','-'); set(H2,'Color','g'); set(H2,'LineWidth',2); set(get(AX(2),'Ylabel'),'String','Probability of being In the Money'); legend(H1,{['Option Price (Monte Carlo)'], ['Option Price (Black Scholes)'], ['99% Confidence interval (Lower)'],['99% Confidence interval (Upper)']},'Location','NorthEast'); legend(H1(2),{'Option Price (Black Shcoles)'},'Location','NorthEast'); legend(H2,{'Probability'},'Location','SouthWest'); grid on; set(h,'WindowStyle','Docked'); %% h= figure; [AX,H1,H2] = plotyy(ExercisePrices,[VanillaPriceDaily BLSPrices CIDaily] , ExercisePrices,ProbabilityITMDaily); xlabel('Exercise Price'); title('Option prices for a Vanilla option using a 1 year - Daily volatility'); Axes_YLabels = get(AX,'Ylabel'); set(Axes_YLabels{1},'String','Option Price') ; set(H1(1),'LineStyle','-'); set(H1(1),'Color','r'); set(H1(1),'LineWidth',2); set(H1(2),'LineStyle','-'); set(H1(2),'Color','b'); set(H1(2),'LineWidth',2); set(H1(3),'LineStyle','--'); set(H1(3),'Color','r'); set(H1(3),'LineWidth',1); set(H1(4),'LineStyle',':'); set(H1(4),'Color','r'); set(H1(4),'LineWidth',1); set(H2,'LineStyle','-'); set(H2,'Color','g'); set(H2,'LineWidth',2); set(get(AX(2),'Ylabel'),'String','Probability of being In the Money'); legend(H1,{['Option Price (Monte Carlo)'], ['Option Price (Black Scholes)'], ['99% Confidence interval (Lower)'],['99% Confidence interval (Upper)']},'Location','NorthEast'); legend(H2,{'Probability'},'Location','SouthWest'); grid on; set(h,'WindowStyle','Docked'); end;