www.gusucode.com > distcomp 案例源码程序 matlab代码 > distcomp/pctdemo_task_mvar.m
function [pVaR, mmVaR] = pctdemo_task_mvar(numTimes, hVal, w, t, nSim, confLevel)
%PCTDEMO_TASK_MVAR Calculate marginal value at risk and value at risk
%using Monte-Carlo simulation.
% [pVaR, mmVaR] = pctdemo_task_mvar(numTimes, hVal, w, t, nSim, ...
% confidenceLevel) returns two cellarrays with numTimes elements.
% Each pair of elements pVaR{i} and mmVaR{i} contains the value at risk of
% the portfolio and the marginal value at risk of the individual stocks in
% the portfolio, respectively.
% Inputs:
% numTimes How many times the simulations should be repeated.
% Must be a positive integer.
% hVal The stock prices
% w The stock weights in the portfolio.
% t The times at which we calculate the VaR and the mVaR.
% nSim The number of simulations to run
% confidenceLevel The confidence level at which we calculate the portfolio
% VaR and the mVaR of the individual stocks.
% Copyright 2007-2011 The MathWorks, Inc.
pVaR = cell(numTimes, 1);
mmVaR = cell(numTimes, 1);
for i = 1:numTimes
[pVaR{i}, mmVaR{i}] = iMVarAndVaR(hVal, w, t, nSim, confLevel);
end
end % End of pctdemo_task_mvar.
function [pVaR, mmVaR] = iMVarAndVaR(hVal, w, t, nSim, confidenceLevel)
%IMVARANDVAR Marginal Value at Risk calculation derived from
%Monte-Carlo simulation.
% [pVaR, mmVaR] = iMVarAndVaR(hVal, w, t, nSim, confidenceLevel)
% returns the value at risk of the portfolio, pVaR, and the marginal value at
% risk of the individual stocks in the portfolio, mmVaR.
% Inputs:
% hVal The stock prices
% w The stock weights in the portfolio.
% t The times at which we calculate the VaR and the mVaR.
% nSim The number of simulations to run
% confidenceLevel The confidence level at which we calculate the portfolio
% VaR and the mVaR of the individual stocks.
% theta represents the range of returns around pVaR used to estimate
% mVaR.
theta = 0.05;
% We let alpha store the probability of losses.
alpha = 100 - confidenceLevel;
alpha = alpha(1, 1);
theta = theta(1, 1);
nSim = nSim(1, 1);
sz = size(hVal);
% The normalized instrument weights (1 x nAsset).
w = w(:)/sum(w);
if sz(2) ~= length(w)
error('pctexample:InvalidWeights', ...
['number of weights must be the same as the number ' ...
'of columns of stock prices']);
end
%% Run Monte-Carlo simulation and calculate portfolio returns.
t = t(:)';
sim_t = 0:max(t);
ind = ismember(sim_t, [0 t]);
% We obtain a matrix of the size time x numSims x numStocks.
sim = iMVaR_seq_multimc(hVal, sim_t, nSim);
% Downsample sim results to the times we asked for.
sim = sim(ind, :, :);
sz = size(sim);
nTimes = sz(1) - 1;
o_nTimes = ones(nTimes, 1);
iVal = sim(o_nTimes, :, :);
sim = sim(2:end, :, :);
% An asset cannot be worth less than zero.
sim(sim <= 0) = NaN;
% Evaluate the instruments return.
ri = (sim - iVal)./iVal;
nSim = sz(2);
nAsset = sz(3);
% Sum ri according to weights and reshape back to original size.
ri = reshape(ri, nTimes*nSim, nAsset);
rp = ri*w;
% The portfolio returns for each sim (numTimes x numSims).
rp = reshape(rp, nTimes, nSim);
ri = reshape(ri, nTimes, nSim, nAsset);
r_i = ri;
r_p = rp;
% Marginal Value at Risk calculation
%
% Some useful variables.
sz = size(r_i);
nTimes = sz(1);
nSim = sz(2);
nAsset = sz(3);
o_nAsset = ones(nAsset, 1);
o_nSim = ones(nSim, 1);
% Evaluate alpha percentile across simulations and transpose to dim 1.
pVaR_t = prctile(r_p', alpha);
pVaR = pVaR_t';
% Finds the confidenceLevel-th percentile (just by counting) of all
% simulation runs to find the value above which the portfolio will end up at
% the confidence level confidenceLevel.
% Find the simulations where r_p is between pVaR+-theta.
mask = (r_p > pVaR(:, o_nSim) - theta) & (r_p < pVaR(:, o_nSim) + theta);
% The number of port sims that end up in the theta gap around VaR.
s_mask = sum(mask, 2);
% Evaluate E(r_i) for the simulations above.
mmVaR = reshape(sum(r_i.*mask(:, :, o_nAsset), 2), nTimes, nAsset) ...
./s_mask(:, o_nAsset);
% Now make sure that the sum of the component VaR's is equal
% to the portfolio VaR (different due to skewed tail in returns).
phi = pVaR ./ (mmVaR*w);
mmVaR = mmVaR .* phi(:, o_nAsset);
end % End of iMVarAndVaR.
function aVal = iMVaR_seq_multimc(hVal, t, nSim)
% iMVaR_SEQ_MULTIMC
% Monte-Carlo simulation of Marginal Value at Risk
% Calculate the number of assets.
nAsset = size(hVal, 2);
nTimes = length(t);
% Calculate the returns statistics.
retVal = (hVal(2:end, :) - hVal(1:end-1, :)) ./ hVal(1:end-1, :);
mRet = mean(retVal);
volat = std(retVal);
corrRnd = zeros(nAsset, nTimes, nSim);
cholMat = chol(corrcoef(retVal))';
for i = 1:nSim
corrRnd(:,:,i) = cholMat*randn(nAsset, nTimes);
end
aVal = zeros(nTimes, nSim, nAsset);
for i = 1:nAsset
mc_mRet = mRet(i);
mc_volat = volat(i);
iVal = hVal(end,i);
rndMat = squeeze(corrRnd(i,:,:));
% Calculate the time length.
tLen = length(t);
% Initialize the delta time vector.
dt = zeros(tLen, 1);
dt(1) = t(1);
dt(2:end) = diff(t);
% Initialize the drift and volatility values.
drifts = mc_mRet.*dt;
stds = mc_volat.*sqrt(dt);
% Incorporate random variations into the simulation.
if (tLen == 1)
dVal = drifts + stds*randn(1, nSim);
else
if size(rndMat, 1) == 1
rndMat = rndMat(:);
end
dVal = cumprod(((drifts(:,ones(1, nSim)) + ...
stds(:,ones(1, nSim)).*rndMat) + 1), 1);
end
% Calculate the expected asset paths.
aVal(:,:,i) = iVal*dVal;
end
end % End of iMVaR_seq_multimc.