Function return values help?

Hello Experts,

I have the function that gets a section (1,2,3 or 4) and gives results of calculation: function [VMean, VStd, VError, MeanDeltaV, MeanVegaV] = Q2(section)

When I enter section = 1 or any other number 1-4 I want the function to return only the section's variables results. For example section 1 calculates VMean, VStd, VError but not MeanDeltaV, MeanVegaV. Please tell me how to make it possible. The full code is:

function [VMean, VStd, VError, MeanDeltaV, MeanVegaV] = Q2(section)

% Spot price satisfies the SDE: dS = S*(rdt + sdW)
% Given parameters:
r = 0.1; % Drift
s = 0.4; % Volatility
K = 1.1; % Strike
T = 60/252; % Time to maturity
M = 50000; % Number of simulations

if section == 1
    % Sampling twice a day, there are 60 days ==> 60*2 = 120 samples.
    N = 120;
    h = T/N;
elseif section == 2 || section == 3 || section == 4
    % Sampling 10 times a day, there are 60 days ==> 60*10 = 600 samples.
    N = 600;
    h = T/N;
end

% Initial stock price S(0) = 1:
S = ones(M,N+1);
% S(t) = S(0)*exp((r - 0.5*s^2)*t + s*W(t)) = the exact price:
W = randn(M,N);
A = (r - 0.5*s^2)*h;
B = s*sqrt(h);
% According to the section (1 or 2), building the stock prices matrix:
for j = 1:N
    S(:,j+1) = S(:,j).*exp(A + B*W(:,j));
end

% Find option values - using max function, find for each simulation a
% maximum value for all the samples = max(S,[],2) ==> substract K and find
% the maximum between the vector received and 0. Multiply by discount
% factor to get the option prices vector:
V = exp(-r*T)*max(max(S,[],2) - K,0);
VMean = NaN;
VStd = NaN;
VError = NaN;
if (section == 1 || section == 2)
    VMean = mean(V);
    VStd = std(V);
    VError = VStd/sqrt(M);
    % If the number of price samples (N) increases the mean value of
    % the option price increases: twice a day VMean = 0.887,
    % 10 times a day 0.0925.
end
% Initializing epsilon values for the derivatives: Delta and Vega Greeeks
% of the option price V:
epsilon = transpose(0.001:0.0001:0.009);
% Using Monte - Carlo to calculate the mean value of Delta and Vega of
% option price V:
MeanDeltaV = NaN;
MeanVegaV = NaN;
% Initialization:
DeltaV = zeros(length(epsilon),1);
VegaV = zeros(length(epsilon),1);

if section == 3
    Splus = zeros(M,N+1);
    Sminus = zeros(M,N+1);
    % Calculating the Delta of option price V:
    for u = 1:length(epsilon)
        % For different epsilon values, calculating the Delta:
        for k = 1:N
            % Splus and Sminus are the matrices of share prices:
            Splus(:,k+1) = (S(:,k) + epsilon(u)).*exp(A + B*W(:,j));
            Sminus(:,k+1) = (S(:,k) - epsilon(u)).*exp(A + B*W(:,j));
            % Vplus and Vminus are the option prices vectors for all M
            % simulations on the k'th sample:
            Vplus = exp(-r*T)*max(max(Splus,[],2) - K,0);
            Vminus = exp(-r*T)*max(max(Sminus,[],2) - K,0);
            % Calculating the dV:
            dV = Vplus - Vminus;   
        end
        % DeltaV = dV/dS(0), (calculated dS(0) using Splus and Sminus):
        DeltaV(u) = mean(dV)/(2*epsilon(u));
    end
    % The mean value of Delta using Monte - Carlo:
    MeanDeltaV = mean(DeltaV);

elseif section == 4 
    Ssplus = zeros(M,N+1);
    Ssminus = zeros(M,N+1);
    % Calculating the Vega of option price V:
    for u = 1:length(epsilon)
        % For different epsilon values, calculating the Vega:
        for k = 1:N
            % For each sample, calculating the parts of the power of the
            % share price who satisfy GBM:
            Aplus = (r - 0.5*(s + epsilon(u))^2)*h;
            Bplus = (s + epsilon(u))*sqrt(h);
            Aminus = (r - 0.5*(s - epsilon(u))^2)*h;
            Bminus = (s - epsilon(u))*sqrt(h);
            % Splus and Sminus are the vectors of share prices for all M
            % simulations on the k'th sample:
            Ssplus(:,k+1) = S(:,k).*exp(Aplus + Bplus*W(:,j));
            Ssminus(:,k+1) = S(:,k).*exp(Aminus + Bminus*W(:,j));
            % Vplus and Vminus are the option prices vectors for all M
            % simulations on the k'th sample:
            Vplus = exp(-r*T)*max(max(Ssplus,[],2) - K,0);
            Vminus = exp(-r*T)*max(max(Ssminus,[],2) - K,0);
            % Calculating the dV:
            dV = Vplus - Vminus;   
        end
        % VegaV = dV/ds, (calculated ds using s + epsilon - (s - epsilon) 
        % for all possible epsilon values):
        VegaV(u) = mean(dV)/(2*epsilon(u));
    end
    % The mean value of Vega using Monte - Carlo:
    MeanVegaV = mean(VegaV);
end

end

Answer 1

[Walter Roberson]

You need to look at nargout . If the user has given (say) 3 output variables, then you need to assign something to at least the first 3 output variables.

[Steve]

Dear Walter, can you please figure out why this function take a lot of time to complete if section == 3? As I don't want to duplicate the same code. And thank you very much for the comment.

[Walter Roberson]

How long is "a lot of time" ?

Have you tried using the profiler ? http://www.mathworks.com/help/matlab/matlab_prog/profiling-for-improving-performance.html