%FINANCIAL MODELS               
%Homework 8, due Thursday Nov. 1st
%Use of Excel spreadsheet or MATHLAB is recommended.

%Average (Asian) option:

clear
n = 1000;
Call = zeros(n,1);
Asian = zeros(n,1);
Sbar = zeros(n,1);


for j=1:n
    S0 = 50;
    S = zeros(n,1);
    vol = .3;
    rCont = .05;
    K = 51;
    T = 1;
    dt = 1/250;
    %?S/S = ( 0.05 – 0.5 ?2 ) ?t + (? ??t ) dW(t) in other words at each
    %increment of timeS(t+ ?t) – S(t)]/S(t)  has a normal distribution with 
    %mean  = ( 0.05 – 0.5 ?2 ) ?t and Variance =  ?2 ?t 

    mean = (0.05-0.5*vol^2)*dt;
    var = vol^2*dt;
    pcntChng = normrnd(mean,var^.5);
    S(1) = S0*(1+pcntChng);

    for i=2:T*250
        pcntChng = normrnd(mean,var^.5);
        S(i) = S(i-1)*(1+pcntChng);  
    end

    Call(j) = max(S(i)-51,0)*exp(-rCont*T);
    Asian(j) = max(sum(S)/(T*250)-51,0);
    Sbar(j) = sum(S)/(T*250);
    
end

Call_Price = sum(Call)/n

Asian_Price = sum(Asian)/n

Estimated_Mean_Average_Stock_Price = sum(Sbar)/n

Estimated_Stdev_Average_Stock_Price = std(Sbar)

hist(Sbar)
title('Histogram: Average Stock Price')

%SAMPLE OUTPUT:
%pricingHW8KittisakPattamasaevi
%Call_Price =
%    5.1628
%Asian_Price =
%    2.9272
%Estimated_Mean_Average_Stock_Price =
%   49.9560
%Estimated_Stdev_Average_Stock_Price =
%   8.6839