exam2_2

function exam2_2
    f1 = @(x)(1/sqrt(6*pi))*exp(-(x.^2)./6);
    f2 = @(x)(1/(0.8862269*sqrt(3*pi))).*(1+((x.^2)/3)).^-2;
    alpha_vector = [0.9:0.01:.99]';
    VaR_gaussian = zeros(1,10);
    VaR_tdistr = zeros(1,10);
    counter_gaussian = 1;
    counter_tdistr = 1;
    for alpha = 0.9:0.01:.99
        z0_gaussian = 2.2;
        z0_tdistr = 1.7;
        left_gaussian = -50;
        right_gaussian = z0_gaussian +50;
        left_tdistr = -50;
        right_tdistr = z0_tdistr + 50;
        z_gaussian = (left_gaussian + right_gaussian)/2;
        z_tdistr = (left_tdistr + right_tdistr)/2;
        err_gaussian = trap(-50,z_gaussian,0.1,f1)-alpha;
        err_tdistr = trap(-50,z_tdistr,0.1,f2)-alpha;
        while abs(right_gaussian - left_gaussian) > 1e-4
            if((trap(-50,z_gaussian,0.1,f1)-alpha)) < 0;
                left_gaussian = z_gaussian;
            else
                right_gaussian = z_gaussian;
            end
            z_gaussian = (left_gaussian + right_gaussian)/2;
            err_gaussian = trap(-50,z_gaussian,0.1,f1)-alpha;
        end
        VaR_gaussian(counter_gaussian) = z_gaussian;
        counter_gaussian = counter_gaussian + 1;
        while abs(right_tdistr - left_tdistr) > 1e-4
            if((trap(-50,z_tdistr,0.1,f2)-alpha)) < 0;
                left_tdistr = z_tdistr;
            else
                right_tdistr = z_tdistr;
            end
            z_tdistr = (left_tdistr + right_tdistr)/2;
            err_tdistr = trap(-50,z_tdistr,0.1,f2)-alpha;
        end
        VaR_tdistr(counter_tdistr) = z_tdistr;
        counter_tdistr = counter_tdistr + 1;
        end %% end of for loop
        plot(alpha_vector,VaR_gaussian,'b-'); hold on;
        plot(alpha_vector,VaR_tdistr,'r-'); hold on;

end %% end of exam2_2

function res = trap(a,b,h,f)
    N = (b-a)/h;
    s = 0.5*(f(a)+f(b));
    for i = 1: N-1
        s = s + f(a+i*h);
    end %% end of for loops
    res = h*s;
end %% end of trap