How a solution depends on a variable

I have a function UE=Explicit(S,sigma,r,T,M,K,gamma,N); and I want to plot how the solution depends on gamma where 0.5<=gamma<=1. All of the other parameters are constants. How can I do this?

Answer 1

[Star Strider]

One approach:

gammav = linspace(0.5, 1, 10);
for k = 1:numel(gammav)
    UE{k} = Explicit(S,sigma,r,T,M,K,gammav(k),N);
end

I have no idea what ‘Explicit’ is or what it produces, so it could be possible to vectorise this (instead of using the loop) depending on how you wrote the function. I am also saving each iteration to a cell array for that reason.

EDIT —

Plotting it depends on what ‘UE’ is. If ‘Explicit’ produces a scalar, this works:

figure
plot(gammav, [UE{:}])
grid

If it produces vectors or matrices, it will be necessary to use other approaches.

[Amanda Hoxell]

The function looks like this, so I guess I have to make a matrice.

function [U,A] = ExplicitJ(S,sigma,r,T,M,K,gamma,N)
smax=4*K;
deltas=smax/M;
deltat=T/N;
V=zeros(M-1,N);
V(:,N)=max(deltas*[1:M-1]-K,0);

jv=ones(1,M-1)*(1-r*deltat)-deltat/deltas^2*sigma^2.*(deltas*[1:M-1]).^(2*gamma);
jm=1/2*deltat/deltas^2*sigma^2*([1:M-1]*deltas).^(2*gamma)-r*deltat/deltas.*(deltas*[1:M-1])/2;
jp=1/2*deltat/deltas^2*sigma^2*(deltas*[1:M-1]).^(2*gamma)+deltat/deltas*r.*(deltas*[1:M-1])/2;
    
A1=diag(jv);
A2=diag(jm(1,2:M-1),-1);
A3=diag(jp(1,1:M-2),+1);
A=A1+A2+A3;

b=zeros(M-1,1);
for n=N:-1:2
b(M-1)=jp(1,M-1)*(smax-K*exp(-r*(T-deltat*n)));
V(:,n-1)=A*V(:,n)+b;
end
V=V(:,1);

end

[Star Strider]

‘so I guess I have to make a matrice’

Yes, most likely.

What are the other arguments to ‘Explicit’?

What output do you want to save (here ‘UE’ will only be ‘U’, since MATLAB will not return the second output unless you specifically ask for it)?

What do you want in terms of a plot? If ‘UE’ is a matrix, you will likely get stacked mesh or surf plots.

[Amanda Hoxell]

The main program is:

S=14;
sigma=0.25;
r=0.1;
T=0.5;
gamma=1;
K=15;
N=10000;
M=200;
deltas=4*K/M;

[UE,A]=Explicit(S,sigma,r,T,M,K,gamma,N)
plot(UE, 'r')

where plot(UE, 'r') plots the solution. I want the same plot but when varying gamma.

[Star Strider]

I just noticed that ‘U’ is not actually assigned anywhere in ‘ExplicitJ’. Should ‘V’ be ‘U’?

Also, since the plot calls ‘Explicit’, did you post the correct function?

[Amanda Hoxell]

Yes you are right, should be . Sorry for the confusion.

Yes, is the correct function. The plot looks like this

[Star Strider]

This works, however, ‘UE’ is uniformly 0 for all values of ‘gammav’.

gammav = linspace(0.5, 1, 10);
for k = 1:numel(gammav)
    [UE(:,k),A]=Explicit(S,sigma,r,T,M,K,gammav(k),N);
end

figure
plot(gammav, UE, '.r')

This code runs without errors.

[Amanda Hoxell]

Thank you!!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

Answer 2

[John D'Errico]

Using gamma as the name of a variable is a bad idea. Regardless,...

Where is the problem? Just substitute a range of values for gamma. Save the solution for each gamma. Then plot, with gamma on the x axis, and your solution on the y axis. WTP?

You can even use tools like fimplicit, which will do the hard work for you. For example,

f = @(gam,y) gam.^2 - y.^2 - 2*gam.*y.^3 + gam.*y + 1;
fimplicit(f)
xlabel 'gam'
ylabel 'y'
grid on

[Amanda Hoxell]

The problem is that I am new to Matlab. I tried the following but it did not work..

gamma_all = 0.5:0.1:1;
y = zeros(1,length(gamma_all));
for i = 1:length(gamma_all)
   gamma = gamma_all(i);
   y(i) = Explicit(S,sigma,r,T,M,K,gamma,N);
end
plot(gamma_all,y)