Matlab code from literature gives errors

have this code from a book I recently looked at, I want to implement the code but I get loads of errors , can someone help me localize the errors or possibly make a runnable example?

function [P,b]=AmericanPrice(r,delta,sigma,K,nx,nt, Xhat,That)
%Usage:P=AmericanPrice(r,delta,sigma,K,nx,nt,Xhat,That) 
%Example:P=AmericanPrice(0.08,0.12,.2,100,50,10,300,3)
dx=Xhat/nx; 
dt=That/nt; 
for i=1:nx-1 
    A(i,i:i+2)=[((r-delta)*dt*i-sigmaˆ2*dt*iˆ2)/2... 
        1+r*dt+sigmaˆ2*dt*iˆ2 
        (-(r-delta)*dt*i-sigmaˆ2*dt*iˆ2)/2]; 
end
P(:,1)=max(K-[0:dx:Xhat],0);

if(delta==0) 
    b(1)=K; 
else
    b(1)=min(K,K*r/delta);
end

for j=2:nt+1 
    bn=0; run=1; 
    while(run) 
        An=[A(1+bn:end,1+bn:end)]; 
        An(end+1,end-1:end)=[-1 1]; 
        An(end+1,1)=1; 
        Cn=[P(bn+2:nx,j-1)’ 0 K-bn*dx]’; 
        Pn=inv(An)*Cn; 
        if(Pn(2)$<$K-((bn+1)*dx)) 
            bn=find(sign(diff(Pn)/dx+1)-1,1,{’last’})+bn; 
        else
            b(j)=bn*dx; run=0; 
        end
    end
    P(:,j)=[K-[0:bn-1]*dx Pn’]; 
end

what i have done so far: i changed the sigmaˆ2 to sigma*sigma, same thing with i. Then i replaced the ’ with '. I did not know what to d o with "..." The error i get is

Undefined function 'find' for input arguments of type 'cell'.

Error in FDM (line 28)
            bn=find(sign(diff(Pn)/dx+1)-1,1,{'last'})+bn;

Answer 1

[Walter Roberson]

Change

              bn=find(sign(diff(Pn)/dx+1)-1,1,{’last’})+bn;

to

              bn=find(sign(diff(Pn)/dx+1)-1,1,’last’)+bn;

[K]

Thank you that did work. If i now want to localize the values created by vector b , how would i do that? All i get now is "ans 51x11 double" ?

[Walter Roberson]

I do not know what you mean by "localize" ?

By the way,

          if(Pn(2)$<$K-((bn+1)*dx))

is not valid syntax. $ is not used in MATLAB except in comments and strings.

[K]

From the book it says " The function returns a matrix P that contains the price of the option at each grid point and a vector b that contains the exercise boundary values for each discrete time point" I want to find vector b values not the matrix P

[Walter Roberson]

Currently you are calling something like

   AmericanPrice(with some list of parameters)

change that to

   [P, b] = AmericanPrice(with some list of parameters);

and then look at b.

[K]

I do run it , first row

function [P,b]=AmericanPrice(r,delta,sigma,K,nx,nt, Xhat,That)

[Walter Roberson]

That is a function declaration, not a function execution.

[K]

I don't understand can you be more specific?

How should I write the function execution? where should I write it?

[Walter Roberson]

At the command line, you should write

[P, b] = AmericanPrice(0.08,0.12,.2,100,50,10,300,3);

and then look at your variable b

[K]

so I should run something like this ?

[P, b] = AmericanPrice(0.08,0.12,.2,100,50,10,300,3);
%Usage:P=AmericanPrice(r,delta,sigma,K,nx,nt,Xhat,That) 
%P=AmericanPrice(0.08,0.12,.2,100,50,10,300,3);
dx=Xhat/nx; 
dt=That/nt; 
for i=1:nx-1 
    A(i,i:i+2)=[((r-delta)*dt*i-sigma*sigma*dt*i*i)/2
        1+r*dt+sigma*sigma*dt*i*i
        (-(r-delta)*dt*i-sigma*sigma*dt*i*i)/2]; 
end
P(:,1)=max(K-[0:dx:Xhat],0);

if(delta==0) 
    b(1)=K; 
else
    b(1)=min(K,K*r/delta);
end

for j=2:nt+1 
    bn=0; run=1; 
    while(run) 
        An=[A(1+bn:end,1+bn:end)]; 
        An(end+1,end-1:end)=[-1 1]; 
        An(end+1,1)=1; 
        Cn=[P(bn+2:nx,j-1)' 0 K-bn*dx]'; 
        Pn=inv(An)*Cn; 
        if(Pn(2)<K-((bn+1)*dx)) 
            bn=find(sign(diff(Pn)/dx+1)-1,1,'last')+bn; 
        else
            b(j)=bn*dx; run=0; 
        end
    end
    P(:,j)=[K-[0:bn-1]*dx Pn']; 
end

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/333266-how-to-fix-an-infinite-recursion#answer_261451 for instructions.