index exceeds the number of array

Hi. I need help with my code. If you could provide help/suggestions, it would be greatly appreciated. Thank you

% generate the tree

K=100; r=0.05; delta=0.1; sigma=0.2; n=100; b=2; dt=1/3;

S=[70;80;90;100;110;120;130];

S1=S*ones(1,1); % stock price at time t = 0

S2=zeros(b,1); % stock price at time t = 1/3

S3=zeros(b*b,1); % stock price at time t = 2/3

S4=zeros(b*b*b,1); % stock price at time t = 1

stderrl=[0.004;0.016;0.039;0.076;0.156;0.139;0.124];

stderrh=[0.004;0.016;0.040;0.078;0.113;0.069;0.049];

truevalue=[0.121;0.670;2.303;5.731;11.341;20;30];

o=length(S);

for k=1:o

for i=1:b

z=normrnd(0,1);

S2(i)=S1(k)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);

end

for i=1:b

for j=1:b

z=normrnd(0,1);

S3((i-1)*b+j)=S2(i)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);

end

end

for i=1:b*b

for j=1:b

z=normrnd(0,1);

S4((i-1)*b+j)=S3(i)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);

end

end

stockprice=NaN*ones(size(S4,1),4);

stockprice(1:size(S1,1),1)=S1;

stockprice(1:size(S2,1),2)=S2;

stockprice(1:size(S3,1),3)=S3;

stockprice(1:size(S4,1),4)=S4;

NaN=0;

% work backward to price the option at each node for the high estimator

theta4=max(S4-K,0);

for i=1:length(S3)

theta3(i)=max(S3(i)-K,((1/b)*exp(-r*(dt))*(sum(theta4((i-1)*b+1:i*b)))));

end

for i=1:length(S2)

theta2(i)=max(S2(i)-K,((1/b)*exp(-r*(dt))*(sum(theta3((i-1)*b+1:i*b)))));

end

for i=1:length(S1)

theta1(i)=max(S1(k)-K, ((1/b)*exp(-r*(dt))*(sum(theta2((i-1)*b+1:i*b)))));

end

% high estimator

bigtheta=NaN*ones(size(theta4,1),4);

NaN=0;

bigtheta(1:size(theta1,1),1)=theta1;

bigtheta(1:size(theta2',1),2)=theta2;

bigtheta(1:size(theta3',1),3)=theta3;

bigtheta(1:size(theta4,1),4)=theta4;

highest(k)=theta1;

% work backward to price the option at each node for the low estimator

for i=1:length(S3)

if max(S3(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(theta4((i-1)*b+1:i*b))));

teta3(i)=max(S3(i)-K);

else

teta3(i)=exp(-r*dt)*(sum(theta4((i-1)*b+1:i*b)));

end

teta3(i)=(1/b)*(sum(theta4((i-1)*b+1:i*b)));

end

for i=1:length(S2)

if max(S2(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(teta3((i-1)*b+1:i*b))));

teta2(i)=max(S2(i)-K);

else

teta2(i)=exp(-r*dt)*(sum(teta3((i-1)*b+1:i*b)));

end

teta2(i)=(1/b)*(sum(teta3((i-1)*b+1:i*b)));

end

for i=1:length(S1)

if max(S1(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(teta2((i-1)*b+1:i*b))));

teta1(i)=max(S1(i)-K);

else

teta1(i)=exp(-r*dt)*(sum(teta2((i-1)*b+1:i*b)));

end

teta1(i)=(1/b)*(sum(teta2((i-1)*b+1:i*b)));

end

end

% low estimator

smalltheta=NaN*ones(size(theta4,1),4);

NaN=0;

smalltheta(1:size(teta1,1),1)=teta1;

smalltheta(1:size(teta2',1),2)=teta2;

smalltheta(1:size(teta3',1),3)=teta3;

smalltheta(1:size(theta4,1),4)=theta4;

lowest(k)=teta1

% 90% confidence interval

z=1.645;

cil=max((S(i)-K),lowest(k)-z*0.124);

cih=highest(k)+z*0.124;

% point estimate

pe=0.5*max((S(i)-K),lowest(k))+0.5*highest(k);

% relative error

% construct the table

T=table(S1,highest,lowest,cil,cih,pe,stderrl,stderrh)

[Tommy]

theta1(i)=max(S1(k)-K, ((1/b)*exp(-r*(dt))*(sum(theta2((i-1)*b+1:i*b)))));

In this line, how do you know the indices given by

(i-1)*b+1:i*b

will not exceed the dimensions of theta2?

[AB]

that's the line that's giving me an error.

so when I take S1 to be 110 for instance, the code works. but since the stock prices have different values 70,80,90,100,110,120,130, I was trying to use a for loop so that it can give the values for highest, and lowest. I don't know if that makes sense. Let me add the original code so u can see what I mean.

% generate the tree

K=100; r=0.05; delta=0.1; sigma=0.2; n=100; b=2; dt=1/3;

S=[70;80;90;100;110;120;130];

S1=110*ones(1,1); % stock price at time t = 0

S2=zeros(b,1); % stock price at time t = 1/3

S3=zeros(b*b,1); % stock price at time t = 2/3

S4=zeros(b*b*b,1); % stock price at time t = 1

stderrl=[0.004;0.016;0.039;0.076;0.156;0.139;0.124];

stderrh=[0.004;0.016;0.040;0.078;0.113;0.069;0.049];

for i=1:b

z=normrnd(0,1);

S2(i)=S1*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);

end

for i=1:b

for j=1:b

z=normrnd(0,1);

S3((i-1)*b+j)=S2(i)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);

end

end

for i=1:b*b

for j=1:b

z=normrnd(0,1);

S4((i-1)*b+j)=S3(i)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);

end

end

stockprice=NaN*ones(size(S4,1),4);

stockprice(1:size(S1,1),1)=S1;

stockprice(1:size(S2,1),2)=S2;

stockprice(1:size(S3,1),3)=S3;

stockprice(1:size(S4,1),4)=S4;

NaN=0;

% work backward to price the option at each node for the high estimator

theta4=max(S4-K,0);

for i=1:length(S3)

theta3(i)=max(S3(i)-K,((1/b)*exp(-r*(dt))*(sum(theta4((i-1)*b+1:i*b)))));

end

for i=1:length(S2)

theta2(i)=max(S2(i)-K,((1/b)*exp(-r*(dt))*(sum(theta3((i-1)*b+1:i*b)))));

end

for i=1:length(S1)

theta1(i)=max(S1-K, ((1/b)*exp(-r*(dt))*(sum(theta2((i-1)*b+1:i*b)))));

end

% high estimator

bigtheta=NaN*ones(size(theta4,1),4);

NaN=0;

bigtheta(1:size(theta1,1),1)=theta1;

bigtheta(1:size(theta2',1),2)=theta2;

bigtheta(1:size(theta3',1),3)=theta3;

bigtheta(1:size(theta4,1),4)=theta4;

highest=theta1;

% work backward to price the option at each node for the low estimator

for i=1:length(S3)

if max(S3(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(theta4((i-1)*b+1:i*b))));

teta3(i)=max(S3(i)-K);

else

teta3(i)=exp(-r*dt)*(sum(theta4((i-1)*b+1:i*b)));

end

teta3(i)=(1/b)*(sum(theta4((i-1)*b+1:i*b)));

end

for i=1:length(S2)

if max(S2(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(teta3((i-1)*b+1:i*b))));

teta2(i)=max(S2(i)-K);

else

teta2(i)=exp(-r*dt)*(sum(teta3((i-1)*b+1:i*b)));

end

teta2(i)=(1/b)*(sum(teta3((i-1)*b+1:i*b)));

end

for i=1:length(S1)

if max(S1(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(teta2((i-1)*b+1:i*b))));

teta1(i)=max(S1(i)-K);

else

teta1(i)=exp(-r*dt)*(sum(teta2((i-1)*b+1:i*b)));

end

teta1(i)=(1/b)*(sum(teta2((i-1)*b+1:i*b)));

end

% low estimator

smalltheta=NaN*ones(size(theta4,1),4);

NaN=0;

smalltheta(1:size(teta1,1),1)=teta1;

smalltheta(1:size(teta2',1),2)=teta2;

smalltheta(1:size(teta3',1),3)=teta3;

smalltheta(1:size(theta4,1),4)=theta4;

lowest=teta1;

% 90% confidence interval

z=1.645;

cil=max((S1(i)-K),lowest-z*0.124);

cih=highest+z*0.124;

% point estimate

pe=0.5*max((S1(i)-K),lowest)+0.5*highest;

% relative error

% construct the table

T=table(S1,highest,lowest,cil,cih,pe)

[Tommy]

In these lines:

for i=1:length(S3)
    if max(S3(i)-K) >= (1/(b-1))*(exp(-r*dt)*(sum(theta4((i-1)*b+1:i*b))));
        teta3(i)=max(S3(i)-K);
    else 
        teta3(i)=exp(-r*dt)*(sum(theta4((i-1)*b+1:i*b)));
    end 
    teta3(i)=(1/b)*(sum(theta4((i-1)*b+1:i*b)));
end

You set teta3(i) within the if-else statement and then immediately overwrite that value. Is that intentional?

Answer 1

[Tommy]

Ah, ok. You flip between treating S1 as a vector containing the different stock prices (which it is in your new code) and as a scalar containing just the stock price at time t = 0 (which it is in your original code).

for i=1:length(S1) % <-- first use
    theta1(i)=max(S1(k)-K, ((1/b)*exp(-r*(dt))*(sum(theta2((i-1)*b+1:i*b)))));
                 % ^ second use
end

For example, in this loop containing the faulty line, you first treat S1 as a scalar. In your original code, length(S1) would be 1, and so the loop would run only once and you wouldn't get an error. However, here S1 contains all of the stock prices from S, so length(S1) is not 1. You acknowledge this in your second use of S1, by indexing with k to pull out the single stock price of interest, but you need to be consistent and use length(S1(k)) in your first use as well.

I tried to take this into consideration below. I also moved the bits where you calculate lowest, cil, cih, and pe to be within the loop, assuming you want to calculate those values for each initial stock price.

% generate the tree
K=100; r=0.05; delta=0.1; sigma=0.2; n=100; b=2; dt=1/3;
S=[70;80;90;100;110;120;130];
S2=zeros(b,1); % stock price at time t = 1/3
S3=zeros(b*b,1); % stock price at time t = 2/3
S4=zeros(b*b*b,1); % stock price at time t = 1
stderrl=[0.004;0.016;0.039;0.076;0.156;0.139;0.124];
stderrh=[0.004;0.016;0.040;0.078;0.113;0.069;0.049];
truevalue=[0.121;0.670;2.303;5.731;11.341;20;30];

N=numel(S);
highest=zeros(N,1);
lowest=zeros(N,1);
cil=zeros(N,1);
cih=zeros(N,1);
pe=zeros(N,1);

for k=1:N
    S1=S(k); % stock price at time t = 0
    for i=1:b
        z=normrnd(0,1);
        S2(i)=S1*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);
    end
    
    for i=1:b
        for j=1:b
            z=normrnd(0,1);
            S3((i-1)*b+j)=S2(i)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);
        end
    end
    
    for i=1:b*b
        for j=1:b
            z=normrnd(0,1);
            S4((i-1)*b+j)=S3(i)*exp((r-delta-(sigma)^2)*(dt)+sigma*sqrt(dt)*z);
        end
    end
    
    stockprice=NaN*ones(size(S4,1),4);
    stockprice(1:size(S1,1),1)=S1;
    stockprice(1:size(S2,1),2)=S2;
    stockprice(1:size(S3,1),3)=S3;
    stockprice(1:size(S4,1),4)=S4;
    NaN=0;
    
    % work backward to price the option at each node for the high estimator
    theta4=max(S4-K,0);
    for i=1:length(S3)
        theta3(i)=max(S3(i)-K,((1/b)*exp(-r*(dt))*(sum(theta4((i-1)*b+1:i*b)))));
    end
    for i=1:length(S2)
        theta2(i)=max(S2(i)-K,((1/b)*exp(-r*(dt))*(sum(theta3((i-1)*b+1:i*b)))));
    end
    for i=1:length(S1)
        theta1(i)=max(S1-K, ((1/b)*exp(-r*(dt))*(sum(theta2((i-1)*b+1:i*b)))));
    end
    
    % high estimator
    bigtheta=NaN*ones(size(theta4,1),4);
    NaN=0;
    bigtheta(1:size(theta1,1),1)=theta1;
    bigtheta(1:size(theta2',1),2)=theta2;
    bigtheta(1:size(theta3',1),3)=theta3;
    bigtheta(1:size(theta4,1),4)=theta4;
    highest(k)=theta1;
    
    % work backward to price the option at each node for the low estimator
    for i=1:length(S3)
        teta3(i)=(1/b)*(sum(theta4((i-1)*b+1:i*b)));
    end
    
    for i=1:length(S2)
        teta2(i)=(1/b)*(sum(teta3((i-1)*b+1:i*b)));
    end
    
    for i=1:length(S1)
        teta1(i)=(1/b)*(sum(teta2((i-1)*b+1:i*b)));
    end
    
    % low estimator
    smalltheta=NaN*ones(size(theta4,1),4);
    NaN=0;
    smalltheta(1:size(teta1,1),1)=teta1;
    smalltheta(1:size(teta2',1),2)=teta2;
    smalltheta(1:size(teta3',1),3)=teta3;
    smalltheta(1:size(theta4,1),4)=theta4;
    lowest(k)=teta1;
    
    % 90% confidence interval
    z=1.645;
    cil(k)=max((S1-K),lowest(k)-z*0.124);
    cih(k)=highest(k)+z*0.124;
    
    % point estimate
    pe(k)=0.5*max((S1-K),lowest(k))+0.5*highest(k);
end

% relative error

% construct the table
T=table(S,highest,lowest,cil,cih,pe,stderrl,stderrh)

This does run without error, and the table it creates has a row for each initial stock price, but you will want to verify that I didn't accidentally mess up some of the logic.

As a side note, wherever you have

NaN=0;

I am not sure this is doing what you might think it is doing. Are you hoping to set NaN values within your matrices to 0? Because this instead creates a variable named NaN with a value of 0, so that in the loop's next iteration, lines such as

stockprice=NaN*ones(size(S4,1),4);

are equivalent to

stockprice=0*ones(size(S4,1),4);

or essentially

stockprice=zeros(size(S4,1),4);

Same result, eventually, but misleading. To set all NaN values within stockprice to 0, you could use

stockprice(isnan(stockprice)) = 0;

However, I'll admit that I'm not 100% sure what you're trying to do there.

[AB]

Thank you so much for all the help..

it was Very helpful, thanks.

[Tommy]

Happy to help!