Derivative of a conditional expectation function obtained by simulation

[Jorge Sabat]

Hi I am trying to use ADiGator to calculate the derivative of a conditional expectation obtained by Montecarlo Simulation. I have the following function:

function y = BSsimulation(x,k,N)
h=1/k(2);
dW=randn(k(2),N);
S=xones(1,N);
S(2:k(2)+1,1:N)=zeros(k(2),N);
for i=1:k(2)
S(i+1,:)=S(i,:).(1+k(3)h+sqrt(h)k(4)dW(i,:));
end
y= mean(exp(-k(3)k(5))*max(0,S(k(2)+1,:)-k(1)));
end

I am trying to run the program as follows:

x = adigatorCreateDerivInput([1 1],'x')
k = adigatorCreateAuxInput([1 5],[K,n,r,sigma,T])
adigator('BSsimulation',{x,k,N},'myderiv')

x =80

y = myderiv(x,k,N)

I see this error after (adigator(.)):
Warning: Removed 'C:\Users\jorge.sabat\Documents\MATLAB\adigator\adigatorTempDir' from the MATLAB path for this MATLAB session.
See 'doc path' for more information.

In adigator>filekeeping at 722
In adigator at 104
Warning: Error in initial test evaluation of user file on given input info
In adigator at 148
Error using randn
Size inputs must be integers.

Error in BSsimulation (line 15)
dW=randn(k(2),N);

Error in adigator (line 146)
eval(TestEvalStr);

If you have any suggestion would be incredible usefull for my research.

Best regards,

Jorge

[Jorge Sabat]

Sorry, just a little thing. For some reason the function above missed the multiplication signs (*).

function y = BSsimulation(x,k,N)
h=1/k(2);
dW=randn(k(2),N);
S=xones(1,N);
S(2:k(2)+1,1:N)=zeros(k(2),N);
for i=1:k(2)
S(i+1,:)=S(i,:).(1+k(3)h+sqrt(h)k(4)dW(i,:));
end
y= mean(exp(-k(3)k(5))*max(0,S(k(2)+1,:)-k(1)));
end

[Matthew J. Weinstein]

Jorge,

Three "~" in a row will let you display code more cleanly here.

As for your problem, you should make "dw" an auxiliary input to the function - randn() is not overloaded and will cause issue otherwise.

Additionally, it seems that it isn't treating "known" auxiliary inputs exactly correct, assuming "k" input is fixed, you can just use:

gx = adigatorCreateDerivInput([1 1],'x')
gdW = adigatorCreateAuxInput([n N])
k  = [K,n,r,sigma,T];
adigator('BSsimulation',{gx,k,N,gdW},'myderiv')

x.f = 80;
x.dx = 1;
y = myderiv(x,k,N,dW);

dydx = y.dx;

also, I think the mean function isn't coded up in adigator so you probably want to change that to sum()/length().

Matt