Help to solve n equations with two unknowns

Hi..

I have n equations of the put-call parity: C=P+PV*F-K*PV, where I have vectors for C, P and K, meaning that I would like to find the two unknowns PV and F by least square. Since I am not very confident with Matlab, I have not been able to find out, how I can code this. Hope that someone can help me.

Thanks

Answer 1

[Matt Fig]

It looks like you have two unknowns and one equation. How do you think there is a unique solution?

PV * F = C - P + K * PV

One solution could be:

PV = 1
F = C - P + K * PV

another solution could be

F = 1
PV = C - P + K * PV

Or, more generally:

PV = A  % A is a constant.
F = (C - P + K * PV)/A

and

F = A % A is a constant
PV = (C - P + K * PV)/A

If there is to be a unique solution, it would seem that there must be another constraining equation.

[John D'Errico]

Matt - I think you missed that C, P, K are all vectors.

[Matt Fig]

No, I got that part. What I missed is where Kristine said that PV and F were _both_ scalar.

Answer 2

[John D'Errico]

The general equation is

   C = P + PV*F - K*PV

given vectors C, P, K, and scalar unknowns PV and F. However, F appears in only one place. Suppose you rewrote this in the similar form

   (C - P)  = T - K*PV

Could you estimate the coefficients T and K? Yes, obviously,

   params = polyfit(K,C-P,1);
   PV = params(1);
   T = params(2);

This is simply a traditional form linear regression problem. Then once you have the constant coefficient T and the parameter PV, recover F as

   K = T/PV;