Hi all, a question is to calculate the instantaneous forward rate of future time t , e.g f(0,t).Data we have are the zero rates of different maturities.I tried the gradient function in matlab but the results were quite off.Any help is appreciated! Thank you.John.

interpolate the zero curve, and find a derivative?

That's the method I am using.But the value i get is quite off.I used the gradient function in matlab.

QuoteOriginally posted by: JohnGuThat's the method I am using.But the value i get is quite off.I used the gradient function in matlab.Why do you want to compute instantaneous forwards? They are a useful theoretical concept, but I have never seen a practical case where you would want to use them. You are better off using discount factors or zero-coupon rates. When you said that the value is off, you compare them to what?The instantaneous forwards are defined as the integrant to use to obtain the (market) discount factors through an integral. They are defined "almost everywhere", they are in particular ill-defined in points where the curve is non-differentiable (in particular in node point of a curve interpolated linearly). Even if your curve is correctly defined in theory, your implementation may be wrong all the time (your implementation is relying on a countable number of points, so all of them may be in the "almost" part of "almost everywhere").

QuoteOriginally posted by: mathmarcQuoteOriginally posted by: JohnGuThat's the method I am using.But the value i get is quite off.I used the gradient function in matlab.Why do you want to compute instantaneous forwards? They are a useful theoretical concept, but I have never seen a practical case where you would want to use them. You are better off using discount factors or zero-coupon rates. When you said that the value is off, you compare them to what?The instantaneous forwards are defined as the integrant to use to obtain the (market) discount factors through an integral. They are defined "almost everywhere", they are in particular ill-defined in points where the curve is non-differentiable (in particular in node point of a curve interpolated linearly). Even if your curve is correctly defined in theory, your implementation may be wrong all the time (your implementation is relying on a countable number of points, so all of them may be in the "almost" part of "almost everywhere").Check out Hull white 1996 paper. I compared my implementation with their results.The forward instantaneous forward rate is used to find the displacement of the tree node for the hull white trinomial tree.