CONVEXIT Function

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CONVEXIT Function

calculates convexity of a non contingent "cash flow"

CONVEXIT( times, flows, ytm)

The inputs to the CONVEXIT function areas follows:

times: is an n-dimensional column vector of times.
flows: is an n-dimensional column vector of cash flows.
rates: is the per-period yield-to-maturity of the cashflow stream.

The CONVEXIT function returns a scalar that is the convexity of a non contingent cash flow. Convexity is essentially a measure of how duration, the sensitivity of price to yield, changes as interest rates change:

C = [1/P] [(d²P)/(dy²)]

With cash flows that are not yield sensitive, and the assumption of parallel shifts to a flat term-structure, convexity is given by

$C = \frac{1}{P (1+y)^2} \sum_{k=1}^K t_k (t_k+1) \frac{c(k)}{(1+y)^{t_k}}$

where P is the present value, y is the effective per period yield-to-maturity, and K is the number of cash flows, the k^th cash flow being c(k) t_k periods from the present.

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