see J.H. Chua,"A Closed-Form Formula for Calculating Bond Duration,"Financial Analysts Journal,May/June 1984,and G.C.Babcock,"Duration as a Weighted Average of Two Factors,"Financial Analysts Journal,March/April 1985.R.Brooks and M.Livingston develop a closed-form measure for convexity in their paper,"A Closed-Form Equation for Bond Convexity,"Financial Analysts Journal,November/December 1989,pp.78-79.