The estimation of nominal and real yield curves from government bonds in Israel
We develop and test a mathematical method of deriving zero yield curve from market prices of government bonds. The method is based on a forward curve approximated by a linear (or piecewise constant) spline and should be applicable even for markets with low liquidity. The best fitting curve is derived by minimizing the penalty function. The penalty is defined as a sum of squared price discrepancies (theoretical curve based price minus market closing price) weighted by trade volume and an additional penalty for non-smoothness of the yield curve. The algorithm is applied to both nominal and CPI linked bonds traded in Israel (some segments of these markets have low liquidity). The resulting two yield curves can be used for derivation of market expected inflation rate. The main problems are low liquidity of some bonds and imperfect linkage to inflation in the CPI linked market. Use of forward curves as the state space for the minimization problem leads to a stable solution that fits the data very well and can be used for calculating forward rates.