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Unformatted text preview: Estimating the benchmark Yield Curve A new approach using Stochastic Frontier Functions Gangadhar Darbha, * Post Doctoral Fellow, Indian School of Business, Hyderabad, India. email: GangadharDarbha @ exchange.isb.edu June 2003 Abstract Estimating a risk free Term Structure of Interest Rates or Zero Coupon Yield Curve from the observed bond prices would involve controlling for the effects of security specific noninterest rate factors that affect bond prices. In this pa per we propose a new framework to estimate benchmark default and liquidity risk free yield curve using the stochastic frontier functions. The methodology explicitly controls for the effects of security specific factors such as age, issue size, coupon and residual maturity on bond prices in estimating the yield curve. Using the daily secondary market data from NSEWDM for the period Jan 1997 to July 2002, we find that the new methodology not only identifies frontier yield curve that is significantly different from the standard zero coupon yield curve and gives reasonable estimates of liquidity premia, but also performs better than the standard yield curve models in terms of predicting bond prices. * Useful contributions from Vardhana Pawaskar and Sudipta Dutta Roy and comments from Subrata Sarkar, Ajay Shah, Chitra Ramakrishna, Ravi Narain, Ganesh Kumar and Ashok Nag are greatfully acknowledged. Thanks are also due to ICICI Research Center and NSE for providing the funding, data and computational infrastructure. 1 Estimating the benchmark Yield Curve A new approach using Stochastic Frontier Functions Gangadhar Darbha 1 Introduction The zero coupon yield curve (ZCYC) or the term structure of interest rates  that characterize the relationship between interest rates in the economy and the term to maturity  forms the basis for the valuation of all fixed income instruments. Modelled as a series of cashflows due at different points of time in the future, the underlying price of such instruments can be calculated as the sum of the present values of the cashflows, each discounted by the rate for the associated term to maturity. When the rates used in discounting are the risk free rates of interest, the resulting value of the fixed income instrument would be its fundamental value devoid of either default or liquidity risks. Risk free rate is the rate of return that is free of default and liquidity risk. It must reflect three components: a rental rate indicating the real return for lending out funds over a investment period thereby forgoing the consumption for which the funds otherwise could be used, inflation, and term risk indicating the risk that the principalâ€™s market value will increase or decrease during the term to maturity. The riskfree interest rate schedule or the benchmark yield curve, therefore, represents the expectations of agents, on an average, about the movements of the above mentioned factors in the economy. Knowledge of the default risk free term structure of interest rates enables one to compute the...
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 Spring '10
 SHILLER
 Normal Distribution, Interest Rates, Yield Curve

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