Treatment of Missing Market Data: Case of bond Yield Curve Estimation

Abstract

Missing observations in market data is a frequent problem in financial studies. The problem of missing data is often overlooked in practice. Missing data is mostly treated using ad hoc methods or just ignored. Our goal is to develop practical recommendations for treatment of missing observations in financial data. We illustrate the issue with an example of yield curve estimation on Russian bond market. We compare three methods of missing data imputation — last observation carried forward, Kalman filtering and EM–algorithm — with a simple strategy of ignoring missing observations. We conclude that the impact of data imputation on the quality of yield curve estimation depends on model sensitivity to the market data. For non-sensitive models, such as Nelson-Siegel yield curve model, final effect is insignificant. For more sensitive models, such as bootstrapping, missing data imputation allows to increase the quality of yield curve estimation. However, the result does not depend on the chosen data imputation method. Both simple last observation carried forward method and more advanced EM–algorithm lead to similar final results. Therefore, when estimating yield curves on the illiquid markets with missing market data, we recommend to use either simple non-sensitive to the data parametric models of yield curve or to impute missing data before using more advanced and sensitive yield curve models.

Keywords

• yield curve
• term structure of interest rates
• bond market
• nelson-siegel method
• liquidity level
• missing data
• emerging markets