The application of different term-structure models to estimate South African real spot rate curve
Keywords:South African inflation-indexed bonds, Parametric yield curve models, Arbitrage-free generalised Nelson Siegel model, Illiquid bond markets, Rotated Dynamic Nelson-Siegel model, Arbitrage-free Vasicek model
The purpose of this study is to investigate the suitable arbitrage-free term-structure model that might be able to fit the South African inflation-indexed spot-rate curve. The instrument has relatively less tradability in the market, which then translates into a lack of adequate data for bond valuation/pricing. Pricing deviations might give inflated/deflated projections on the value of government debt; consequently, higher estimated interest cost to be paid. A proper valuation of these instruments is mandatory as they form part of government funding/borrowing and the country’s budgeting processes in the medium term. The performance of newly developed non-linear multifactor models that follows the Nelson-Siegel (1987) framework was compared to the arbitrage-free Vasicek (1977) model and linear parametric models to assess any significant deviations in forecasting the real spot-rate curve over a short period. Models with constant parameters (i.e. linear parametric, cubic splines, Nelson-Siegel (1987) and Svensson (1994)) gave a perfect fit, they proved to marginally lose fitting capabilities during periods of higher volatility. Therefore, it could be concluded that the application of either Nelson-Siegel (1987) model or Svensson (1994) model on forecasting South African real spot-rate curve gave a perfect fit. However, for a solid conclusion to be derived, it is imperative to explore the performance of these models over a period of stressed market and economic conditions.
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