The application of different term-structure models to estimate South African real spot rate curve

Abstract

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.

Forecasting the South African Real Spot-rate Curve During Covid-19 Stress

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The aim of this study is to investigate the performance of forecasting the South African real spot rate curve using different mathematical term-structure models during the Covid-19 period. This study follows previous studies by Reid (2009) and Mashoene et al, 2021) where dynamic term-structure models performed well compared to static term-structure models over normal market conditions. For high volatility, normality often breaks, which might result in a need for recalibration in the currently used methodology or a total change in the methodology.

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“…Including the hypothesis test of equal means to supplement traditional backtesting analysis proved that the recalibration process added some advantage to Nelson and Siegel (1987) and Svensson (1994) term-structure models. Based on the study by Mashoene et al (2021), it was indicated that these term-structure models were perfect for the real spot rates in South Africa; however, it was observed that they do lose capabilities in fitting real spot rates during periods of high stress. As such, it can be concluded that both Nelson andSiegel (1987) andSvensson (1994) term-structure models with the option to recalibrate model parameters over different economic environments remain perfect for estimating current and future real spot rates in South Africa.…”

“…It was proven in work done by Mashoene et al (2021) that Nelson & Siegel (1987) and Svensson (1994) models gave a better fit on the real spot rate curve in South Africa and also gave a reasonable forecast. However, it was also noted that their forecasting capabilities are marginalised during stressed economic conditions.…”

The effect of COVID-19 in estimating the South African real spot-rate curve

“…As detailed in the work done by Mashoene et al (2021), it is noted that the National Treasury's current budgeting processes and debt management risk measures are based on the econometric methodology to forecast the short (3-month) and long (10-year) term points. Other points on the yield curve are interpolated based on the output of these two benchmark points.…”

“…As such, a deflationary economic environment's effect might significantly reduce the capabilities of static term-structure models in fitting and forecasting the South African real spot-rate curve. This was proven in both Reid (2009) and Mashoene et al (2021) that term structure models with static parameters [i.e. Nelson and Siegel (1987) and Svensson (1994) models] were able to capture movements in the South African real spot-rate curve.…”