Three essays on interest rate modeling

Abstract

This dissertation presents three essays that explore and propose methodological modifications to adapt yield curve modeling to the context of emerging markets using data from Indian bond markets. While no arbitrage affine term structure models are theoretically attractive for modeling the yield curve, they suffer from poor empirical performance. The re- cently proposed arbitrage-free Nelson-Siegel (AFNS) model retains the empirical tractability and fit of the Dynamic-Nelson-Siegel model while being arbitrage free. Adapting the AFNS model, however, directly to India is difficult because of the concentration of liquidity in bonds at few maturities. In the first essay, we explicitly incorporate liquidity within the AFNS framework to estimate the yield curve for India. We find strong empirical evidence in support of the liquidity adjusted specifications, with liquidity-augmented models providing better in-sample fit, and the likelihood ratio tests rejecting the restrictions assumed in the benchmark model. Economic theory suggests a bidirectional relationship between yield and macroe- conomic factors such as output and in ation. Modern macro-finance affine term structure (MTSM) models incorporate (`span') macroeconomic factors by describ- ing term structure as a linear combination of macroeconomic and yield curve fac- tors. This suggests macroeconomic factors could be expressed inversely as a linear combination of the yields implying that macroeconomic factors should not contain any additional information not captured by the current yield curve. The regression evidence from the literature suggests otherwise, and this contradiction has been referred to as the `spanning puzzle'. In the second essay, we explore the spanning puzzle using Indian data within our AFNS specification. We provide empirical and simulation evidence in favor of an alternative unspanned MTSM specification. The unspanned specification produces risk premium estimates that have a stronger association with excess returns of the bonds. In India, commercial banks can borrow from (lend to) the RBI at repo (reverse repo) rate. This suggests that the overnight call rate should remain in the corri- dor bound by these two rates. There is evidence, however, that call rates often breach the corridor. Additionally, because of the marginal standing facility, there is a possibility of multiple corridors. The third essay takes a closer look at this phenomenon and tries to model the corridor as a Jacobi di usion process which has been successfully used to model exchange rate corridors in the international nance literature. In particular, we model the dynamics of Indian overnight rate as a soft corridor by adapting the Jacobi diffusion process in a regime-switching state-space framework.