Stochastic Interest Rate Model and Its Applications: A Case for India

Abstract

In this dissertation the main focus area was to use one factor interest rate models in India to obtain the descriptive nature and risk profile of money markets in India. For the period of 2012-2020 we found that CIR (1985) model fits and describes the interest rate path for India much better than Vasicek model. Both of these models were calibrated to make each of their parameters pseudo time varying and maximum likelihood estimation (MLE) was used to find optimal model parameters. We used daily weighted average of call money market rates as input data for calibration. Under the assumptions of constant relative risk aversion (CRRA) and decreasing absolute risk aversion (DARA) of CIR model, we used the closed form solutions to obtain bond prices and yields on 3 month T-bill. Average 10 year yield curve for the period 2012-20 was also forecasted and it was observed that Indian yield curve has a hump shape, with higher yields on longer dated bonds. We find that there exists higher term premium for longer dated bonds, for example, term premium on 10 year G-Sec has increased at a faster rate, relative to shorter maturity bonds, with the trend getting stronger since 2016 with an exception in year 2019. For risk profiling, the paper uses Expected-shortfall (ES) and Value-at-Risk (VaR) on 3 month bonds. It was found that expected shortfall normalized for yield stood at 25% on average for the period 2012-20. This means that traders in the money market need to constantly look out for price risk, to hedge for this, we propose that the trader uses call options on bonds. We find that fair prices of call options for CIR distribution function under Blacks-Scholes model will be an expensive hedging strategy. But that said, the Greeks for these call options (Rho, Delta and Gamma) show that the call option will not be sensitive to interest rate and bond price changes and hence will be a stable hedging strategy. The paper concludes that this is because of very high speed of mean reversion and low volatility in interest rate paths. This result can be associated with credibility, transparency and clear policy decisions made by the Indian central bank and newly formed Monetary Policy Committee (MPC). It was also seen that MPC has been successful to lower volatility by 9 times since its inception while maintaining the same high levels of speed of reversion in interest rates.