U.S. Short-Term Interest Rate Path Simulation and Derivatives Pricing: An ARIMA-GARCH Approach

This study develops and evaluates a hybrid ARIMA–GARCH model with Student-t innovations to simulate the U.S. short-term interest rate path and price the interest rate caplet. As a key monetary policy tool and a fundamental benchmark in financial markets, the behaviour of short-term interest rates is characterised by volatility clustering and non-Gaussian innovations, features that constant-volatility lognormal models inadequately capture. Utilising the U.S. 3-Month Treasury Bill rate as a proxy for the short rate, this study estimates the model parameters and simulates 10,000 Monte Carlo paths over a three-month horizon. A caplet is then valued under a short-rate framework with payoffNτmax(rT-K,0), and pathwise discounting, and the resulting price is compared with a Black–76 benchmark. The empirical results indicate strong volatility persistence and heavy-tailed innovations, supporting the need for time-varying volatility and non-Gaussian errors. In pricing, the ARIMA–GARCH–t Monte Carlo approach yields a significantly higher caplet value than the Black–76 benchmark, underscoring the sensitivity of derivative values to volatility and distributional assumptions. Overall, the proposed framework provides a more realistic representation of short-rate risk and a more defensible basis for caplet valuation, with practical value for hedging and stress testing in interest-rate markets.