Pricing Double Barrier Options with Time-Varying Interest using Standard, Antithetic, and Control Variate Monte Carlo

Abstract

This study develops an integrated framework for pricing double barrier options under time-varying interest rates by combining ARIMA-based forecasting with Monte Carlo simulations. Monthly U.S. Treasury Bill rates from 2019–2025 are modeled using the ARIMA(2,2,0) process to generate dynamic risk-free rates, which are incorporated into three Monte Carlo approaches standard, antithetic variate, and control variate. Tesla Inc. stock prices are used as the underlying asset modeled through Geometric Brownian Motion. The integration of ARIMA-based dynamic rates within the Monte Carlo framework enables more realistic pathwise discounting and improves simulation convergence. The results show that the control variate method provides the most accurate and stable estimates for knock-in call options, whereas the antithetic variate technique yields superior accuracy for knock-in put, knock-out call, and knock-out put options. Overall, the combined use of ARIMA-forecasted interest rates and variance-reduction techniques enhances the precision and stability of double barrier option valuation under dynamic financial conditions.