Analytically Pricing European Options Under a Two-Factor Stochastic Interest Rate Model With a Stochastic Long-Run Equilibrium Level

Abstract We construct a new stochastic interest rate model with two stochastic factors, by introducing a stochastic long-run equilibrium level into the Vasicek interest rate model which follows another Ornstein–Uhlenbeck process. With the interest rate under the Black–Scholes model being assumed to follow the newly proposed model, a closed-form representation of European option prices is successfully presented, when the analytical characteristic function of the underlying log-price under a forward measure is derived. To assess the model performance, a preliminary empirical study is conducted using S&P 500 index and its options, with the Vasicek model and an alternative two-factor Vasicek model taken as benchmarks.