Pricing of Ratchet equity-indexed annuities under stochastic interest rates

We consider the valuation of simple and compound Ratchet equity-indexed annuities (EIAs) in the presence of stochastic interest rates. We assume that the equity index follows a geometric Brownian motion and the short rate follows the extended Vasicek model. Under a given forward measure, we obtain an explicit multivariate normal characterization for multiple log-returns on the equity index. Using such a characterization, closed-form price formulas are derived for both simple and compound Ratchet EIAs. An efficient Monte Carlo simulation scheme is also established to overcome the computational difficulties resulting from the evaluation of high-dimensional multivariate normal cumulative distribution functions (CDFs) embedded in the price formulas as well as the consideration of additional complex contract features. Finally, numerical results are provided to illustrate the computational efficiency of our simulation scheme and the effects of various model and contract parameters on pricing.