# Antonino Zanette: Pricing Ratchet equity-indexed annuities with early surrender risk in a CIR++ model

Source: Seminar for probability, statistics, and financial mathematics

Antonino Zanette, University of Udine

**Abstract**

We consider the problem of computing simple Ratchet equity-indexed annuities (EIAs) when the asset value depends on the CIR++ stochastic interest rate. We propose two different procedures. The former is based on asymptotic expansion techniques and permits to obtain first order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without global minimum contract value. The latter permits to treat general payoffs with minimum contract value and early exercise feature using an appropriate lattice method. The Ratchet insurance contract with early surrender risk is treated as Bermudan-style contingent claim that can be exercised at each reset date. Numerical comparisons show the reliability of both proposed methods.