A Dimension-Reduction Algorithm for the Valuation of Surrender Option in EIA Contracts with Stochastic Interest Rates

• Main Authors: BO-JHIH JHUANG, 莊博智
• Other Authors: Chih-Kai Chang
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/57992034664269667303

碩士 === 逢甲大學 === 統計與精算所 === 99 === This paper proposes a fast algorithm for the fair valuation of a ratchet-type equity-indexed annuity (EIA) contract with surrender options under Vasicek stochastic interest rate models. This paper first applies the Black-Scholes method to reduce the two-dimensional tree structure to single one. Next, to overcome the path dependent problem inherent in the ratchet-type bonus option, a recursive formula is derived to implement the backward computation. Numerical Analysis indicates that surrender options are more valuable with the increase of interest rates. High interest rate volatility enhances both the bonus and surrender option values entitled to the policyholder. A numerical experiment also shows that a high proportion of risky assets may decrease the surrender option value but increase the bonus option value, implying a net increase of liability for the insurer.