Abstract

Journal of Actuarial Practice

Volume 11, 2004

Rapid Calculation of the Price of Guaranteed Minimum Death Benefit Ratchet Options Embedded in Annuities

Eric R. Ulm

Abstract

This paper presents a new method of obtaining quick and accurate values and deltas for discrete lookback options using Taylor series expansions. This method is applied to the case of ratchet guaranteed minimum death benefits attached to annuity contracts, and the method is extended to include annuities where a fixed fund is attached to the variable account. Finally, both the speed and the accuracy of the method are compared to Monte Carlo simulation and the exact analytic solution. The Taylor expansion method is shown to be faster and, in most cases, more accurate than the alternative methods.

Key words and phrases: Taylor series, multivariate normal, lookback option, Monte Carlo simulation, risk, lognormal distribution, Black-Scholes formula, geometric Brownian motion

Corresponding Author:

Eric R. Ulm

Department of Statistics and Actuarial Science

University of Central Florida

Orlando FL 32816

E-mail: eulm@mail.ucf.edu