Analyses of retirement benefits with options

a r t i c l e i n f o JEL classifications: C15 G13 Keywords: Contingent claim Early exercise Retirement benefit Simulation Stochastic interest rate This study applies the contingent claim approach to evaluate retirement benefits with the options of choosing the maximum defined benefit and defined contribution pension plans. A least-squares Monte Carlo simulation values complex retirement benefits that feature the properties of multiple variables, early exercise, stochastic interest rates, and several embedded options. Furthermore, this study examines the impacts of different forms of early decrements of the value of retirement benefits with options. The world is facing increasingly salient issues of aging as the population of people aged older than 65 years continues to grow. 1 In this context, retirement programs are becoming more important, because people must rely on the pension benefits to support themselves for the rest of their lives, after they retire from work. Retirement benefits are usually paid according to two approaches: defined benefits (DBs) or defined contributions (DCs). In Australia, Italy, and some states in the United States, retirement benefit programs are designed to offer the maximum of two alternative benefit values (DB and DC), equivalent to a better-of option (Smithson, 1998). Employees have the option to choose from the maximum of the two underlying assets when they retire (Johnson, 1987; Stulz, 1982). When an employee is allowed to retire early, American options also are embedded in the retirement benefit program. Option pricing methodologies first were used in the valuation of investment guarantees by Boyle and Schwartz (1977). Wilkie (1989) discusses option pricing techniques for pension benefit payments in the United Kingdom. Shimko (1989, 1992) develops a contingent claim approach to value insurance claims. Sherris (1995) extends the contingent claim approach to the case of retirement benefits. Ever since Black and Scholes (1973) conducted a renowned European option closed-form solution, the development and application of option evaluations have attracted concern from academia and practice. There also has been plenty of research and actual costs devoted to attempting to find a reasonable price of a derivative by the most efficient and precise method, to benefit both the exchange proceeding that of financial merchandises and analyzing strategies to manage risk. Except for the simplest European option, there are many other exotic options traded in the market. The Black and Scholes (1973) formula can only evaluate a simple European option, whereas several numerical methods exist …