notes/options_explanation.md

title: Embedded options in Cash Balance plan author: Nathan Esau date: June 21, 2015

Executive summary

Three embedded guarantees in cash balance plans:

  1. "money-back guarantee": return of participant pay credits at benefit commencement
  2. "enhanced money-back guarantee": return of participant pay credits at benefit commencement with a fixed return which might be offered to participant to protect against inflation.
  3. "cash-balance guarantee": provides a minimnum interest rate credit to be earned each year. For example, an interest credit rating that provides a yield on 30 year treasury bond but not less than some maximum, say 4.0% per annum.

(1) and (2) are valued using closed form adaptation of Black-Scholes formula, and (3) is valued using Monte-Carlo simulation of risk-neutral rate (Hull White)

Introduction

2011 SOA paper accomplished three objectives:

  1. Defined embedded options using two categories:
    • Behavior driven (e.g. retirement, termination)
    • Based on underlyingh financial phenomena
  2. Drew parallels between embedded pension plan options and those in life insurance and financial markets
  3. Provided results of a survey on prevalence of embedded options in DB plans.

Note that embedded option and guarantees refer to the same thing.

Background

Cash balance plans

Interest crediting rates

Guarantees

Two categories:

  1. Guarantee a minimum cumulative rate of return when crediting rate is based on actual portfolio return or equity index only.
  2. Guarantee minimum annual rate of return when crediting rate is bond based.

Money-back guarantee:

Enhanced money-back guarantee:

Minimum annual interest rate guarantee:

Historical analysis of cash balance plan guarantees



nathanesau/StocVal documentation built on May 23, 2019, 12:18 p.m.