Executive Stock Options

Abstract

As a part of the compensation package many companies provide executives with executive stock options, which are call options with additional restrictions. They provide some financial advantages to the executives and help the company retain the service of the executives who improve the company’s earnings and management.

Until recently the values of the executive stock options were not required to be disclosed in the company?s financial reports. But recent statements from the Financial Accounting Standards Board (FASB) have made it necessary to value these executive stock options. The valuation of executive stock options is also required for investors and financial practitioners. This paper considers the award of performance-based executive stock options when the stock price at the time of stock option award exceeds a given preassigned value. It is assumed that the stock price follows a geometric Brownian motion, and that the number of stock options awarded at any time depends on the stock price at that time.

A valuation formula is derived using the method of Esscher transforms for a multiyear award plan. The closed-form formula derived is similar to the Black-Scholes formula for options and utilizes the standard bivariate normal distribution function, which is available in statistical software. In this paper the number of stock options awarded is assumed to be in a specific form, but the theory presented can be modified to suit other forms of award structure. Moreover, by suitable choice of parameters, a valuation formula is also presented for the award of fixed-value executive stock options grants; this formula is also in a closed form and involves cumulative distribution values of the standard normal random variable. Numerical illustrations of the use of the valuation formulas are presented.     

Excess Mortality In Asia Associated With Cigarette Smoking

Abstract

Cigarette smoking has reached epidemic proportions in many Asian countries, and epidemiologists predict massive increases in the number of smoking-related deaths in future decades. This information is of great interest to insurers who would like to sell coverage in these markets with smoker/nonsmoker-distinct pricing. This review examines excess mortality due to cigarette smoking in Asia as determined by a second-quarter 1998 Internet search of the world’s English-language medical literature for references published during the preceding five years. Studies to date which observed fairly low relative risks of mortality in smokers compared with nonsmokers in Asia despite a high prevalence of smoking can be explained by the fact that health outcome data represent early experience. Given similar associations between smoking and mortality in Asian and Western studies, it is likely that mortality patterns of smokers in Asia eventually will mirror those seen in the U.S. and the United Kingdom.     

The Impact of the Inpatient Prospective Payment System and Diagnosis-Related Groups

Abstract

The outpatient prospective payment system for the Medicare program became effective Aug. 1, 2000, as mandated by the Balanced Budget Act of 1997. This outpatient program complements Medicare’s inpatient prospective payment system, which was introduced in 1983. A survey of the literature over the past 20 years is undertaken to review the effects of the inpatient prospective payment system and diagnosis-related groups (DRGs) on inpatient hospital utilization, expenditures, and outcomes. The level of the DRG payment has been questioned, as well as the process of adjusting the payment levels from one year to the next. In addition, past research has speculated that the DRG classification may not be sensitive to severity and is subject to coding ambiguities. These conclusions can be used as input to future research on the new outpatient program, as well as updating research on the inpatient program.     

Implementation of Four Models for Outstanding Liabilities in Winbugs: A Discussion of a Paper by Ntzoufras and Dellaportas

Abstract

Ntzoufras and Dellaportas (2002) described four models for outstanding claim amounts of the “reported but not settled” variety. Two of the models incorporated claim-counts data in addition to the claim amounts themselves in order to add a hierarchical stage in the usual log-normal and state-space models. The purpose of this discussion is to describe how the models presented in Ntzoufras and Dellaportas may be implemented using WinBUGS. The use of WinBUGS to implement the Bayesian analysis of a number of other actuarial models was considered by Scollnik (2001).     

Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equivalent Utility

Abstract

The author applies the principle of equivalent utility to price and reserve equity-indexed life insurance. Young and Zariphopoulou (2002a, b) extended this principle to price insurance products in a dynamic framework. However, in those papers, the insurance risks were independent of the risky asset in the financial market. By contrast, the death benefit for equity-indexed life insurance is a function of a risky asset; therefore, this paper further extends the principle of equivalent utility. In a second extension, the author applies the principle of equivalent utility to calculate reserves, as introduced by Gerber (1976). In a related paper, Moore and Young (2002) price equity-indexed pure endowments, the building blocks of equity-indexed life annuities.     

Issues for Implementing Phased Retirement in Defined Benefit Plans

Abstract

U.S. society is aging. The nature of work has changed from work that requires physical strength to work based on knowledge. As a result, workers are beginning to phase into retirement rather than going directly from full-time work to full retirement. From a retirement income perspective, many final-average-pay defined benefit plans have features that make phased retirement difficult at best and detrimental at worst. U.S. pension law and regulations present barriers to phased retirement if the phased retiree wants to receive a portion of available pension benefits during phased retirement.

This paper examines private sector options to encourage phased retirement and to eliminate the disincentives that currently affect defined benefit plans. It offers alternative calculations of final average pay that do not penalize the part-time worker. It also demonstrates that the plan’s early retirement reduction and late retirement increase can be set to maintain actuarial equity throughout phased retirement. The paper presents benefit calculations with equal actuarial values for various payout patterns.

The paper discusses the coordination between phased retirement and subsidized early retirement. Finally, the paper notes some of the changes in ERISA that will be needed to facilitate phased retirement in defined benefit plans, especially for participants who want to receive pension distributions while working part time.