Résumé. Cet article traite de la comptabilité pour les investissements en actions d'une compagnie d'assurance‐vie. On y analyse différentes procédures permettant de comptabiliser des changements non réalisés dans les valeurs du marché des titres de son portefeuille d'investissements. Ces procédures s'échelonnent de la comptabilisation directe des valeurs du marché à la méthode couramment utilisée par les compagnies canadiennes d'assurance‐vie et qui consiste en un lissage complet. On propose des statistiques sommaires qui décrivent les propriétés des chiffres comptables obtenus à partir des diverses procédures de lissage. On considère ces statistiques sommaires comme étant des moyens compacts et économiques de résumer les effets des procédures pour des lecteurs d'états financiers. La deuxième partie de l'article décrit comment un groupe d'utilisateurs particulier peut obtenir une classification des possibilités comptables. On suggère le processus analytique de hiérarchie (Saaty 1980) pour combiner les jugements de différentes personnes dans un groupe de préférence. On illustre par une petite étude‐pilote la faisabilité de la méthode pour classifier diverses propositions concernant le traitement comptable des investissements en actions des compagnies d'assurance‐vie.

Abstract. This paper deals with the accounting for equity investments by a life insurance company. Various procedures for recognizing unrealized changes in market values of securities in its investment portfolio are analyzed. These range from direct recognition of market values to the method currently employed by Canadian life insurance companies which involves extensive smoothing. Summary statistics are suggested that describe the properties of the resulting accounting numbers obtained from various smoothing procedures. These summary statistics are viewed as compact, cost effective ways of summarizing the effects of the procedures for financial statement readers. The second part of the paper describes how a particular user group can obtain a ranking among various accounting alternatives. The Analytic Hierarchy Process (Saaty 1980) is proposed for combining the judgments of different individuals into a group preference. The feasibility of the method is illustrated using a small pilot study to rank various proposals concerning the accounting treatment of life insurance companies' equity investments.

A procedure is developed for the valuation of options when there are two underlying state variables. The approach involves an extension of the lattice binomial approach developed by Cox, Ross, and Rubinstein to value options on a single asset. Details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables. This procedure can be used to price any contingent claim whose payoff is a piece-wise linear function of two underlying state variables, provided these two variables have a bivariate lognormal distribution. The accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for European options. One advantage of the lattice approach is that it handles the early exercise feature of American options. In addition, it should be possible to use this approach to value a number of financial instruments that have been created in recent years.

This paper develops a Monte Carlo simulation method for solving option valuation problems. The method simulates the process generating the returns on the underlying asset and invokes the risk neutrality assumption to derive the value of the option. Techniques for improving the efficiency of the method are introduced. Some numerical examples are given to illustrate the procedure and additional applications are suggested.

ABSTRACT Often futures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets. We explore the implications of the quality option on the futures price. We develop a method for pricing the quality option for the general case of n deliverable assets and provide numerical illustrations of its significance. Even when the asset prices are very highly correlated, this option can have nontrivial value, especially when there is a large number of deliverable assets. We analyze the impact of the timing option and its interaction with the quality option. A procedure is developed for valuing the timing option in the presence of the quality option, and some numerical estimates are obtained.

Often futures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets. We explore the implications of the quality option on the futures price. We develop a method for pricing the quality option for the general case of n deliverable assets and provide numerical illustrations of its significance. Even when the asset prices are very highly correlated, this option can have nontrivial value, especially when there is a large number of deliverable assets. We analyze the impact of the timing option and its interaction with the quality option. A procedure is developed for valuing the timing option in the presence of the quality option, and some numerical estimates are obtained.

This paper analyses the distribution of returns on a hedged portfolio, consisting of a European call option and its associated stock, when the portfolio is rebalanced at discrete time intervals. Under the assumptions of the Black-Scholes model this distribution is particularly skew. In tests of the average return on a hedged portfolio this skewness leads to biased t-statistics. The paper explores the nature and extent of this bias and suggests procedures for overcoming it. Other aspects of discrete hedging are also discussed.

This paper examines some implications of using an estimate of the variance in option valuation models. This procedure produces biased option values. It is shown that the magnitude of this bias is not large. The dispersion induced in the option price is more significant particularly for parameter values of practical interest. The nature and extent of this dispersion is examined by numerical examples. The paper suggests how a Bayesian approach could be used to cope with the estimation error.

Option replication is discussed in a discrete-time framework with transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black-Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values.