In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent." We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules, and by quantile-based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.

The assertion about swaps being mutually beneficial is examined. A simple example of interest rate swaps is first built, to emphasize the point overlooked in usual studies: the parties to a swap may well exchange (interest payments) default risks of different values. Fair prices of swaps and swaptions are then given, in a default free context, as well as in the case of possible default. In the latter case, credit insurance with level premiums requires the study of mathematical reserves.

Martingale methods are used to study interest rate risk in a market with two fundamental assets: savings accounts and zero coupon bonds. Discounted prices of bonds have to be a martingale for a risk-neutral probability. Specifications are given when the instantaneous rate of interest is adapted to a Brownian motion or follows a diffusion.

This paper deals with issues concerning the core as a solution concept for games in coalitional form as well as the use of these games in representing economies of a certain formal type. Side-payment games are imbedded in the more general class of no-side-payment games. It is shown that to a given side-payment game having an empty core one may associate two different no-side-payment games with the same (nonempty) core: the “envelope” and the “geometrical cover.” The discrepancy is explained in terms of market games.