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The Valuation of Multivariate Contingent Claims in Discrete Time Models

Journal of Finance 1984 39(1), 207-228
ABSTRACT There are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables. Familiar cases of such claims include options on a portfolio of options, options whose exercise price is stochastic, and options to exchange one asset for another. This paper derives risk neutral valuation relationships (RNVRs) in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases: joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors, and joint normally distributed underlying variables and constant absolute risk aversion preferences, respectively. This methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds, multicurrency option bonds, and investment options.

The Valuation of Options When Asset Returns Are Generated by a Binomial Process

Journal of Finance 1984 39(5), 1525-1539
ABSTRACT This paper values options on assets whose returns, over a finite interval of time, are generated by a binomial process. It shows that a simple valuation relationship, between the option and the underlying stock, obtains if investors have preference functions that belong to a particular class, even if opportunities to hedge do not exist. One particular application of the theory is in the case where the stock price over a finite interval could increase by an amount, fall by the same amount, or stay at the same level. The results in this paper may be viewed as the foundation of the preference‐based approaches to obtaining a risk neutral valuation relationship.

Estimation of Implicit Bankruptcy Costs

Journal of Finance 1984 39(3), 629
This paper presents a new methodology, quasilinear estimation, for efficiently estimating economic variables reflected in the prices of corporate securities. For example, ex ante bankruptcy costs are not directly observable, however, if these costs are sufficiently large, then current security prices are affected and bankruptcy costs can be indirectly measured. When bankruptcy costs and other relevant parameters are known, there are many numerical solution techniques that can be used to determine security prices. One technique, the method of lines, is compatible with quasilinear estimation, which has been employed extensively in the physical sciences for the estimation of coefficients in differential equation models. We demonstrate that quasilinear estimation is a potentially reliable and efficient technique for the estimation of corporate bankruptcy costs and the asset variance from security prices.

Estimation of Implicit Bankruptcy Costs

Journal of Finance 1984 39(3), 629-642
ABSTRACT This paper presents a new methodology, quasilinear estimation, for efficiently estimating economic variables reflected in the prices of corporate securities. For example, ex ante bankruptcy costs are not directly observable, however, if these costs are sufficiently large, then current security prices are affected and bankruptcy costs can be indirectly measured. When bankruptcy costs and other relevant parameters are known, there are many numerical solution techniques that can be used to determine security prices. One technique, the method of lines, is compatible with quasilinear estimation, which has been employed extensively in the physical sciences for the estimation of coefficients in differential equation models. We demonstrate that quasilinear estimation is a potentially reliable and efficient technique for the estimation of corporate bankruptcy costs and the asset variance from security prices.

Theory and Behavior of Multiple Unit Discriminative Auctions

Journal of Finance 1984 39(4), 983-1010
ABSTRACT This paper reports the results of controlled experiments designed to test the Harris‐Raviv generalization of the Vickrey theory of bidding in multiple unit discriminative auctions. The paper also discusses further development of the theory—in a way suggested by the experimental results—to include bidders with distinct risk preferences.