We develop a numerical approximation method for valuing multivariate contingent claims. The approach is based on an n-dimensional extension of the lattice binomial method. Closed-form solutions for the jump probabilities and the jump amplitudes are obtained. The accuracy of the method is illustrated in the case of European options when there are three underlying assets.
Wben several investors with different risk aversions trade competitively in a capital market, the allocation of wealth fluctuates randomly among them and acts as a state variable against which each market participant will want to hedge. This hedging motive complicates the investors ' portfolio choice and the equilibrium in the capital market. This article features two investors, with the same degree of impatience, one of them being logarithmic and the other having an isoelastic utility function. They face one risky constant-return-to-scale stationary production opportunity and they can borrow and lend to and from each other. The behaviors of the allocation of wealth and of the aggregate capital stock are characterized, along with the behavior of the rate of interest, the security market line, and the portfolio boldings. The two-investor equilibrium problem is as basic to financial economics as is the two-body problem to mechanics. Yet, to my knowledge, no complete description of the dynamic interaction between two investors
This article analyzes the volume of trade in a multiperiod noisy rational expectations model. When traders receive private signals at the first trading date and are allowed a second round of trade, two type of equilibria exist. In the first, traders do not learn about the average private signal from the second round of trade, and all trade takes place at the first date. In the second, traders do learn from the second round, and trade thus takes places at both the first and second dates. The article characterizes volume when a public signal is disclosed at the second date.
Technical analysis, or the use of past prices to infer private information, has value in a model in which prices are not fully revealing and traders have rational conjectures about the relation between prices and signals. A two-period dynamic model of equilibrium is used to demonstrate that rational investors use historical prices in forming their demands and to illustrate the sensitivity of the value of technical analysis to changes in the values of the exogenous parameters.
In this article we construct a model in which a consumer's utility depends on the consumption history. We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closed form in this general equilibrium setting to rationalize the observed stickiness of the consumption series relative to the fluctuations in stock market wealth. The sample paths of consumption generated from this model imply lower variability in consumption growth rates compared to those generated by models with separable utility functions. We then present partial equilibrium model similar to Merton (1969, 1971) and extend Merton's results on optimal consumption and portfolio rules to accommodate nonseparability in preferences. Asset pricing implications of our framework are briefly explored.
This article presents a model that provides insights about various measures of portfolio performance. The model explores several criticisms of these measures. These include the problem of identifying an appropriate benchmark portfolio, the possibility of overestimating risk because of market-timing ability, and the failure of informed investors to earn positive risk-adjusted returns because of increasing risk aversion. The article argues that these need not be serious impediments to performance evaluation.
The author presents a self-contained exposition of selected topics in the theory of financial markets with applications to corporate finance. The book covers only topics sanctioned by tradition. About one-quarter of the book is devoted to the one-period model with certainty. Half the book deals with the one-period model with uncertainty, and the remaining quarter with multiperiod models with uncertainty, both discrete and continuous. The one-period model with certainty starts with topics from the standard theory of the consumer and discusses consumer preferences and their representation by utility functions. The author then defines arbitrage trading strategies and uses the assumed properties of preferences to show that equilibrium in this model excludes arbitrage trading strategies. In the absence of arbitrage trading strategies all securities earn the same rate of return. The price functional, which maps terminal cash flows into initial prices, is additive, and the irrelevance of corporate financial structure and dividend policy follows from the additivity of the price functional.
Journal Article Market Trading Structures and Asset Pricing: Evidence from the Treasury-Bill Markets Get access Avraham Kamara Avraham Kamara University of Washington Search for other works by this author on: Oxford Academic Google Scholar The Review of Financial Studies, Volume 1, Issue 4, October 1988, Pages 357–375, https://doi.org/10.1093/rfs/1.4.357 Published: 14 March 2015
This article investigates the structure on preferences required to derive Ross's arbitrage pricing theory (APT). It is shown that only ordinal preferences are required. In particular, the APT does not require that agents possess preferences representable as risk-averse expected utility functions. This characteristic of the APT is not shared by the standard equilibrium-based capital asset pricing models.
Most modern financial research can be characterized as theoretical or empirical, or a mix of the two. Theoretical finance can be divided in the way that theoretical economics is. Neoclassical research stems from the neoclassical economics of perfectly competitive markets that have no imperfections or frictions, such, as taxes, transaction costs, externalities, or information asymmetries. By definition, imperfect markets research includes all other topics, such as the study of taxes, institutions, and topics stemming from information economics. Darrell Duffie's new book is an introduction to neoclassical finance that emphasizes topics in the intersection of theoretical finance and the mathematical economics of general equilibrium. The book is designed to take the student from first principles to the frontiers of finance-oriented general equilibrium theory. The book contains a rigorous introduction to the necessary topics in probability and stochastic control and is a good source for that material. It also contains a good summary of general equilibrium theory, including the required background mathematics. Each theorem from the general equilibrium literature is presented in a form that is general enough to be applicable to continuous-time models in finance but is as simple as possible given that level of generality. Other variations are mentioned in the literature reviews at the end of each section.