The duration of employment has been studied by Betancourt and Clague (1981), Winston and McCoy (1974) and Betancourt (1986). Results obtained, summarized in Section 3 below, supposed homotheticity of production functions and a constant speed or intensity of capital usage. The simultaneous cost minimising determination of speed and duration is studied here with an explicit analytical expression being developed relating duration to parameters of interest, including returns to scale and the substitution elasticity, both traditionally measured. The propositions of Betancourt, Clague and Winston and McCoy are then established using differential analysis.

Minimal discounted distorted expectations across a range of stress levels are employed to model risk acceptability in markets. Interactions between discounting and stress levels used in measure changes are accommodated by lowering discount rates for the higher stress levels. Acceptability parameters represent a maximal and minimal discount rate, a maximal stress level and the speed of rate reduction in response to stress. An explicit model relating credit default swap (CDS) prices to default probabilities is formulated with a view to making the default risk market acceptable. Data on CDS prices and default probabilities for the six major US banks obtained from the Risk Management Institute of the National University of Singapore is employed to estimate parameters defining acceptability and the movements in market implied recovery rates. We observe that the financial crisis saw an increase in the maximal discount rate and its spread over the minimal rate along with an increase in the maximal stress level being demanded for acceptability and a stable pattern for the speed of rate adjustment through the period. The maximal rate, rate spread and stress levels have come down but with periods in the interim where they have peaked as they did in the crisis. Recovery rates have oscillated and they did fall substantially but have recovered towards 40 percent near the end of the period.

The financial monitoring system is formalized as an economic primitive in addition to preferences, endowments, production sets and asset spans. New definitions of budget constraints and economic equilibria follow. The concept of a general equilibrium is then appropriately revised to accommodate this perspective on the role of a financial monitoring system. Implications for asset pricing are derived and the relationship of equilibria to risk management considerations is discussed.

Employing continuous arbitrage pricing principles, closed-form expressions for the term structure of interest rates as functions of two specific rates are developed. Model restrictions to the two one-dimensional submodels are tested and rejected, thereby supporting the hypothesis that the term structure is at least two-dimensional. Evidence is also presented that supports the view that the informational content of the term structure lies in its longer maturities.

We show in any economy trading options, with investors having mean-variance preferences, that there are arbitrage opportunities resulting from negative prices for out of the money call options. The theoretical implication of this inconsistency is that mean-variance analysis is vacuous. The practical implications of this inconsistency are investigated by developing an option pricing model for a CAPM type economy. It is observed that negative call prices begin to appear at strikes that are two standard deviations out of the money. Such out-of-the money options often trade. For near money options, the CAPM option pricing model is shown to permit estimation of the mean return on the underlying asset, its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data covering the period January 1992–September 1994. It is found that the mean rate of return though positive, is poorly identified. The estimates for the volatility are stable and average 11%, while those for the planning horizon average 0.95. The hypothesis that the planning horizon is a year can not be rejected. The one parameter Black–Scholes model also marginally outperforms the three parameter CAPM model with average percentage errors being respectively, 3.74% and 4.5%. This out performance of the Black–Scholes model is taken as evidence consistent with the mean-variance analysis being vacuous in a practical sense as well.

A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. Theprocess is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options.The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model developed here.

We present a new approach for positioning, pricing, and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization. Our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable. By assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure, we derive a counterpart to the first fundamental theorem of asset pricing. We also derive a counterpart to the second fundamental theorem, which leads to unique derivative security pricing and hedging even though markets are incomplete. For products that are not spanned by the liquid assets of the economy, we show how our methodology provides more realistic bid–ask spreads.

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case of Merton-type formula is shown to result, provided jump probabilities are replaced by their corresponding Arrow-Debreu prices.