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Asset Prices in an Exchange Economy with Habit Formation

This paper analyzes asset prices in a representative agent exchange economy with habit-forming preferences. For a general class of utility indices and endowment processes, the authors characterize the optimal demand for consumption and derive explicit solutions for the interest rate and asset risk premia. They show that consumption smoothness may obtain even when the interest rate is stochastic. The consumption capital asset pricing model may not hold when the endowment process has stochastic coefficients; asset risk premia are larger under mild assumptions. The interest rate depends on the growth in the standard of living. Malliavin calculus is employed in the analysis. Copyright 1991 by The Econometric Society.

MONTE CARLO VALUATION OF AMERICAN OPTIONS THROUGH COMPUTATION OF THE OPTIMAL EXERCISE FRONTIER

This paper introduces a Monte Carlo simulation method for pricing multidimensional American options. The method is based on the computation of the optimal exercise frontier. It is simple, efficient and flexible, suitable for multidimensional options. We consider options that can be exercised at a finite number of points, and compute the points of the exercise frontier recursively. We introduce an algorithm that converges very quickly to the value of the optimal exercise frontier.For multidimensional options, we fix the values of all the paramethers but one (usually the underlying security) and compute the value of the underlying at the optimal exercise frontier. Since the method converges very quickly, it is relatively fast (at least for low-dimensional options) to construct a grid for the frontier. One of the advantages of computing the optimal exercise frontier is that it can be used in subsequent computations that will only require application of plain vanilla Monte Carlo simulationThe method also allows a quick computation of the hedging portfolio. We present examples and we compare the numbers we get to other existing papers and show that at a low computational cost our results are as good as the best with the advantage that we simultaneously compute the optimal exercise frontier (which will simplify further any subsequent computations).

Equilibrium asset prices and exchange rates

Abstract In a two-country two-good world, we construct an intertemporal international general equilibrium for two logarithmic representative agents. Financial markets are fully integrated and independently incomplete. The equilibrium expected rate of change of the exchange rate increases with the differential of interest rates and the volatility of the domestic equity markets and decreases with the covariance between domestic and foreign equity markets. The equilibrium volatility of the exchange rate is the sum of the volatilities due to idiosyncratic factors in the financial markets and a term that represents the difference of weights in the common international factor.

Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves

We consider the problem of a Central Bank that wants the exchange rate to be as close as possible to a given target, and in order to do that uses both the interest rate level and interventions in the foreign exchange market. We model this as a mixed classical-impulse stochastic control problem, and provide for the first time a solution to that kind of problem. We give examples of solutions that allow us to perform an interesting economic analysis of the optimal strategy of the Central Bank.

Asset Pricing Implications of Benchmarking: A Two-Factor CAPM

The paper considers the equilibrium effects of an institutional investor whose performance is benchmarked to an index. In a partial equilibrium setting, the objective of the institutional investor is modelled as the maximization of expected utility (an increasing and concave function, in order to accommodate risk aversion) of final wealth minus a benchmark. In equilibrium this optimal strategy gives rise to the two-beta CAPM: together with the market beta a new risk-factor (termed active management risk) is brought into the analysis. This new beta is defined as the normalized (to the benchmarks variance) covariance between the asset excess return and the excess return of the market over the benchmark index. The empirical test supports the models predictions. The cross-section return on the active management risk is positive and significant, especially after 1990, when institutional investors became the representative agent of the market.

OPTIMAL DIVIDEND POLICY WITH MEAN-REVERTING CASH RESERVOIR

Motivated by empirical evidence and economic arguments, we assume that the cash reservoir of a financial corporation follows a mean reverting process. The firm must decide the optimal dividend strategy, which consists of the optimal times and the optimal amounts to pay as dividends. We model this as a stochastic impulse control problem, and succeed in finding an analytical solution. We also find a formula for the expected time between dividend payments. A crucial and surprising economic result of our paper is that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments. This results in a reduction of the probability of default of the firm.

Optimal risk-sharing with effort and project choice

We consider first-best risk-sharing problems in which “the agent” can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the functional form of the option is obtained as a solution to an ordinary differential equation. In the general case, the optimal contract is a fixed point of a functional that connects the agents and the principals maximization problems. We apply martingale/duality methods familiar from optimal consumption-investment problems.

Monte Carlo computation of optimal portfolios in complete markets

We introduce a method that relies exclusively on Monte Carlo simulation in order to compute numerically optimal portfolio values for utility maximization problems. Our method is quite general and only requires complete markets and knowledge of the dynamics of the security processes. It can be applied regardless of the number of factors and of whether the agent derives utility from intertemporal consumption, terminal wealth or both. We also perform some comparative statics analysis. Our comparative statics show that risk aversion has by far the greatest influence on the value of the optimal portfolio.

Optimal Allocation to Hedge Funds : An Empirical Analysis

What percentage of their portfolio should investors allocate to hedge funds? The only available answers to the above question are set in a static mean-variance framework, with no explicit accounting for uncertainty on the active managers ability to generate abnormal return, and usually generate unreasonably high allocations to hedge funds. In this paper, we apply the model introduced in Cvitanic et al (2002b Working Paper USC) for optimal investment strategies in the presence of uncertain abnormal returns to a database of hedge funds. We find that the presence of the model risk significantly decreases an investors optimal allocation to hedge funds. Another finding of this paper is that low beta hedge funds may serve as natural substitutes for a significant portion of investor risk-free asset holdings.

INCOMPLETE INFORMATION WITH RECURSIVE PREFERENCES

We consider the case of an agent with recursive preferences (Stochastic Differential Utility or SDU) who cannot observe the random drift of the stock price process. This partial information problem can be transformed into a problem with full information, in which the drift is replaced by its expected value conditional on the information given by the stock price history. We are then in a position to use recent results for maximizing SDUs under full information and their connection to Forward-Backward Stochastic Differential Equations. They enable us to study qualitative differences between the cases with full and partial information. We also analyze some special cases in which we obtain semi-explicit results and compute the SDU numerically.