Marcel Rindisbacher

Heterogeneous preferences and equilibrium trading volume

The classic Lucas asset pricing model with complete markets stresses aggregate risk and, hence, fails to investigate the impact of agents heterogeneity on the dynamics of the equilibrium quantities and measures of trading volume. In this paper, we investigate under what conditions non-informational heterogeneity, i.e., differences in preferences and endowments, leads to non trivial trading volume in equilibrium. Our main result comes in form of a non-informational no trade theorem which provides necessary and sufficient conditions for zero trading volume in a dynamically efficient, continuous time Lucas market model with multiple goods and securities.

Representation formulas for Malliavin derivatives of diffusion processes

Abstract.We provide new representation formulas for Malliavin derivatives of diffusions, based on a transformation of the underlying processes. Both the univariate and the multivariate cases are considered. First order as well as higher order Malliavin derivatives are characterized. Numerical illustrations of the benefits of the transformation are provided.

Asymptotic Properties of Monte Carlo Estimators of Derivatives

We study the convergence of Monte Carlo estimators of derivatives when the transition density of the underlying state variables is unknown. Three types of estimators are compared. These are respectively based on Malliavin derivatives, on the covariation with the driving Wiener process, and on finite difference approximations of the derivative. We analyze two different estimators based on Malliavin derivatives. The first one, the Malliavin path estimator, extends the path derivative estimator of Broadie and Glasserman (1996) to general diffusion models. The second, the Malliavin weight estimator, proposed by Fournie et al. (1999), is based on an integration by parts argument and generalizes the likelihood ratio derivative estimator. It is shown that for discontinuous payoff functions, only the estimators based on Malliavin derivatives attain the optimal convergence rate for Monte Carlo schemes. Estimators based on the covariation or on finite difference approximations are found to converge at slower rates. Their asymptotic distributions are shown to depend on additional second-order biases even for smooth payoff functions.

Optimal Portfolio Allocations with Hedge Funds

This paper analyzes optimal investment decisions, in the presence of non-redundant hedge funds, for investors with constant relative risk aversion. Factor regression models with optionlike risk factors and no-arbitrage principles are used to identify and estimate the market price of hedge fund risk, the volatility coefficients of hedge fund returns and the correlation between hedge fund and market returns. Timing ability causes stochastic fluctuations in these return characteristics. Outside investors optimally hold hedge funds for diversification purposes and are motivated to hedge fluctuations in return components caused by timing ability. The paper examines the portfolio structure and behavior and the impact of timing and selection abilities. Incorporating carefully selected hedge fund classes in asset allocation strategies can be a source of economic gains.

Monte Carlo methods for derivatives of options with discontinuous payoffs

Various Monte Carlo methods have been proposed to estimate the derivatives of contingent claims prices. The Monte Carlo approximate likelihood ratio estimator is studied. Recent convergence results are extended in order to show that the Monte Carlo approximate likelihood ratio derivative estimator is asymptotically equivalent, up to a second-order bias component, to an estimator based on a covariation approximation, the Monte Carlo Covariation estimator. Both converge slower than the Monte Carlo Malliavin derivative estimators. Theoretical convergence results are illustrated in a numerical experiment dealing with the risk management of digital options in a CEV model.

Asset Pricing with Regime-Dependent Preferences and Learning

This paper studies equilibrium in a pure exchange economy with unobservable Markov switching consumption growth regimes and regime-dependent preferences. Variations in risk attitudes have fundamental effects on the structure of equilibrium. Explicit solutions are provided for the market price of risk, the interest rate, stock and bond prices, and asset return volatilities. Calibration shows that this one-factor model can simultaneously support empirical long run values of the market price of risk, the interest rate, the stock market volatility, the equity premium and the moments of the consumption growth rate. Dynamic properties of the model are examined. An implied recession index is constructed and its performance evaluated. The ability to explain the dividend strips puzzle, the term structure of interest rates and the predictive behavior of the term premium are studied.

The Private Information Price of Risk

The Private Information Price of Risk (PIPR) represents the incremental price of risk assessed when private information becomes available. The PIPR plays a prominent role in models with private information. It determines the perception of risk for the recipient of a private information signal. It lies at the heart of the optimal consumption-portfolio policies of such an informed agent. It drives the return performance of an informed fund manager. It is an essential component of the welfare gains derived by investors in professionally managed funds.

Chapter 21 Simulation Methods for Optimal Portfolios

Abstract This chapter surveys and compares Monte Carlo methods that have been proposed for the computation of optimal portfolio policies. The candidate approaches include the Monte Carlo Malliavin derivative (MCMD) method proposed by Detemple et al. [Detemple, J.B., Garcia, R., Rindisbacher, M. (2003). A Monte-Carlo method for optimal portfolios.  Journal of Finance 58, 401–446], the Monte Carlo covariation (MCC) method of Cvitanic et al. [Cvitanic, J., Goukasian, L., Zapatero, F. (2003). Monte Carlo computation of optimal portfolio in complete markets. Journal of Economic Dynamics and Control 27, 971–986], the Monte Carlo regression (MCR) method of Brandt et al. [Brandt, M.W., Goyal, A., Santa-Clara, P., Stroud, J.R. (2005). A simulation approach to dynamic portfolio choice with an application to learning about return predictability. Review of Financial Studies 18, 831–873] and Monte Carlo finite difference (MCFD) methods. The asymptotic properties of the various portfolio estimators obtained are described. A numerical illustration of the convergence behavior of these estimators is provided in the context of a dynamic portfolio choice problem with exact solution. MCMD is shown to dominate other approaches.

Diffusion Models of Asset Prices

This paper reviews the literature on asset pricing in diffusion models. The first part is devoted to equilibrium models based on the representative agent paradigm. Explicit formulas for fundamental equilibrium quantities such as the state price density, the interest rate and the market price of risk are presented. Valuation formulas for stocks and contingent claims are also provided. Numerical implementation of the model is carried out in a setting with constant relative risk aversion. The second part of the paper focuses on multiagent models with complete financial markets. Characterizations of equilibrium are reviewed and numerical algorithms for computation are proposed.

Insider Information, Arbitrage and Optimal Portfolio and Consumption Policies

This article extends the standard continuous time financial market model pioneered by Samuelson (1969) and Merton (1971) to allow for insider information. The paper derives necessary and sufficient conditions for arbitrage opportunities of insiders and presents optimal portfolio strategies for investors having anticipative information. We prove that if the investment horizon of an insider ends after his initial information advantage has disappeared, an insider has arbitrage opportunities if and only if the anticipative information is so informative that it contains zero-probability events given initial public information. When it ends before or when anticipative information does not contain such events we derive expressions for optimal consumption and portfolio policies and examine the effects of anticipative information on the optimal policies of an insider. Optimal insider policies are shown not to be fully revealing. Anticipative information is of no value and therefore does not affect the optimal behavior of insiders if and only if it is independent from public information. We show that arbitrage opportunities allow to replicate arbitrary consumption streams such that the insiders budget constraint is not binding. Consequently, Mertons consumption-investment problem has no solution whenever investment horizons are longer than resolution times of signals and insider information contains events whose occurrence is not believed. If the true signal is perturbed by independent noise this problem can be avoided. But since in this case investors never learn the true anticipative information we argue that this does not capture an important feature of insider information. We also show that the valuation of contingent claims measurable with respect to public information at maturity is invariant to insider information if the latter does not allow for arbitrage opportunities. In contrast contingent claims have no value for insiders with anticipative information generated by signals with continuous distribution.