Asset pricing with loss aversion

The use of standard preferences for asset pricing has not been very successful in matching asset price characteristics, such as the risk-free interest rate, equity premium and the Sharpe ratio, to time series data. Behavioral finance has recently proposed more realistic preferences such as those with loss aversion. Research is starting to explore the implications of behaviorally founded preferences for asset price characteristics. Encouraged by some studies of Benartzi and Thaler [1995. Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics 110 (1), 73–92] and Barberis et al. [2001. Prospect theory and asset prices. Quarterly Journal of Economics CXVI (1), 1–53] we study asset pricing with loss aversion in a production economy. Here, we employ a stochastic growth model and use a stochastic version of a dynamic programming method with an adaptive grid scheme to compute the above mentioned asset price characteristics of a model with loss aversion in preferences. As our results show using loss aversion we get considerably better results than one usually obtains from pure consumption-based asset pricing models including the habit formation variant.     

News shocks and asset price volatility in general equilibrium

We study equity price volatility in general equilibrium with news shocks about future productivity and monetary policy. As West (1988) shows, in a partial equilibrium present discounted value model, news about the future cash flow reduces asset price volatility. We show that introducing news shocks in a canonical dynamic stochastic general equilibrium model may not reduce asset price volatility under plausible parameter assumptions. This is because, in general equilibrium, the asset cash flow itself may be affected by the introduction of news shocks. In addition, we show that neglecting to account for policy news shocks (e.g., policy announcements) can potentially bias empirical estimates of the impact of monetary policy shocks on asset prices.     

Asset price dynamics with heterogeneous beliefs and local network interactions

In this paper we investigate the effects of network topologies on asset price dynamics. We introduce network communications into a simple asset pricing model with heterogeneous beliefs. The agents may switch between several belief types according to their performance. The performance information is available to the agents only locally through their own experience and the experience of other agents directly connected to them. We model the communications with four commonly considered network topologies: a fully connected network, a regular lattice, a small world, and a random graph. The results show that the network topologies influence asset price dynamics in terms of the regions of stability, amplitudes of fluctuations and statistical properties.     

Bounded rationality,anchoring-and-adjustment sentiment,and asset pricing

This paper presents a framework that incorporates an investor’s limited attention and anchoring and adjustment sentiment and their joint effects on asset pricing, with endogenous cost of neglecting part of the dividends and the asymmetric rationality levels of investors. We find that the combined effect of the two bounded rationality factors is often embodied in the “loss”, and the retail investors are insensitive to market sentiment and forced to pay more cognitive loss. A higher level of investor rationality and bullish market sentiment will jointly increase demand and then prices, while the effects of different bounded rationality factors are asymmetric.     

Adaptive learning and monetary exchange

This paper investigates three classic questions in monetary theory: How can an intrinsically worthless asset, such as fiat money, maintain value as a medium of exchange? What are the short-run and long-run effects of a change in the money supply? What is the social cost of inflation? I answer these questions using a microfounded model of monetary exchange that replaces the rational expectations assumption with an adaptive learning rule. First, I show that monetary exchange is a robust arrangement in the sense that agents are able to learn the stationary monetary equilibrium while the non-monetary equilibrium is unstable under learning. Second, an unanticipated monetary injection has real effects in the short-run because learning the value of money takes time. In the long run, agents successfully learn the value of money, hence money is neutral. Third, under a constant money growth policy, an increase in the growth rate of money increases output in the short-run producing a short-run Phillips curve. A ten percent increase in the money growth rate has a social cost of 0.41 percent of output per year. Alternatively, a ten percent decrease in the money growth rate has a social benefit of 0.37 percent of output per year.     

Econometric analysis of structural systems with permanent and transitory shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah [1989. The dynamic effects of aggregate demand and supply disturbances. The American Economic Review 79, 655–673], and shows that structural equations with known permanent shocks cannot contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto [2001. Estimating shocks and impulse response functions. Journal of Applied Econometrics 16, 371–387], Shapiro and Watson [1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148], King et al. [1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840], Gali [1992. How well does the ISLM model fit postwar US data? Quarterly Journal of Economics 107, 709–735; 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249–271] and Fisher [2006. The dynamic effects of neutral and investment-specific technology shocks. Journal of Political Economy 114, 413–451].     

More hedging instruments may destabilize markets

This paper formalizes the idea that more hedging instruments may destabilize markets when traders have heterogeneous expectations and adapt their behavior according to performance-based reinforcement learning. In a simple asset pricing model with heterogeneous beliefs the introduction of additional Arrow securities may destabilize markets, and thus increase price volatility, and at the same time decrease average welfare. We also investigate whether a fully rational agent can employ additional hedging instruments to stabilize markets. It turns out that the answer depends on the composition of the population of non-rational traders and the information gathering costs for rationality.     

Asset Pricing with Observable Stochastic Discount Factors

The stochastic discount factor model provides a general framework for pricing assets. By specifying the discount factor suitably it encompasses most of the theories currently in use, including CAPM and consumption CAPM. The SDF model has been based on the use of single and multiple factors, and on latent and observed factors. In most situations, and especially for the term structure, single factor models are inappropriate, whilst latent variables require the somewhat arbitrary specification of generating processes and are difficult to interpret. In this paper we survey the principal different implementations of the SDF model for bonds, equity and FOREX and propose a new approach. This is based on the use of multiple factors that are observable and modelling the joint distribution of excess returns and the factors using a multi–variate GARCH–in–mean process. We argue that in general single equation and VAR models, although widely used in empirical finance, are inappropriate as they do not satisfy the no–arbitrage condition. Since risk premia arise from conditional covariation between the returns and the factors, both a multi–variate context and having conditional covariances in the conditional mean process, is essential. We explain how apparent exceptions, such as the CIR and Vasicek models, in fact meet this requirement — but at a price. We explain our new approach, discuss how it might be implemented and present some empirical evidence, mainly from our own researches. Partly, to enable comparisons to be made, the survey also includes evidence from recent empirical work using more traditional approaches.     

Learning competitive pricing strategies by multi-agent reinforcement learning

In electronic marketplaces automated and dynamic pricing is becoming increasingly popular. Agents that perform this task can improve themselves by learning from past observations, possibly using reinforcement learning techniques. Co-learning of several adaptive agents against each other may lead to unforeseen results and increasingly dynamic behavior of the market. In this article we shed some light on price developments arising from a simple price adaptation strategy. Furthermore, we examine several adaptive pricing strategies and their learning behavior in a co-learning scenario with different levels of competition. Q-learning manages to learn best-reply strategies well, but is expensive to train.     

Indifference pricing with uncertainty averse preferences

We consider the indifference valuation of an uncertain monetary payoff from the perspective of an uncertainty averse decision maker. We study how the indifference valuation depends on the decision maker’s attitudes toward uncertainty. We obtain a characterization of comparative uncertainty aversion and various characterizations of increasing, decreasing, and constant uncertainty aversion.     

Option pricing with an illiquid underlying asset market

We examine how price impact in the underlying asset market affects the replication of a European contingent claim. We obtain a generalized Black–Scholes pricing PDE and establish the existence and uniqueness of a classical solution to this PDE. Unlike the case with transaction costs, we prove that replication with price impact is always cheaper than superreplication. Compared to the Black–Scholes case, a trader generally buys more stock and borrows more (shorts and lends more) to replicate a call (put). Furthermore, price impact implies endogenous stochastic volatility and an out-of-money option has lower implied volatility than an in-the-money option. This finding has important implications for empirical analysis on volatility smile.     

Implementation of competitive nonlinear pricing: tariffs with inclusive consumption

The paper studies how the optimal nonlinear quantity-payment allocation can be truthfully implemented by optional tariffs in a differentiated goods duopoly. Consumers choose from a menu of tariffs and are subsequently billed according to this. We find that implementation by simple two part tariffs may not be a feasible strategy in a duopoly because the optimal nonlinear tariff exhibits a convexity for lower quantities. We show that the optimal outcome can be implemented if the firms can use two part tariffs with inclusive consumption. The fixed fee includes a free consumption allowance, whereas subsequent consumption is charged according to a steep unit price. That way the firm is able to secure voluntary participation without violating the incentive constraint. The paper shows some examples from the telecommunications industry where firms offer two part tariffs with free call minutes to low demand segments.     

Dynamic advertising and pricing with constant demand elasticities

In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.     

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect.We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.     

Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends

In the literature there appear various kinds of binomial trees for pricing options on stocks under geometric Brownian motions (GBMs) with known cash dividends. The aim of this paper is to compare the performance of the existing binomial trees in aspect of the convergence rates, which are usually used to measure precisely how fast the approximate values converge to the exact one, and to give a theoretical proof of the convergence rates for the interpolation binomial trees which are based on a model that excludes the arbitrage possibilities. Also the paper extends the studies to the regime-switching models with known cash dividend payment.     

Learning in linear models with expectational leads

Models with expectational leads typically admit multiple rational expectations solutions. Based on the ordinary least-squares algorithm, this paper provides an adaptive learning scheme which allows a forecasting agent to select a particular solution on economic grounds. Conditions are given under which this scheme converges to rational expectations solutions globally for all initial conditions. We strengthen convergence results in relaxing standard assumptions and in providing conditions ensuring algorithm convergence which are easier to verify and to interpret than those previously known.     

Learnability of an equilibrium with private information

This paper investigates the learnability of an equilibrium with private information. Agents of each type have their own private information about an exogenous variable and conduct adaptive learning with a heterogeneously misspecified perceived laws of motion (PLM) that includes only this variable. The paper shows that the existence of private information has a nonnegative impact on the learnability of the equilibrium; that is, the condition for learnability is unaffected or relaxed by heterogeneity and/or misspecification in PLMs caused by private information. In a New Keynesian model with private information about fundamental shocks, the learnability of the equilibrium is ensured by the Taylor principle of monetary policy. The paper also confirms that these results hold true not only in the presence of private information, but also in a variety of informational structures.     

Price and quantity competition among heterogeneous suppliers with two-part pricing: applications to clubs, local public goods, networks, and growth controls

Models of club goods, local public goods, and growth controls appear to have theoretical structures distinct from usual oligopoly models. This article shows, however, that they are special cases of a generalized oligopoly model that incorporates the possibility of two-part pricing and externalities between consumers (either congestion or network externalities). Our generalized two-part pricing model not only serves as a synthesis of a wide range of models but also allows us to obtain several new results on equilibrium prices. Another advantage of our model is that it can be interpreted as a reduced form of more complicated models that have spatial structures. This facilitates extension to the case where firms are heterogeneous and the number of firms is arbitrary.     

Explicit characterizations of financial prices with history-dependent utility

The present paper demonstrates how explicit representations of financial prices and returns can be derived in economies with history-dependent utility. While the techniques are applicable to a wide range of economies, they are applied to a representative consumer economy where (i) the consumer’s preferences exhibit habit formation, and (ii) purchases of the consumption good also gives rise to a flow of services. Solutions are computed for the case of multiplicative or nonlinear habit formation, and additive service flows. Other applications are also indicated.