Learning,large deviations and rare events

We examine the role of generalized stochastic gradient constant gain (SGCG) learning in generating large deviations of an endogenous variable from its rational expectations value. We show analytically that these large deviations can occur with a frequency associated with a fat-tailed distribution even though the model is driven by thin-tailed exogenous stochastic processes. We characterize these large deviations, driven by sequences of consistently low or consistently high shocks and then apply our model to the canonical asset pricing framework. We demonstrate that the tails of the stationary distribution of the price–dividend ratio will follow a power law.     

The influence of investment experience on market prices: laboratory evidence

We run laboratory experiments to analyze the impact of prior investment experience on price efficiency in asset markets. Before subjects enter the asset market they gain either no, positive, or negative investment experience in an investment game. To get a comprehensive picture about the role of experience we implement two asset market designs. One is prone to inefficient pricing, exhibiting bubble and crash patterns, while the other exhibits efficient pricing. We find that (i) both, positive and negative, experience gained in the investment game lead to efficient pricing in both market settings. Further, we show that (ii) the experience effect dominates potential effects triggered by positive and negative sentiment generated by the investment game. We conjecture that experiencing changing price paths in the investment game can create a higher sensibility on changing fundamentals (through higher salience) among subjects in the subsequently run asset market.     

Asset Price And Current Account Dynamics

We examine the interaction between asset market and current account in a small open economy. In an overlapping generations economy in which land and money are available assets, the interaction between the land price and current account dynamics is shown to generate a plausible (asset price) specie-flow mechanism. We apply them to a number of issues. Domestic credit policy is neutral in the long run: one unit of foreign reserve increase offsets one unit of credit reduction. Next, the association between the endowment of land and foreign asset accumulation depends on parameters of the model. Finally, we examine the dynamic adjustment s following a once-and-for-all capital inflow. When the adjustment involves running current account deficit, the recipient country's foreign reserve position is permanently lowered. Furthermore, the steady state level of national wealth is permanently reduced. [E4, F3]     

Asset prices in a Huggett economy

This paper explores asset pricing in economies where there is no direct insurance against idiosyncratic risks but other assets can be used for self-insurance, subject to exogenously-imposed borrowing limits. We analyze an endowment economy, based on Huggett (1993) [11], both with and without aggregate risk. Our main innovation is that we obtain full analytical tractability by studying the case with “maximally tight” borrowing constraints. We illustrate by looking at riskless bonds, equity, and the term structure of interest rates, and we show that the model can reproduce many features of observed asset prices when idiosyncratic risks are quantitatively reasonable.     

Existence and efficiency of equilibrium in infinite economies with finite aggregate wealth

Summary. We prove the existence and efficiency of equilibrium in economies with infinitely many consumers in which there are finitely many agents who own a positive portion of the aggregate endowment. We prove existence for commodity spaces which are employed in the general equilibrium asset pricing models and use incomplete and intransitive preferences. We discuss the importance of existence of finitely many agents who own a positive portion of the aggregate endowment in obtaining efficient equilibrium. For general equilibrium asset pricing applications we require forward properness only at individually rational Pareto optimal allocations. We provide an Arrow-Debreu model for these economies. We also give an application of our approach and results by employing Stochastic Differential Utility as the utility of each consumer in an infinite horizon model.     

Incomplete markets: transverse financial structures

Summary. In a multiperiod economy with incomplete markets and assets with payoff depending on the price history (e.g., asset and derivatives), we show that in order to get endowment generic existence of an equilibrium it is not needed to alter settlement features such as when payments are made and when the asset is traded. This is non-trivial as each such characteristic introduces a non-generic subclass of financial instruments. We show essentially that expiry date payments are the only payments that one needs perturbing (if at all). For previous periods - the P&L discovery map - is the one relevant for wealth transfers. This map transfers wealth between one period and the next by associating to each portfolio next period potential profit and losses as a function of the revealed information at the node. All present values involved can in general - because of backward induction pricing structure - be appropriately controlled via expiry payoffs only. This enables us to extend two-period work and introduce Transverse Financial Structures for multiperiod economies, where one cannot identify the payoffs of financial instruments to the P&L discovery map (in other words we introduce some financial ingeneering for Transverse Financial Structures). We capitalize on that difference using unexploited “maturity payout degrees of freedom” and rolling back the uncertainty tree. As an application of this approach we prove a conjecture by Magill and Quinzii that commodity forward contracts lead to endowment generic existence of an equilibrium in a multiperiod set-up. Received: June 25, 1999; revised version: April 4, 2001     

High equity premia and crash fears - Rational foundations

Summary. We show that in a Lucas endowment economy in which the process for dividends is described by a lattice tree subject to infrequent but observable structural breaks, in equilibrium recursive rational learning may inflate the equity risk premium and reduce the risk-free interest rate for low levels of risk aversion. The key condition for these results to obtain is the presence of sufficient initial pessimism. The relevance of these findings is magnified by the fact that under full information our artificial economy cannot generate asset returns matching the empirical evidence for any positive relative risk aversion.Received: 20 September 2003, Revised: 27 April 2005, JEL Classification Numbers: D83, E44, G12.I am indebted to Mordecai Kurz (the co-Editor), one anonymous Referee, Gabriele Camera, Sadayuki Ono, Olesia Verchenko, and Allan Timmermann for many useful comments. I also think seminar paticipants at the European Economic Association meetings in Stockholm (August 2003) and the Midwest Economics Association in St. Louis (March 2003).     

Two-period trading sentiment asset pricing model with information

We present a dynamic asset pricing model with investor sentiment and information, which shows that the investor sentiment plays a systematic and important role in the asset prices and the information is gradually incorporated into prices. The model has an analytical solution to the sentiment equilibrium price. We find that sentiment trading quantity not only increases the market liquidity, but also causes the asset prices' overreaction if the intensity of sentiment demand is more than a constant value. Therefore, the continuing overreactions result in a short-term momentum and a long-term reversal. The model could offer a partial explanation to some financial anomalies such as price bubbles, high volatility, asset prices' overreaction and so on.     

Learning,estimation, and the stability of rational expectations

The stability of the rational expectations equilibrium of a simple asset market model is studied in a situation where a group of traders learn about the relationship between the price and return on the asset using ordinary least squares estimation, and then use their estimates in predicting the return from the price. The model which they estimate is a well-specified model of the rational expectations equilibrium, but a misspecified model of the situation in which the traders are learning. It is shown that for appropriate values of a stability parameter the situation converges almost surely to the rational expectations equilibrium.     

Fundamentals, information, and international capital flows: A welfare analysis

In the recent discussion surrounding the design of a new international financial architecture, enhancing transparency has widely been proposed as a policy essential for increasing the efficiency of international capital markets. This paper uses a simple two-country (two-agent) general equilibrium model with incomplete markets and production to explore the welfare consequences of an increase in public information about country-specific fundamentals (increase in transparency). An improvement in the quality of information has two effects on the ex ante welfare of individual countries: A direct effect that increases the efficiency of global capital allocation and welfare, and an indirect general equilibrium effect that increases asset price volatility and may decrease welfare. When the degree of risk-aversion is low, at least one country will gain from an increase in information quality. If the degree of risk-aversion is high, then there are robust examples of economies for which an increase in information hurts all countries. The paper also discusses how certain institutional arrangements (international derivative markets, international agency) could ensure that all countries gain from better information by providing insurance against information-induced asset price risk.     

马尔可夫调制模型下交换期权的定价

在这篇文章中,假定市场经济状态由一个两状态马尔可夫链描述,风险资产满足一个两状态的马尔可夫调制过程。当市场处于高波动状态时,风险资产的价格满足跳扩散过程;当市场处于稳定状态时,风险资产的价格满足几何布朗运动.通过测度变换的技术,得到了交换期权的定价公式。最后,利用蒙特卡洛方法给出了期权价值的数值结果。     

Time-varying exchange rate exposure and exchange rate risk pricing in the Canadian Equity Market

This paper aims to extend the existing literature on foreign exchange rate risk pricing. Unlike the existing studies on Canada, we use six alternative bilateral and one multilateral exchange rate proxies. Furthermore, using both a two-factor and a three-factor capital asset pricing model (CAPM), we test for the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. The estimated results based on both the ordinary least squares (OLS) and generalized least squares (GLS) estimation techniques confirm that exchange rate risk in the Canadian equity market is priced and that the pricing of this risk is time-varying. This result holds for all seven exchange rate proxies. Our empirical analysis also suggests the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. This relationship is found to be insensitive to variations in the world market return.     

Market equilibrium with heterogeneous recursive-utility-maximizing agents

Summary This paper considers a heterogeneous agent Lucas style exchange economy. For a class of recursive utility functions containing the standard additive expected utility functions, I demonstrate that there exist market equilibria characterized by stationary (ergodic) Markov processes for consumption, portfolio holdings, asset prices and the unobserved utilities. No assumptions about market completeness are made, and there are no restrictions on the underlying information filtration.Other contributions of this paper include: (i) an existence and uniqueness theorem of intertemporal utility for the general class of recursive generators; (ii) the optimum principle as well as its corresponding Euler equation derived for the agent's consumption and portfolio choice problem under recursive utility, and (iii) a single-agent equilibrium asset pricing formula which generalizes that of Epstein and Zin (1989).This paper is a part of my PhD dissertation at the University of Toronto. I would like to thank Larry Epstein for his enthusiastic supervision, helpful discussion and valuable comments. Thanks also to Tan Wang and especially Darrell Duffie for valuable comments.     

No-arbitrage, state prices and trade in thin financial markets

We examine how non-competitiveness in financial markets affects the choice of asset portfolios and the determination of equilibrium prices. In our model, potential arbitrage is conducted by a few highly specialized institutional investors who recognize and estimate the impact of their trades on financial prices. We apply a model of economic equilibrium, based on Weretka (, 2007a), in which price effects are determined endogenously as part of the equilibrium concept. For the case in which markets allow for perfect insurance, we argue that the principle of no-arbitrage asset pricing is consistent with non-competitive behavior of the arbitragers and extend the fundamental theorem of asset pricing to the non-competitive setting.     

Asset pricing theory and the valuation of Canadian paintings

Abstract.  The valuation of Canadian paintings is analysed empirically. Using a sample of auction prices for major Canadian painters for the period 1968–2001, we run hedonic regressions to analyse the influence of various factors, including painter identity, on auction prices, as well as to construct a market price index. This index is used in a second‐stage analysis in which we analyse the properties of Canadian art viewed as an investment asset. We apply standard asset pricing theory, as incorporated in the capital asset pricing model (CAPM), to the analysis of price movements in the market for Canadian paintings.     

Wealth Inequality and Asset Pricing

In an Arrow–Debreu exchange economy with identical agents except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the risk-free rate. We first show that wealth inequality raises the equity premium if and only if the inverse of absolute risk aversion is concave in wealth. We then show that the equilibrium risk-free rate is reduced by wealth inequality if the inverse of the coefficient of absolute prudence is concave. We also prove that the combination of a small uninsurable background risk with wealth inequality biases asset pricing towards a larger equity premium and a smaller risk-free rate.     

A nonparametric kernel regression approach for pricing options on stock market index

Previous options studies typically assume that the dynamics of the underlying asset price follow a geometric Brownian motion (GBM) when pricing options on stocks, stock indices, currencies or futures. However, there is mounting empirical evidence that the volatility of asset price or return is far from constant. This article, in contrast to studies that use parametric approach for option pricing, employs nonparametric kernel regression to deal with changing volatility and, accordingly, prices options on stock index. Specifically, we first estimate nonparametrically the volatility of asset return in the GBM based on the Nadaraya–Watson (N–W) kernel estimator. Then, based on the N–W estimates for the volatility, we use Monte Carlo simulation to compute option prices under different settings. Finally, we compare the index option prices under our nonparametric model with those under the Black–Scholes model and the Stein–Stein model.     

Efficiency in an Economy with Fixed Costs

It is by now well known that in an economy with increasing returns, first-best efficiency may be impossible to attain through an equilibrium concept based on market prices, even if firms are regulated to follow marginal cost pricing. We examine the efficiency issue in a special but important class of economies in which the only source of nonconvexities is the presence of fixed costs. Even in this context, it is possible that none of the equilibria based on marginal cost pricing are efficient (unless additional, strong assumptions are made). We argue that available results on the existence of an efficient two-part tariff equilibrium rely on very strong assumptions, and we provide a positive result using a weak surplus condition. Our approach can also be used to establish the existence of an efficient marginal cost pricing equilibrium with endogenously chosen lump-sum taxes if the initial endowment is efficient in the economy without the production technology.     

Competitive equilibria of economies with a continuum of consumers and aggregate shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of competitive equilibrium is proven and a recursive characterization is established. In particular, it is shown that for any competitive equilibrium, there is a payoff equivalent competitive equilibrium that is generated by a suitably defined recursive equilibrium.     

Factor Substitution and Relative Factor Prices

This paper examines the effects of factor endowments on factor prices in a three‐factor, two‐commodity general‐equilibrium model with endogenous commodity demand and prices. Unlike the conventional small open‐economy model that assumes constant commodity prices, factor substitution influences the direction of these effects. When a factor endowment increases, complementarity with the expanding factor benefits an unchanged factor, but substitutability harms it. If the unchanged factors are complements, there is a possibility of a rise in the expanding factor's price. A comparison of this closed‐economy model with the small open‐economy model reveals the role of international trade, which dampens the effect on the expanding factor's price.