Stochastic equilibria for economies under uncertainty with intertemporal substitution

We consider the model of a stochastic pure exchange economy with a finite set of agents whose preferences exhibit local substitution in the sense of Hindy and Huang (1992). In order to prove the existence of Arrow–Debreu equilibria, it is assumed in Bank and Riedel (2001) that smooth subgradients exist (Assumption 1 in Bank and Riedel (2001)) and that they are uniformly bounded from above and away from zero (Assumption 2 in Bank and Riedel 2001). In this paper, we prove that the existence of smooth subgradients implies local properness of preferences. By a slight improvement of classical existence results of the literature, we prove that the local properness of preferences is a sufficient condition for the existence of equilibria, rendering Assumption 2 in Bank and Riedel (2001) superfluous. This work was partially done while F. Riedel was visiting Ceremade at Université Paris–Dauphine     

Discounting earnings with stochastic discount rates

This paper presents new equity valuation formulae in closed form that extend the abnormal earnings growth (AEG) valuation of Ohlson [2005. “On Accounting-Based Valuation Formulae.” Review of Accounting Studies 10: 323–347] to the cases of time-varying or stochastic cost of capital as in Ang and Liu [2004. “How to Discount Cash Flows with Time-Varying Expected Returns.” Journal of Finance 59 (6): 2745–2783] or to cases of stochastic interest rates as in Ang and Liu [2001. “A General Affine Earnings Valuation Model.” Review of Accounting Studies 6: 397–425]. Interest rates are modelled by quadratic term structure models, which are not hindered by restrictions to factors correlation or by other shortcomings of affine term structure models in discounting long-term earnings. This is crucial since valuation can be very sensitive to the correlation between the factors driving earnings and interest rates. Positive correlation reduces price-earnings ratios according to US data. Valuation is also sensitive to the ‘volatility’ of abnormal earnings growth. The residual earnings risk-neutral valuation of Ang and Liu (2001) is adapted to quadratic term structure models.     

Stock index dynamics and derivatives pricing with stochastic interest rates

The paper analyzes the equilibrium valuation of stock index derivatives in an economy with stochastic interest rates and with a representative agent having time-additive power utility. The equilibrium short interest rate dynamics and the equilibrium term structure of interest rates are described by an affine one-factor term structure model. In equilibrium the value of the stock index is a non-trivial function of the short interest rate. The paper investigates the consequences of the induced stock index dynamics for the theoretical spreads between index forward prices and index futures prices and the consequences for the valuation of options on stock index futures.The paper was written while the author was a visiting scholar at Department of Finance, Kellogg Graduate School of Management, Northwestern University. I thank for helpful comments and suggestions from Gurdip Bakshi, Avi Bick, Menachem Brenner (the editor), Zhiwu Chen, San-Lin Chung, Mark Fisher, Andreas Höger, Marti Subrahmanyam, two anonymous referees, and participants at the Western Finance Association meeting in San Diego, the European Financial Management Association meeting in Istanbul, the European Finance Association meeting in Vienna, and the Center of Analytical Finance workshop at University of Aarhus. Financial support from the Danish Natural Science and Social Science Reasearch Councils is gratefully acknowledged.     

Risk-taking incentives of executive stock options and the asset substitution problem

Various theoretical models show that managerial compensation schemes can reduce the distortionary effects of financial leverage. There is mixed evidence as to whether highly levered firms offer less stock‐based compensation, a common prediction of such models. Both the theoretical and empirical research, however, have overlooked the leverage provided by executive stock options. In principle, adjusting the exercise prices of executive stock options can mitigate the risk incentive effects of financial leverage. We show that the near‐universal practice of setting option exercise prices near the prevailing stock price at the date of grant effectively undoes most of the effects of financial leverage. In a large cross‐sectional sample of Canadian option‐granting firms, we find evidence that executives' incentives to take equity risk are negatively rather than positively related to the leverage of their employers.     

Capital market equilibrium with externalities, production and heterogeneous agents

The paper studies general equilibrium in an economy with externalities, production and heterogeneous agents. The model developed builds on Brock [Brock, W.A., 1982. Asset prices in a production economy. In: McCall, J.J. (Ed.), The Economics of Information and Uncertainty. University of Chicago Press, Chicago, pp. 1–43] and Merton [Merton, R.C., 1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510]; it involves both a stock market and a market for loans, together with negative externalities produced by a subset of firms. Importantly, the technological production structure of the firms is reflected in the properties of the shares traded in the stock market. Agents are heterogeneous in their financial choices, potentially discriminating against the firms producing a negative externality. The model sheds light on the utility costs of the discriminating behavior and on the impact on the price of the stock issued by the firm which is responsible for the externality. The model is used to study the factors which may magnify or reduce the impact of discrimination. A set of discriminated firms may be seriously affected only if the discriminating investors command a large portion of overall wealth and/or they do not represent important diversification instruments. The model can be applied to understanding the effects of socially responsible investment, whereby investors discriminate against companies belonging to some sectors which are perceived as socially dangerous or unethical.     

The relative efficiency of market-based environmental policy instruments with imperfect compliance

We study how the relative cost efficiency of three market-based instruments—emission taxes, tradable permits and output taxes—is influenced by the combination of accounting for incomplete compliance and pre-existing labor taxes. First, accounting for violations makes the policy instruments less effective so that environmental damages have to be larger to justify a policy. Secondly, including fines in a second-best setting provides a new means of collecting government revenues and of lessening existing tax distortions. We show that the relative position of grandfathered tradable permits vis-à-vis emission taxes improves considerably when incomplete compliance is incorporated in a second-best setting. A simple AGE model illustrates the results.      

Equilibrium in Competitive Insurance Markets Under Adverse Selection and Yaari's Dual Theory of Risk

Under Yaari's dual theory of risk, we determine the equilibrium separating contracts for high and low risks in a competitive insurance market, in which risks are defined only by their expected losses, that is, a high risk is a risk that has a greater expected loss than a low risk. Also, we determine the pooling equilibrium contract when insurers are assumed non-myopic. Expected utility theory generally predicts that optimal insurance indemnity payments are nonlinear functions of the underlying loss due to the nonlinearity of agents' utility functions. Under Yaari's dual theory, we show that under mild technical conditions the indemnity payment is a piecewise linear function of the loss, a common property of insurance coverages.     

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.     

湖南水污染税的税制设计及征收效应的一般均衡分析

湖南省"两型社会"的深化建设、首批环境税的开征试点、湘江污染的重点治理等事件将湖南省水污染税改革推向了历史的舞台。借鉴国外水污染税开征经验,文章系统地设计了湖南省水污染税征收的基本框架,运用可计算一般均衡(CGE)模型模拟征收水污染税对宏观经济、产业结构、污染物减排等产生的影响。结果表明:开征水污染税宏观经济受损的长期影响要大于短期;对绝大部分行业都带来了不同程度的负面影响,其中短期合成材料制造业产出下降最大,而长期毛纺织和染整精加工业受损最大;然而征收水污染税减少重金属等污染物排放,氨氮、化学需氧量下降尤为显著。     

A stochastic differential game for optimal investment of an insurer with regime switching

We introduce a model to discuss an optimal investment problem of an insurance company using a game theoretic approach. The model is general enough to include economic risk, financial risk, insurance risk, and model risk. The insurance company invests its surplus in a bond and a stock index. The interest rate of the bond is stochastic and depends on the state of an economy described by a continuous-time, finite-state, Markov chain. The stock index dynamics are governed by a Markov, regime-switching, geometric Brownian motion modulated by the chain. The company receives premiums and pays aggregate claims. Here the aggregate insurance claims process is modeled by either a Markov, regime-switching, random measure or a Markov, regime-switching, diffusion process modulated by the chain. We adopt a robust approach to model risk, or uncertainty, and generate a family of probability measures using a general approach for a measure change to incorporate model risk. In particular, we adopt a Girsanov transform for the regime-switching Markov chain to incorporate model risk in modeling economic risk by the Markov chain. The goal of the insurance company is to select an optimal investment strategy so as to maximize either the expected exponential utility of terminal wealth or the survival probability of the company in the ‘worst-case’ scenario. We formulate the optimal investment problems as two-player, zero-sum, stochastic differential games between the insurance company and the market. Verification theorems for the HJB solutions to the optimal investment problems are provided and explicit solutions for optimal strategies are obtained in some particular cases.     

General equilibrium pricing with multiple dividend streams and regime switching

In this paper, we investigate a regime switching Lucas economy in continuous time, with multiple dividend streams and labour income. We determine the asset prices in equilibrium in the economy with regime switching, and derive a system of partial differential equations for the asset prices and the short interest rate. The solutions for the endogenous short interest rate, the bond price and the yield of the bond are obtained. We also consider applications of the equilibrium model and show that the model implies a rich framework for the term structure of interest rates. We demonstrate how the regime switching economy helps to improve the model-implied annual excess rate of return. This assists in explaining the famous equity premium puzzle.     

Growth to value: Option exercise and the cross section of equity returns

We propose a general equilibrium model to study the link between the cross section of expected returns and book-to-market characteristics. We model two primitive assets: value assets and growth assets that are options on assets in place. The cost of option exercise, which is endogenously determined in equilibrium, is highly procyclical and acts as a hedge against risks in assets in place. Consequently, growth options are less risky than value assets, and the model features a value premium. Our model incorporates long-run risks in aggregate consumption and replicates the empirical failure of the conditional capital asset pricing model (CAPM) prediction. The model also quantitatively accounts for the pattern in mean returns on book-to-market sorted portfolios, the magnitude of the CAPM-alphas, and other stylized features of the cross-sectional data.     

Covariance of discounted compound renewal sums with a stochastic interest rate

Formulas have been obtained for the moments of the discounted aggregate claims process, for a constant instantaneous interest rate, and for a claims number process that is an ordinary or a delayed renewal process. In this paper, we present explicit formulas on the first two moments and the joint moment of this risk process, for a non-trivial extension to a stochastic instantaneous interest rate. Examples are given for Erlang claims number processes, and for the Ho–Lee–Merton and the Vasicek interest rate models.     

Time-Varying Variance Risk Premium and the Predictability of Chinese Stock Market Return

A number of studies have shown that the variance risk premium (VRP), defined as the difference between risk-neutral and physical expected variances, has strong predictive power for the excess stock market return, and this predictability peaks at 3- to 6-month prediction horizons. However, little research presents empirical evidences for Chinese stock market due to the absence of option market. Under general equilibrium asset pricing framework, this article estimates time-varying VRP using the Chinese stock market data. We find that the estimated VRP predicts the excess Chinese stock market return, and this forecasting power is stronger at 4- and 5-month horizons, which is consistent with the findings of existing literature.     

Nonparametric estimation and testing of stochastic discount factor

This paper attempts to estimate stochastic discount factor (SDF) proxies nonparametrically using the conditional Hansen–Jagannathan distance. Nonparametric estimation can not only avoid misspecification when dealing with nonlinearity in the model but also provide more precise information about the local properties of the estimators. Empirical studies show that our method performs better than the alternative parametric polynomial models, and furthermore, we find that the return on aggregate wealth can sufficiently explain the SDF proxies when one deals with nonlinearity appropriately.