Empirical Tests of the Consumption-Oriented CAPM

The empirical implications of the consumption-oriented capital asset pricing model (CCAPM) are examined, and its performance is compared with a model based on the market portfolio. The CCAPM is estimated after adjusting for measurement problems associated with reported consumption data. The CCAPM is tested using betas based on both consumption and the portfolio having the maximum correlation with consumption. As predicted by the CCAPM, the market price of risk is significantly positive, and the estimate of the real interest rate is close to zero. The performances of the traditional CAPM and the CCAPM are about the same.     

Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

Optimal multi-period consumption and investment with short-sale constraints

This article examines agents’ consumption-investment problem in a multi-period pure exchange economy where agents are constrained with the short-sale of state-dependent risky contingent claims. In equilibrum, agents hold options written on aggregate consumption in their optimal portfolios. Furthermore, under the specific case of quadratic utility, the optimal risk-sharing rule derived for the pricing agent leads to a multifactor conditional consumption-based capital asset pricing model (CCAPM), where excess option returns appear as factors.     

Turbo warrants under stochastic volatility

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]) has considered the pricing of turbo warrants under the Black–Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.     

A perfect storm in the financial market

This study provides a model explaining how small changes in asset prices may disrupt an entire financial market. Based on the capital asset pricing model (CAPM), our model implies that during a market crash, asset price changes affect the relative distribution of the CAPM betas of individual assets and force all tradable assets to co-move. Using US stock market data, our empirical results are consistent with the model’s predictions. Overall, the study aids understanding of the price patterns of assets during substantial market downturns, such as financial crises.     

Transaction costs,liquidity risk,and the CCAPM

In this paper, we make a liquidity adjustment to the consumption-based capital asset pricing model (CCAPM) and show that the liquidity-adjusted CCAPM is a generalized model of Acharya and Pedersen (2005). Using different proxies for transaction costs such as the effective trading costs measure of Hasbrouck (2009) and the bid-ask spread estimates of Corwin and Schultz (2012), we find that the liquidity-adjusted CCAPM explains a larger fraction of the cross-sectional return variations.     

Pricing of the currency risk in the Canadian equity market

Based on a three-factor international capital asset pricing model, we examine whether the world market, the local market and the currency risks are priced in the Canadian equity market. The analysis presented in this paper is based on data collected from 2003 to 2010. As the dataset also includes the period of global financial crisis, we examine the issue of risk pricing in the full sample as well as in before and after global financial crisis periods. Unlike most existing studies, the empirical results presented in this paper are based on (i) the quasi maximum likelihood estimation (QMLE) based multivariate GARCH-in-Mean specification and (ii) the generalized method of moments (GMM) techniques. Our empirical analysis based on weekly data on 58 largest Canadian firms indicates that the currency as well as the local and the world market risks are priced in the Canadian equity market. This result holds for all exchange currency rates proxies and in all sample periods. We find that the price of the world market, the local market and the currency risks is time-varying and the Canadian equity market is partially segmented.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve Pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations in the presence of short- andlong-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.     

Hedging jump risk,expected returns and risk premia in jump-diffusion economies

This article presents a pure exchange economy that extends Rubinstein [Bell J. Econ. Manage. Sci., 1976, 7, 407–425] to show how the jump-diffusion option pricing model of Black and Scholes [J. Political Econ., 1973, 81, 637–654] and Merton [J. Financ. Econ., 1976, 4, 125–144] evolves in gamma jumping economies. From empirical analysis and theoretical study, both the aggregate consumption and the stock price are unknown in determining jumping times. By using the pricing kernel, we determine both the aggregate consumption jump time and the stock price jump time from the equilibrium interest rate and CCAPM (Consumption Capital Asset Pricing Model). Our general jump-diffusion option pricing model gives an explicit formula for how the jump process and the jump times alter the pricing. This innovation with predictable jump times enhances our analysis of the expected stock return in equilibrium and of hedging jump risks for jump-diffusion economies.     

信用风险缓释工具定价研究

通过对信用风险缓释工具定价进行研究得出:(1)CRM定价的主要影响因素包括无风险基准利率,标的债券的风险敞口、违约概率、违约损失率和期限,以及CRM期限等。(2)同期国债利率和央行票据利率作为CRM的基准利率较为恰当,且模型定价对不同期限、不同信用等级的CRM定价区分度较为合理,模型定价与CRM发行交易定价较为接近,适合我国现阶段CRM产品定价。(3)可以从完善CRM定价基础数据库、探索CRM定价无风险基础利率、创新CRM标的债券评级制度、引导CRM市场主体多元化和优化CRM市场做市商制度等方面提出CRM定价优化对策。     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital AssetPricing Model (CCAPM), Pareto optimal consumption allocationsare characterized by each agent's consumption process beingadapted to the filtration generated by the aggregate consumptionprocess of the economy. The wealth processes of the agents,however, are adapted to the finer filtration generated by aggregateconsumption and the conditional distribution of future aggregateconsumption. Therefore, in order to achieve pareto optimal consumptionallocations, a sufficiently varied set of assets must existsuch that any wealth process adapted to this finer filtrationcan be implemented by dynamically trading in that set of assets.We provide sufficient conditions for the existence of such aset of assets based on dynamically trading contingent claimson aggregate consumption. In addition, we give sufficient conditionsfor the existence of equilibria in a dynamically effectivelycomplete market in which agents are only able to trade in contingentclaims on aggregate consumption, the market portfolio of firms,and a (numeraire) zero-coupon bond. We demonstrate the roleof short- and long-term contingent claims on aggregate consumptionfor the implementation of Pareto optimal allocations inthe presenceof short- and long-term risks. In addition, in the presenceof personal risks, we demonstrate the role of insurance contracts.JEL Classification: G13.     

First steps towards an equilibrium theory for Lévy financial markets

For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before that, only flow consumption is allowed. The agent’s utility function is assumed to be additive, defined via strictly increasing, strictly concave smooth felicity functions which are bounded below (thus, many CRRA and CARA utility functions are included). For technical reasons we require for our equilibrium existence result that only pathwise continuous trading strategies are permitted in the demand set. The resulting equilibrium asset price processes depend on the agent’s risk aversion (through the felicity functions). Even in our simple, straightforward economy, the equilibrium asset price processes will essentially only be (stochastic) exponential Lévy processes when they are already geometric Brownian motions. Our equilibrium asset pricing formulae can also be modified to obtain explicit equilibrium derivative pricing formulae.     

我国商业银行贷款定价的最优化模型设计

随着我国加入WTO,国内金融市场逐步与国际金融市场接轨,国家也逐渐放开对企业贷款利率上限的管制,商业银行可以根据信贷市场需求确定合理的贷款价格,使贷款利率能充分补偿银行所承担的信用风险以确保安全性和赢利性。本文首先阐述目前商业银行贷款定价方法中存在的问题,指出由于我国信贷市场中普遍存在信息不对称这一情况,已经严重影响了商业银行的经营和决策水平;再结合委托-代理框架,套用最优控制理论,给出一个信息不对称时的合理的贷款定价模型;最后针对如何有效提高我国商业银行运作和管理水平给出一些操作性建议。     

行为如何影响资产定价——理论模型与实证分析

本文基于金融经济学中状态价格与随机折现因子等理论的分析,认为资产定价会受到行为因素的影响.在此基础上本文提出了状态价格函数,并建立了行为影响资产定价的多项式模型.     

Catching up with the Americans

This paper develops an international version of the consumption-based capital asset pricing (CCAPM), which we refer to as “catching up with the Americans.” Previous CCAPM research develops the concept of “catching up with the Joneses,” where a representative economic agent exhibits higher marginal utility of consumption as a result of higher past per capita consumption in his own country. Catching up with the Americans, on the other hand, is an international habit-preference hypothesis. It extends the idea of catching up with the Joneses by stating that consumers of non-U.S. countries gain higher marginal utility of consumption as a result of higher past American consumption growth. Contrary to much of the CCAPM literature, we test this version of the model using long bond rates rather than equity returns. However, like most of the previous research on the CCAPM, the catching up with the Americans model fails to explain the relationship between consumption and asset returns.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

Estimating default barriers from market information

Brockman and Turtle [J. Finan. Econ., 2003, 67, 511–529] develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To eliminate this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive, but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of the asset value and the asset volatility of Brockman and Turtle.     

A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q.JEL Classification: D52, G13     

Can Costs of Consumption Adjustment Explain Asset Pricing Puzzles?

We investigate Grossman and Laroque's (1990) conjecture that costs of adjusting consumption can account, in part, for the empirical failure of the consumption-based capital asset pricing model (CCAPM). We incorporate small fixed costs of consumption adjustment into a CCAPM with heterogeneous agents. We find that undetectably small consumption adjustment costs can account for much of the discrepancy between the observed variance of nondurable aggregate consumption growth and the predictions of the CCAPM, and can partially reconcile nondurable consumption data with the observed equity premium. We conclude that the CCAPM's implications are nonrobust to extremely small adjustment costs.     

Pricing Weather Derivatives Using the Indifference Pricing Approach

Abstract

This paper adopts an incomplete market pricing model–the indifference pricing approach–to analyze valuation of weather derivatives and the viability of the weather derivatives market in a hedging context. It incorporates price risk, weather/quantity risk, and other risks in the financial market. In a mean-variance framework, the relationship between the actuarial price and the indifference price of weather derivatives is analyzed, and conditions are obtained concerning when the actuarial price does not provide an appropriate valuation for weather derivatives. Conditions for the viability of the weather derivatives market are examined. This paper also analyzes the effects of partial hedging, natural hedges, basis risk, quantity risk, and price risk on investors’ indifference prices by examining the distributional impacts of the stochastic variables involved.