A Fair Pricing Approach to Weather Derivatives

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of the value of the growth optimal portfolio, it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: C16, G10, G13     

A Pricing Framework for Real Estate Derivatives

New methods are developed here for pricing the main real estate derivatives — futures and forward contracts, total return swaps, and options. Accounting for the incompleteness of this market, a suitable modelling framework is outlined that can produce exact formulae, assuming that the market price of risk is known. This framework can accommodate econometric properties of real estate indices such as predictability due to autocorrelations. The term structure of the market price of risk is calibrated from futures market prices on the Investment Property Databank index. The evolution of the market price of risk associated with all five futures curves during 2009 is discussed.     

居民最优消费与投资组合 ——基于不完全市场的分析

运用动态最优控制理论与随机金融分析方法,研究由劳动收入的特质风险与借贷约束导致的非完全市场对消费者最优投资和消费策略、波动及福利损失的影响,得到相应的动态最优投资和消费策略.研究发现:非完全市场会显著抑制消费者的消费动机和投资动机,并加剧消费波动和投资波动.此外,财务困境下非完全市场会对消费者造成高达40％ 的福利损失.     

A Generalized Earnings‐Based Stock Valuation Model with Learning

We present a stock valuation model in an incomplete‐information environment in which the unobservable mean of earnings growth rate (MEGR) is learned and price is updated continuously. We calibrate our model to a market portfolio to empirically evaluate its performance. Of the 8.84% total risk premium we estimate, the earnings growth premium is 4.57%, the short‐rate risk contributes 3.38%, and the learning‐induced risk premium on the unknown MEGR is 0.89% (a nontrivial 10% of the total risk premium). This result highlights the significant learning effect on valuation, implying an additional risk premium in an incomplete‐information environment.     

The Effect of Information Quality on Optimal Portfolio Choice

Three types of agents acting on different information sets are considered: fully informed agents, insiders, and outsiders. Differences in information quality are shown to affect the properties of their optimal portfolios. For an outsider, the share of wealth invested in the stock is decreasing in the variance of the stock. However, for an insider, the effect of an increasing stock variance on the optimal portfolio weight is ambiguous. In a calibration to U.S. data, the confidence intervals of the insider's demand for the stock converge, whereas the outsider's confidence intervals become wider.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced byan expected-utility maximizing investor who, over a given timehorizon, is constrained to hold an asset which cannot be replicatedby dynamic trading and which therefore does not have a uniqueno-arbitrage price. We first derive the private valuation whichthe investor assigns to the nontraded asset in order to determinehis optimal investment in the traded assets. We thereby showthat, as part of this portfolio, the investor hedges the privatevaluation process of the nontraded asset, rather than its marketprice process. We also study the price at which the investorwould be willing to sell the nontraded asset if he were subsequentlyprohibited from trading in it, as well as the amount the investorwould be willing to pay to remove the trading restriction. Allthree values are shown to depend in an intuitive manner on theinvestor’s risk aversion, the residual risk of the nontradedasset unhedged by the traded assets, the difference betweenthe constrained holding and optimal unconstrained holding ofthe asset and the length of the time horizon over which theasset cannot be traded. JEL Classification: G11     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.     

Heterogeneous Background Risks and Portfolio Choice: Evidence from Micro‐level Data

We construct a set of household‐level background risk variables to capture the covariance structure of three nonfinancial assets and two financial assets. These risks are in general statistically significant and economically important for a household's stock market participation and stockholdings. A one‐standard‐deviation increase in background risks reduces the participation probability by 11% and the stockholdings‐to‐wealth ratio by 4%. The volatilities of labor income, housing value, and business income reduce a household's participation and stockholdings. A household with labor income highly correlated with stock (bond) returns is less (more) likely to invest in stock.     

The Subjective Valuation of Indexed Stock Options and Their Incentive Effects

We analyze the potential role of indexed stock options in future pay‐for‐performance executive compensation contracts. We present a unified framework for index‐linked stock options, discuss their incentive effects, argue that indexation schemes based on the capital‐asset pricing model (CAPM) are the most suitable for executive compensation, and derive a subjective pricing model for the class of CAPM‐based indexed stock options. Contrary to earlier work, executives would not be motivated to take on investment projects with high idiosyncratic risk once their lack of wealth diversification and degree of risk aversion are factored into the analysis.     

Bear beta

We test whether bear market risk, time variation in the probability of future bear market states, is priced. We construct an Arrow–Debreu security that pays off in bear market states (AD Bear) from traded Standard & Poor’s (S&P) 500 index options and use its returns to measure bear market risk. We find that bear beta (exposure to bear market risk) has a strong relation with expected stock returns that is robust, persistent, and remains strong among liquid and large stocks. Historical bear beta also predicts future bear market risk exposure. We conclude that bear market risk is priced in the cross section of stock returns.     

The Valuation of Contingent Claims under Portfolio Constraints: Reservation Buying and Selling Prices

With constrained portfolios contingent claims do not generally havea unique price that rules out arbitrage opportunities.Earlier studies have demonstratedthat when there are constraints on the hedge portfolio,a no-arbitrage price interval for any contingent claim exists.I consider the more realistic case where the constraints are imposed on the total portfolio of each investor and define reservation buying and selling prices for contingent claims. I derive propertiesof these prices, show how they can be computed numerically, and study two simple examples in which the reservation prices and the corresponding hedging strategies are compared to the Black–Scholes setting.     

The Equity Premium: Consistent with GDP Growth and Portfolio Insurance

We find that the long‐term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply‐side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926–2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.     

天气衍生品的运作机制与精算定价

天气衍生品是为了规避天气风险给天气敏感行业带来收入的不稳定性而兴起的创新型风险管理工具,其实质是通过衍生合约对天气风险进行分割、重组和交易的证券化产品。不同于传统金融衍生品,天气衍生品的价值取决于温度、湿度或降雨量等天气指数。本文在分析天气衍生品市场发展的基础上,重点探讨了最常见的天气期货和天气期权的运作机制及其精算定价。     

Have European Stocks become More Volatile? An Empirical Investigation of Idiosyncratic and Market Risk in the Euro Area

We examine the dynamics of idiosyncratic risk, market risk and return correlations in European equity markets using weekly observations from 3515 stocks listed in the 12 euro area stock markets over the period 1974–2004. Similarly to Campbell et al. (2001) , we find a rise in idiosyncratic volatility, implying that it now takes more stocks to diversify away idiosyncratic risk. Contrary to the US, however, market risk is trended upwards in Europe and correlations are not trended downwards. Both the volatility and correlation measures are pro‐cyclical, and they rise during times of low market returns. Market and average idiosyncratic volatility jointly predict market wide returns, and the latter impact upon both market and idiosyncratic volatility. This has asset pricing and risk management implications.     

Conditional Asset Pricing and Stock Market Anomalies in Europe

This study provides European evidence on the ability of static and dynamic specifications of the Fama‐French (1993) three‐factor model to price 25 size‐B/M portfolios. In contrast to US evidence, we detect a small‐growth premium and find that the size effect is still present in Europe. Furthermore, we document strong time variation in factor risk loadings. Incorporating these risk fluctuations in conditional specifications of the three‐factor model clearly improves its ability to explain time variation in expected returns. However, the model still fails to completely capture cross‐sectional variation in returns as it is unable to explain the momentum effect.     

The Traditional Hedging Model Revisited with a Nonobservable Convenience Yield

This article examines the hedging of constrained commodity positions with futures contracts. We extend the study of Adler and Detemple (1988a, 1988b) to include a partial information framework where the convenience yield is not observable. As a consequence, futures prices depend on investor's beliefs regarding the value of the convenience yield, and every component of the hedge is impacted by these beliefs. We achieve a decomposition of the demand that clarifies the impact on the optimal hedge of the beliefs, the spot price and the risk‐free rate as well as the hedging horizon.     

The Sophisticated and the Simple: the Profitability of Contrarian Strategies

A variety of variables have been used to form contrarian portfolios, ranging from relatively simple measures, like book‐to‐market, cash flow‐to‐price, earnings‐to‐price and past returns, to more sophisticated measures based on the Ohlson model and residual income model (RIM). This paper investigates whether: (i) contrarian strategies based on RIM perform better or worse than those based on the Ohlson model; (ii) contrarian strategies based on more sophisticated valuation models (e.g. Ohlson and RIM) perform much better than the relatively simpler ranking variables that have been used so extensively in the finance literature. Given that the RIM and Ohlson models require greater information inputs and technical know‐how, and make different implicit assumptions on future abnormal earnings, it is important to ascertain if they offer significantly greater contrarian profits to outweigh the increased costs that they entail. Indeed, our surprising finding is that simple cash flow‐to‐price measures appear to do almost as well as the more sophisticated alternatives. One would have expected the sophisticated models to significantly outperform the simple cash flow to price model for the reasons given by Penman (2007) .