On the Spurious Correlation Between Sample Betas and Mean Returns

Abstract

Cornerstone asset pricing models, such as capital asset pricing model (CAPM) and arbitrage pricing theory (APT), yield theoretical predictions about the relationship between expected returns and exposure to systematic risk, as measured by beta(s). Numerous studies have investigated the empirical validity of these models. We show that even if no relationship holds between true expected returns and betas in the population, the existence of low-probability extreme outcomes induces a spurious correlation between the sample means and the sample betas. Moreover, the magnitude of this purely spurious correlation is similar to the empirically documented correlation, and the regression slopes and intercepts are very similar as well. This result does not necessarily constitute evidence against the theoretical asset pricing models, but it does shed new light on previous empirical results, and it points to an issue that should be carefully considered in the empirical testing of these models. The analysis points to the dangers of relying on simple least squares regression for drawing conclusions about the validity of equilibrium pricing models.     

卖空约束下的公司债券定价

信用溢价之谜是近年来在资产定价领域中热点研究问题之一,本文试图从结构化模型角度对这一问题做出解释。通过引入市场卖空约束条件,我们建立了新的公司债券定价模型。由于卖空约束在现实市场中普遍存在,因此建立这种结构化模型是具有实际意义的。实证研究表明该模型可以得出比现有模型更高的信用溢价,能很好地解释信用溢价之谜。     

The influence of corporate taxes on pricing and capital structure in property-liability insurance

A change in the corporate tax level can have a significant impact on rate making and capital structure for insurance companies. The purpose of this paper is to study this effect on competitive equity-premium combinations for different asset and liability models while retaining a fixed safety level. This is a crucial consideration as a change in the tax rate leads, in general, to a different risk of insolvency. Hence, fixing the safety level serves to isolate the effect of taxes without shifting the insurer’s risk situation whenever taxes are varied. The model framework includes stochastic assets as well as stochastic claims costs. We further compare the results for liability models with and without a jump component. Insurance rate making is conducted using option pricing theory.     

American option prices in a Markov chain market model

This paper is a sequel to our previous paper ‘A New Paradigm in Asset Pricing’ in which we construct a model for asset pricing in a world where the randomness is modeled by a Markov chain. In this paper we develop a theory of optimal stopping and related variational inequalities for American options in this model. A version of Saigal's Lemma is established and numerical results obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

考虑政府约束的再制造闭环供应链差别定价博弈模型

本文考虑政府对废弃产品回收的奖惩约束措施,针对一类由制造商、零售商构成的再制造闭环供应链系统,基于博弈论方法研究了新产品和再制造品存在定价差别时集中决策和分散决策模式下的定价策略,得出了闭环供应链成员的最优定价策略和利润,并分析了政府约束措施对闭环供应链运作的影响。研究表明:集中决策下供应链效率高于Stackelberg博弈分散决策,为此设计了一个收益共享协调定价契约实现了闭环供应链的协调,进而分析了政府回收约束情况下再制造过程利润超过制造过程的再制造优先条件。算例分析验证了定价策略及协调机制的有效性。     

Esscher transforms and consumption-based models

The Esscher transform is an important tool in actuarial science. Since the pioneering work of Gerber and Shiu (1994), the use of the Esscher transform for option valuation has also been investigated extensively. However, the relationships between the asset pricing model based on the Esscher transform and some fundamental equilibrium-based asset pricing models, such as consumption-based models, have so far not been well-explored. In this paper, we attempt to bridge the gap between consumption-based models and asset pricing models based on Esscher-type transformations in a discrete-time setting. Based on certain assumptions for the distributions of asset returns, changes in aggregate consumptions and returns on the market portfolio, we construct pricing measures that are consistent with those arising from Esscher-type transformations. Explicit relationships between the market price of risk, and the risk preference parameters are derived for some particular cases.     

Projection Pricing

A significant problem in modern finance theory is how to price assets whose payoffs are outside the span of marketed assets. In practice, prices of assets are often assigned by using the capital asset pricing model (CAPM). If the market portfolio is efficient, the price obtained this way is equal to the price of an asset whose payoff, viewed as a vector in a Hilbert space of random variables, is projected orthogonally onto the space of marketed assets. This paper looks at the pricing problem from this projection viewpoint. It is shown that the results of the CAPM formula are duplicated by a formula based on the minimum-norm portfolio, and this pricing formula is valid even in cases when there is no efficient portfolio of risky assets. The relation of the pricing to other aspects of projection are also developed. In particular, a new pricing formula, called the correlation pricing formula, is developed that yields the same price as the CAPM, but is likely to be more accurate and more convenient than the CAPM in some cases.     

Asymptotic asset pricing and bubbles

We define the concept of asymptotic superreplication, and prove a duality principle of asset pricing for sequences of financial markets (e.g., weakly converging financial markets and large financial markets) based on contiguous sequences of equivalent local martingale measures. This provides a pricing mechanism to calculate the fundamental value of a financial asset in the asymptotic market. We introduce the notion of asymptotic bubbles by showing that this fundamental value can be strictly lower than the current price of the asset. In the case of weakly converging markets, we show that this fundamental value is equal to an expectation of the terminal value of the asset in the weak-limit market. From a practical perspective, we relate the asymptotic superreplication price to a limit of quantile-hedging prices. This shows that even when a price process is a true martingale, it can have properties similar to a bubble, up to a set of small probability. For practical applications, we give examples of weakly converging discrete-time models (e.g. some GARCH models) and large financial models that present bubbles.     

金融资产定价的统一视角及其在风险管理中的应用

在"资本资产定价基本原理"的基础上,通过对于传统定价方法过程的分析和总结,推导了金融资产定价的统一公式,并指明了效用理论中关于人的效用的刻画可以通过该公式中的权重系数体现出来,构成结合了效用理论和个体差异的"金融资产定价的统一视角";针对这一"统一视角",该文举出一例,将其应用于个人投资股票市场风险管理的实践中.     

Binary option pricing using fuzzy numbers

A binary option is a type of option where the payout is either fixed after the underlying stock exceeds the predetermined threshold (or strike price) or is nothing at all. Traditional option pricing models determine the option’s expected return without taking into account the uncertainty associated with the underlying asset price at maturity. Fuzzy set theory can be used to explicitly account for such uncertainty. Here we use fuzzy set theory to price binary options. Specifically, we study binary options by fuzzifying the maturity value of the stock price using trapezoidal, parabolic and adaptive fuzzy numbers.     

Arbitrage in skew Brownian motion models

Empirical skewness of asset returns can be reproduced by stochastic processes other than the Brownian motion with drift. Some authors have proposed the skew Brownian motion for pricing as well as interest rate modelling. Although the asymmetric feature of random return involved in the stock price process is driven by a parsimonious one-dimensional model, we will show how this is intrinsically incompatible with a modern theory of arbitrage in continuous time. Application to investment performance and to the Black-Scholes pricing model clearly emphasize how this process can provide some kind of arbitrage.     

Asymptotic approach to the pricing of geometric asian options under the CEV model

This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.     

股票价格服从指数O-U过程的再装期权定价

期权及其定价理论是目前金融管理,金融工程研究的前沿与热点问题.本文在标的资产的价格服从指数O-U过和模型假设下,运用G irsanov定理获得了该过程的唯一等价鞅测度.用期权定价的鞅方法,得出了再装期权的定价公式.     

The arbitrage pricing theorem with incomplete preferences

This paper proves existence of equilibrium and the arbitrage pricing theorem for an asset exchange economy, where individuals' preferences may be incomplete or intransitive. This extends existing results to more general preferences. We also prove the arbitrage pricing theorem for a theory of choice under uncertainty by Bewley [Bewley, T. F. (2002), Knightian decision theory: part I, Decisions in Economics and Finance 25, 79–110.]. These preferences model Knightian uncertainty by preferences which may be incomplete but satisfy independence.     

摩擦市场中无套利、近似无套利与没有免费午餐

本文研究具有摩擦的证券市场中资产定价,即在局部凸拓扑空间中弱与强无套利、弱与强近似无套利及弱与强没有免费午餐.我们建立了这三个概念之间的关系并且解决了资产定价理论的估值问题.     

存在价格差异的闭环供应链定价策略及契约协调

以零售商回收模式为对象,采用博弈论方法,研究再制造产品与新产品存在销售价格差异以及废旧产品存在回收价格差异时闭环供应链的定价策略及契约协调问题。对闭环供应链系统在分散决策和集中决策下的定价模型进行了分析,得到了系统各成员的最优定价策略和利润,发现分散决策会造成系统效率的损失。为此提出一种改进的特许经营费用契约对闭环供应链进行协调,使得闭环供应链系统不仅消除了"双重边际化"的问题,而且实现了完美协调。算例分析验证了定价策略及契约协调机制的有效性。     

Option pricing and hedging for optimized Lévy driven stochastic volatility models

This paper pays attention to Ornstein-Uhlenbeck (OU) based stochastic volatility models with marginal law given by Classical Tempered Stable (CTS) distribution and Normal Inverse Gaussian (NIG) distribution, which are subclasses of infinite activity Lévy processes and are compared to finite activity Barndorff-Nielsen and Shephard (BNS) model. They are applied to option pricing and hedging in capturing leptokurtic features in asset returns and clustering effect in volatility that are consistently observed phenomena in underlying asset dynamics. The analytical formula of option pricing can be obtained through use of characteristic functions and Fast Fourier Transform (FFT) technique. Additionally, we introduce two hybrid optimization techniques such as hybrid Particle Swarm optimization (PSO) algorithm and hybrid Differential Evolution (DE) algorithm into parameters calibration schemes to improve the calibration quality for newly constructed models. Finally, we conduct experiments on Chinese emerging option markets to examine the performance of proposed models exploiting hybrid optimization techniques.     

Option pricing when the regime-switching risk is priced

We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.     

Trading volume in models of financial derivatives

This paper develops a subordinated stochastic process model for an asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, the paper makes use of the under-used market statistic of transaction count as a suitable proxy for the information flow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn. Both the asset price and the number of trades are used in parameter estimation. The underlying process is found to be fast mean reverting, and this is exploited to perform an asymptotic expansion. The implied volatility skew is then used to calibrate the model.