Hedge Fund Indices: Reconciling Investability and Representativity

Following a growing concern among investors about the quality of hedge fund index return data, this paper addresses the question of whether designing hedge fund indices that fulfil the usual requirements (in particular representative and investable) is or not a feasible task, given a variety of features that are specific to that industry. To test whether or not investability should necessarily come at the cost of representativity, we use a well‐known methodology in the asset pricing literature based on the concept of factor replicating portfolios. Our results suggest that it is actually possible to construct representative indices based on a limited number of funds that are open to new investments, except perhaps in the case of equity market neutral strategies, provided that: i) these funds are suitably selected and ii) a portfolio is constructed with the objective of replicating the common trend in hedge fund returns for a given strategy. A range of robustness tests are performed that show that high correlation of the factor replicating portfolios with the common factor of returns for each strategy is remarkably stable with respect to modifying the number of funds in the replicating portfolio or changing the frequency of rebalancing.     

Option pricing with quadratic volatility: a revisit

This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct several errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of option pricing formulas to improve computational performance. Our exposition is based entirely on probabilistic arguments, adding a fresh perspective and new intuition to the existing PDE-dominated literature on the subject. Our main tools are martingale methods and shifts of probability measures; the fact that the underlying process is typically a strict local martingale is carefully considered throughout the paper.     

Option Replication in Discrete Time with Transaction Costs

Option replication is discussed in a discrete-time framework with transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black-Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values.     

A Non-Parametric Option Pricing Model: Theory and Empirical Evidence

In this paper, we propose an empirically-based, non-parametric option pricing model to evaluate S&P 500 index options. Given the fact that the model is derived under the real measure, an equilibrium asset pricing model, instead of no-arbitrage, must be assumed. Using the histogram of past S&P 500 index returns, we find that most of the volatility smile documented in the literature disappears.     

Learning to forecast the exchange rate: Two competing approaches

This paper compares two competing approaches to model foreign exchange market participants' behavior: statistical learning and fitness learning. These learning mechanisms are applied to a set of predictors: chartist and fundamentalist rules. We examine which of the learning approaches is best in terms of replicating the exchange rate dynamics within the framework of a standard asset pricing model. We find that both learning methods reveal the fundamental value of the exchange rate in the equilibrium but only fitness learning creates the disconnection phenomenon and only statistical learning replicates volatility clustering. None of the mechanisms is able to produce a unit root process but both of them generate non-normally distributed returns.     

Presidential Address: Liquidity and Price Discovery

This paper examines the implications of market microstructure for asset pricing. I argue that asset pricing ignores the central fact that asset prices evolve in markets. Markets provide liquidity and price discovery, and I argue that asset pricing models need to be recast in broader terms to incorporate the transactions costs of liquidity and the risks of price discovery. I argue that symmetric information‐based asset pricing models do not work because they assume that the underlying problems of liquidity and price discovery have been solved. I develop an asymmetric information asset pricing model that incorporates these effects.     

无套利定价理论及未来研究方向

本文首先对以无套利假设作为理论基础的经典金融资产定价理论进行了梳理。然后,基于经典理论的预测结果与实际金融市场数据不能很好吻合的事实,以及行为金融学所指出的无套利定价理论的局限性,提出以一价定律作为金融资产定价的理论出发点具有重要的理论和现实意义。     

The optimal timing of the transfer of hidden reserves in the German and Austrian tax systems

The lower-of-cost-or-market principle implies that assets may be sold above book value, by which hidden reserves are disclosed. To avoid taxation of these hidden reserves, in German-speaking countries companies are allowed to transfer them to a newly purchased asset within a fixed time period. In this paper, the optimal timing of hidden reserves transfers is developed with special attention to the term structure of interest rates and interest rate risk, and using the replicating principle known from the field of finance. The paper presents one model under certainty and, as a generalization of this model, another model under interest rate risk. In both models, the criterion used for decision-making is the value of the right to transfer, which can be interpreted as the initial cost of a replicating/hedging strategy for tax payments saved/incurred. In the model under certainty, the net present value concept is used to derive the value of the right to transfer. The procedure used in the model under interest rate risk is a combination of flexible planning and the no-arbitrage approach common in derivatives pricing. It is shown that the right to transfer hidden reserves with flexible timing is equivalent to an American-style exchange option. In addition, the impact of term-structure volatility on the value of the right to transfer is analyzed. The technique presented in this paper can also be used to solve other timing problems resulting from trade-offs between early and late tax payments/tax benefits. Copyright © 2002 John Wiley & Sons, Ltd.     

A financial CCAPM and economic inequalities

This paper considers a wealth heterogeneous multi-agent (MA) financial pricing CCAPM model. It is based on the following observations: (a) A distinction between what agents are willing to pay for consumption and what they actually pay. The former is a function of a number of factors including the agent’s wealth and risk preferences and the latter is a function of all other agents’ aggregate consumption or equivalently, their wealth committed to consumption. (b) Unlike traditional pricing models that define a representative agent underlying the pricing model, this paper assumes that each agent is in fact ‘Cournot-gaming’ a market defined by all other agents. This results in a decomposition of an n-agents game into n games of two agents, one a specific agent and the other a synthetic agent (a proxy for all other agents), on the basis of which an equilibrium consumption price solution is defined. The paper’s essential results are twofold. First, a Martingale pricing model is defined for each individual agent expressing the consumer willingness to pay (his utility price) and the market price—the price that all agents pay for consumption. In this sense, price is unique defined by each agent’s ‘Cournot game’ Agents’ consumption are then adjusted accordingly to meet the market price. Second, the pricing model defined is shown to account for agents wealth distribution pointing out that all agents valuations are a function of their and others’ wealth, the information they have about each other and other factors which are discussed in the text. When an agent has no wealth or cannot affect the market price of consumption, then this pricing model is reduced to the standard CCAPM model while any agent with an appreciable wealth compared to other agents, is shown to value returns (and thus future consumption) less than wealth-poor agents. As a result, this paper will argue that even in a financial market with an infinite number of agents, if there are some agents that are large enough to affect the market price by their decisions, such agents have an arbitrage advantage over the poorer agents. The financial CCAPM MA pricing model has a number of implications, some of which are considered in this paper. Finally, some simple examples are considered to highlight the applicability of this paper to specific financial issues.     

Martingalized historical approach for option pricing

In a discrete time option pricing framework, we compare the empirical performance of two pricing methodologies, namely the affine stochastic discount factor (SDF) and the empirical martingale correction methodologies. Using a CAC 40 options dataset, the differences are found to be small: the higher order moment correction involved in the SDF approach may not be that essential to reduce option pricing errors. This paper puts into evidence the fact that an appropriate modelling under the historical measure associated with an adequate correction (that we call here a “martingale correction”) permits to provide option prices which are close to market ones.     

中小企业债务融资产品定价影响因素分析

中小企业资产规模小、抗风险能力差,其融资面临较大的困难,极大地影响中小企业的发展。为了解决中小企业融资难的问题,本文对中小企业融资现状进行分析,结合中国目前中小企业融资的实际情况,提出了中小企业债务融资产品定价多元回归模型,分析了影响中小企业债券类产品定价的主要因素。     

International Corporate Tax Avoidance Practices: Evidence from Australian Firms

This paper examines the international corporate tax avoidance practices of publicly listed Australian firms. Based on a hand-collected sample of 203 publicly listed Australian firms over the 2006–2009 period (812 firm-years), our regression results indicate that there are several practices Australian firms use to aggressively reduce their tax liabilities. Specifically, we find that thin capitalization, transfer pricing, income shifting, multinationality, and tax haven utilization are significantly associated with tax avoidance. In fact, based on the magnitude and significance levels of the regression coefficients in our study, thin capitalization and transfer pricing represent the primary drivers of tax avoidance, whereas income shifting and tax haven utilization are less important. Finally, our additional regression results show that tax havens are likely to be used together with thin capitalization and transfer pricing to maximize international tax avoidance opportunities via the increased complexity of transactions carried out through tax havens.     

The QLBS Q-Learner goes NuQLear: fitted Q iteration,inverse RL,and option portfolios

The QLBS model is a discrete-time option hedging and pricing model that is based on Dynamic Programming (DP) and Reinforcement Learning (RL). It combines the famous Q-Learning method for RL with the Black–Scholes (–Merton) (BSM) model's idea of reducing the problem of option pricing and hedging to the problem of optimal rebalancing of a dynamic replicating portfolio for the option, which is made of a stock and cash. Here we expand on several NuQLear (Numerical Q-Learning) topics with the QLBS model. First, we investigate the performance of Fitted Q Iteration for an RL (data-driven) solution to the model, and benchmark it versus a DP (model-based) solution, as well as versus the BSM model. Second, we develop an Inverse Reinforcement Learning (IRL) setting for the model, where we only observe prices and actions (re-hedges) taken by a trader, but not rewards. Third, we outline how the QLBS model can be used for pricing portfolios of options, rather than a single option in isolation, thus providing its own, data-driven and model-independent solution to the (in)famous volatility smile problem of the Black–Scholes model.     

Return generating process and the determinants of term premiums

This paper examines asset pricing theories for treasury bonds using longer maturities than previous studies and employing a simple multi-factor model. We allow bond factor loadings to vary over time according to term structure variables. The model examines not only the time variation in the expected returns of bonds but also their unexpected returns. This allows us to explicitly test some asset pricing restrictions which are difficult to study under existing frameworks. We confirm that the pure expectation theory of the term structure of interest rates is rejected by the data. Our empirical study of a two-factor model finds substantial evidence of time-varying term-premiums and factor loadings. The fact that factor loadings vary with long-term interest rates and yield spreads suggest that bond return volatilities are sensitive to interest rate levels.     

Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results

Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, though, including the efficacy of the standard alternating direction implicit (ADI) numerical methods for solving SV and LSV pricing problems. In general, the amount of required computations for these methods is very substantial. In this paper, we address some of these issues and propose a viable alternative to the standard ADI methods based on Galerkin-Ritz ideas. We also discuss various approaches to solving the corresponding pricing problems in a semi-analytical fashion. We use the fact that in the zero correlation case some of the pricing problems can be solved analytically, and develop a closed-form series expansion in powers of correlation. We perform a thorough benchmarking of various numerical solutions by using analytical and semi-analytical solutions derived in the paper.     

Option Pricing and Replication with Transactions Costs

Transactions costs invalidate the Black-Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. Discrete revision using Black-Scholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. This paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision. The technique permits calculation of the transactions costs of option replication and provides bounds on option prices.     

The two-fund separation theorem revisited

This paper resolves two issues regarding the traditional capital asset pricing model with one risk-free asset which seem to have been overlooked in the literature. First, it provides an elementary and complete proof of the two-fund separation theorem which accounts for the fact that asset demand may become undefined if the limiting slopes of the investor’s indifference curves are finite. Second, it shows that an additional limiting condition on investors’ risk aversions is generally necessary to guarantee existence of an equilibrium. Moreover, a generalized existence result is formulated which includes investors who in equilibrium may not invest in risky assets and a simple condition ensuring positive equilibrium asset prices is given.     

Pricing commercial mortgages and their mortgage-backed securities

This article has taken considerable effort to accurately model the complexity of a commercial mortgage and its mortgage-backed security. In fact, it is the first example in the general literature on mortgage pricing to present a comprehensive set of numerical results in which the valuation of a mortgage-backed security is explicitly tied to that of the underlying mortgage. The conclusion we reach is that option pricing provides an accurate and flexible approach to valuing the complex mortgage instruments now being developed in the financial community.     

Contrarian Investment and Macroeconomic Risk

It is now widely accepted that contrarian, or value investment strategies deliver superior returns. Gregory, Harris and Michou (2001) examine the performance of contrarian investment strategies in the UK and find that value strategies formed on the basis of a wide range of measures of value have delivered excess returns that are both statistically and economically significant. However, while value strategies appear to be profitable, the reason for their superior perform‐ ance is far from clear. Under the contrarian model, value strategies are profitable because they are contrarian to naïve strategies such as those that erroneously extrapolate past performance, while under the rational pricing model, value strategies are profitable because they are fundamentally riskier in some sense. In this paper, we discriminate between these two possibilities by undertaking a comprehensive investigation of the relationship between the returns to value investment strategies and various macroeconomic state variables that in a multi‐factor asset pricing model could reasonably be taken as proxies for risk. Moreover, we examine whether the returns to value strategies predict future GDP, consumption and investment growth over and above the contribution of the Fama and French (1993 and 1996) SMB, HML and market factors. While the SMB and HML factors behave in a manner consistent with the rational pricing model, we show that some value strategies in the UK are able to generate excess returns that do not seem to be related to known risk factors.     

西方资产定价理论中的实体经济因素考察——以CAPM模型与B-S期权定价模型为例

本文根据马克思主义经济学有关实体经济因素决定虚拟资本价格的基本原理,分析和评价了CAPM与B-S模型;认为CAPM模型的建模思路存在重大错误;同时还发现,利息率是虚拟资本价格决定中与实体经济连接的重要桥梁,但在虚拟资本价格决定中,仅有利息率一个指标并不能充分反映实体经济的决定作用;本文还因B-S模型建模思路充分考虑了实体经济因素,而从马克思主义经济学角度给予客观评价。