Corporate security prices in structural credit risk models with incomplete information

The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to determine the price dynamics of traded securities, one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filtering problem for a stopped diffusion process and apply results from the filtering literature to this problem. In this way, we obtain an stochastic partial differential equation characterization for the filter density. Moreover, we characterize the default intensity under incomplete information and determine the price dynamics of traded securities. Armed with these results, we study derivative assets in our setup: We explain how the model can be applied to the pricing of options on traded assets and we discuss dynamic hedging and model calibration. The paper closes with a small simulation study.     

No Arbitrage in Discrete Time Under Portfolio Constraints

In frictionless securities markets, the characterization of the no-arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997).     

Pricing Options With Curved Boundaries1

This paper provides a general valuation method for the European options whose payoff is restricted by curved boundaries contractually set on the underlying asset price process when it follows the geometric Brownian motion. Our result is based on the generalization of the Levy formula on the Brownian motion by T. W. Anderson in sequential analysis. We give the explicit probability formula that the geometric Brownian motion reaches in an interval at the maturity date without hitting either the lower or the upper curved boundaries. Although the general pricing formulae for options with boundaries are expressed as infinite series in the general case, our numerical study suggests that the convergence of the series is rapid. Our results include the formulae for options with a lower boundary by Merton (1973), for path-dependent options by Goldman, Sossin, and Gatto (1979), and for some corporate securities as special cases.     

ASSET PRICE BUBBLES IN INCOMPLETE MARKETS*

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the “no free lunch with vanishing risk (NFLVR)” and “no dominance” assumptions. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. We propose a new theory for bubble birth that involves a nontrivial modification of the classical martingale pricing framework. This modification involves the market exhibiting different local martingale measures across time—a possibility not previously explored within the classical theory. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles; (ii) European call options and discounted forward prices have bubbles whose magnitudes are related to the asset's price bubble; (iii) with no dividends, American call options are not exercised early; (iv) European put‐call parity in market prices must always hold, regardless of bubbles; and (v) futures price bubbles can exist and they are independent of the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.     

Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims—an underlying frictionless linear pricing rule—that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches—a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule—the supremum of the underlying frictionless linear pricing rules—for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.     

TUG‐OF‐WAR,MARKET MANIPULATION,AND OPTION PRICING

We develop an option pricing model based on a tug‐of‐war game. This two‐player zero‐sum stochastic differential game is formulated in the context of a multidimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the nonlinear and completely degenerate infinity Laplace operator.     

Conflicts of Interest Arising from the Prudent Investor Rule: Ethical Implications for Over-the-Counter Derivative Securities

The Prudent Investor Rule creates a potential ethical dilemma for investment advisors selling over-the-counter financial products issued by their firms. The "opportunity" to defraud investors using complex, over-the-counter derivative securities designed for client-specific risk management is much higher than for exchange traded securities. This paper emphasizes the ethical responsibility held by trustees and their organizations to eliminate potential conflict of interests through internal control and monitoring. Independent evaluations of the performance of investment advisors and independent appraisals of complex over-the-counter securities are important in reducing the risks of conflicts of interest. Recent lessons learned from the corporate ethics crisis and requirements of the 2002 Sarbanes Oxley Act would suggest that conflict of interest must be eliminated with third party validation of derivative pricing. By performing due diligence and validation, the trustee is able to satisfy the requirements under the Prudent Investor Rule.     

The Value of Imputation Tax Credits on Australian Hybrid Securities

Hybrid securities are becoming an increasingly important component of the capital structure of Australian firms. While displaying characteristics of both debt and equity, one principal equity attribute of hybrids is their ability to pay franked dividends. This enables resident domestic investors to claim corporate tax payments as a credit against personal tax obligations under Australia's dividend imputation tax system. This paper estimates a value for the ‘franking credits’ that attach to hybrid securities by examining stock price changes around ex‐dividend dates. We add to the literature that examines the ex‐day price changes of ordinary shares (OS) in that the hybrid securities we examine have high dividend yields and are relatively insensitive to market movements. Therefore the signal‐to‐noise ratio is much higher than for OS. Our analysis reveals that cum‐dividend day prices on hybrid securities do not include any value for franking credits. This result is consistent with the notion that the price‐setting investor in the Australian market is a foreign investor who places no value on franking credits.     

The unethical exploitation of shareholders in management buyout transactions

The accurate pricing of securities in the capital markets depends upon the markets being both efficient and fair. In management buyout transactions (MBOs), the price bid by inside managers enhances the efficient pricing of securities but raises a reasonable doubt about the fairness to existing shareholders. This study addresses this fairness question in MBOs and offers short-term and long-term legal alternatives which allow both the efficiency and fairness criteria to be met. In the short-term the case law established in the Basic v. Levinson decision for merger negotiation disclosures should be applied to MBO transactions. Over the longer horizon, legislative changes should be made to existing securities laws. Applying the investor protection principles of the 1933 and 1934 securities acts to MBO transactions will suppress the temptation of managers to extract shareholder wealth for their personal gain. Frederick P. Schadler, Assistant Professor of Finance at East Carolina University, in Greenville, North Carolina. Research interests include security issuances, investment banking, and ethical issues related to securities regulation. He has presented papers at regional and national meetings and has published in the Journal of Financial and Strategic Decisions and the Memphis State University Law Review. Jack E. Karns, an Associate Professor of Business Law at East Carolina University. Research is directed toward corporate law, securities, and government regulation of business issues including ethical considerations. He has published in numerous legal journals including the Dickinson, University of Richmond, and Memphis State University Law Reviews.     

OPTIMAL TIMING FOR AN INDIVISIBLE ASSET SALE

In this paper, we investigate the pricing via utility indifference of the right to sell a non‐traded asset. Consider an agent with power utility who owns a single unit of an indivisible, non‐traded asset, and who wishes to choose the optimum time to sell this asset. Suppose that this right to sell forms just part of the wealth of the agent, and that other wealth may be invested in a complete frictionless market. We formulate the problem as a mixed stochastic control/optimal stopping problem, which we then solve. We determine the optimal behavior of the agent, including the optimal criteria for the timing of the sale. It turns out that the optimal strategy is to sell the non‐traded asset the first time that its value exceeds a certain proportion of the agent's trading wealth. Further, it is possible to characterize this proportion as the solution to a transcendental equation.     

Non-convex optimal portfolio sets and constant relative risk aversion

This paper shows by example that, under constant relative risk aversion (CRRA), the set of optimal portfolios can be non-convex even in the presence of a complete set of Arrow-Debreu securities. This implies that, with exclusively CRRA investors, market models without a strong distributional assumption such as that of the capital asset pricing model cannot be tested by testing the optimality of the market portfolio, or by assuming a representative investor. This demonstration extends the key result of Dybvig and Ross [Dybvig, P. H., & Ross S. A. (1982). Portfolio efficient sets. Econometrica, 50, 1525–1546], who showed an example of non-convexity with less restrictive utility assumptions but which could not apply to the case of a complete set of Arrow-Debreu securities.     

Pricing Barrier Options with Time–Dependent Coefficients

We consider the problem of pricing derivative securities which involve a barrier clause. We give general techniques to calculate, or estimate accurately, barrier option prices, using methods for estimating diffusion process boundary hitting times. The solution gives a simple, easy–to–use, method for calculating barrier option prices.     

THE MEANING OF MARKET EFFICIENCY

Fama defined an efficient market as one in which prices always “fully reflect” available information. This paper formalizes this definition and provides various characterizations relating to equilibrium models, profitable trading strategies, and equivalent martingale measures. These various characterizations facilitate new insights and theorems relating to efficient markets. In particular, we overcome a well‐known limitation in tests for market efficiency, i.e., the need to assume a particular equilibrium asset pricing model, called the joint‐hypothesis or bad‐model problem. Indeed, we show that an efficient market is completely characterized by the absence of both arbitrage opportunities and dominated securities, an insight that provides tests for efficiency that are devoid of the bad‐model problem. Other theorems useful for both the testing of market efficiency and the pricing of derivatives are also provided.     

Is volatility risk priced in the securities market? Evidence from S&P 500 index options

The authors examine whether volatility risk is a priced risk factor in securities returns. Zero‐beta at‐the‐money straddle returns of the S&P 500 index are used to measure volatility risk. It is demonstrated that volatility risk captures time variation in the stochastic discount factor. The results suggest that straddle returns are important conditioning variables in asset pricing, and investors use straddle returns when forming their expectations about securities returns. One interesting finding is that different classes of firms react differently to volatility risk. For example, small firms and value firms have negative and significant volatility coefficients, whereas big firms and growth firms have positive and significant volatility coefficients during high‐volatility periods, indicating that investors see these latter firms as hedges against volatile states of the economy. Overall, these findings have important implications for portfolio formation, risk management, and hedging strategies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:617–642, 2007     

Pricing by Arbitrage Under Arbitrary Information

A substantial applications literature on pricing by arbitrage has effectively restricted information to that arising solely from securities markets; return distributions are then governed solely by past prices. We reconsider pricing by arbitrage in markets rendered incomplete by arbitrary information, which, moreover, may influence required returns. We show that contingent claims depending solely on securities' normalized price histories are priced by arbitrage if and only if all risk-adjusted probabilities agree upon the law of primitive securities' normalized prices. We show how existing diffusion-based results can be preserved, and resolve an issue relating to Merton's (1973) stochastic interest rate model.     

OPTION PRICING USING THE TERM STRUCTURE OF INTEREST RATES TO HEDGE SYSTEMATIC DISCONTINUITIES IN ASSET RETURNS1

This paper demonstrates the use of term-structure-related securities in the design of dynamic portfolio management strategies that hedge certain systematic jump risks in asset return. Option pricing formulas based on the absence of arbitrage opportunities in this context are also developed. the analysis is for the case where assets returns are driven by a finite number of Brownian motions and an m-variate point process. the inclusion of :the additional traded assets in the term structure makes it possible to hedge systematic jumps imbedded in the m variate point process.     

Static hedging and pricing of exotic options with payoff frames

We develop a general framework for statically hedging and pricing European‐style options with nonstandard terminal payoffs, which can be applied to mixed static–dynamic and semistatic hedges for many path‐dependent exotic options including variance swaps and barrier options. The goal is achieved by separating the hedging and pricing problems to obtain replicating strategies. Once prices have been obtained for a set of basis payoffs, the pricing and hedging of financial securities with arbitrary payoff functions is accomplished by computing a set of “hedge coefficients” for that security. This method is particularly well suited for pricing baskets of options simultaneously, and is robust to discontinuities of payoffs. In addition, the method enables a systematic comparison of the value of a payoff (or portfolio) across a set of competing model specifications with implications for security design.     

Coefficient of determination in a simultaneous equation model: A pedagogic note

The simultaneity of the market for securities has been recognized by a number of finance authors. Simkowitz and Jones [10] advocate the use of a simultaneous equation system to capture some of the relationships among the securities in a homogeneous set. Simkowitz and Logue [11], and Jones and Simkowitz [6], have performed studies using a simultaneous equation system in a capital asset pricing framework. Marcis and Smith [9] call for the use of the simultaneous methodology when there is a strong residual correlation between securities. Simultaneous equation systems have been used in other areas of finance by authors such as Barnea [1], Herbst [5], and Logue and Lindvall [8]. This note explores how anomalies concerning the coefficient of determination (R²) mentioned in previous research could have occured. Conditions under which the (R²) does not have its usual properties and an example is given.     

金融衍生品的定价能力研究:以中国市场权证为例

文章应用线性多因子模型研究了我国权证的定价能力,发现权证是非冗余的,故对风险资产的收益率有解释能力,且对小公司和价值股的解释能力强于大公司和成长股.文章还利用随机贴现因子的思想,用GMM方法做了稳健性检验.两种方法从不同角度得到同样的结论,权证价格中包含定价因素,金融衍生品的发展能提高市场定价效率,使市场趋于完全.     

投资者注意力指标测度的研究综述与展望

投资者注意力从认知心理学视角开启了行为金融学新的研究范式,并对金融资产定价和财务行为产生了深远的影响。而实证研究中如何科学测度投资者注意力一直是该领域研究的难点问题。文章通过对已有文献的梳理,从竞争性信息的干扰程度、信息的显著和易处理程度以及交易特性三个方面对投资者注意力的测度文献进行了系统整理和分析,重点在导入认知心理学的理论基础上,对比分析了这三方面指标的优缺点、注意问题及其适应范围,最后提出了未来的研究展望。