Semi‐efficient valuations and put‐call parity

We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely, absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy‐and‐hold strategies (called static efficiency). A valuation process for a payoff is then called semi‐efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk‐neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put‐call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put‐call parity respecting valuation formulas in the classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also define and characterize completeness for general semimartingale financial markets and connect this to the classic theory.     

Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1

This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.     

Does corporate hedging affect firm valuation? Evidence from the IPO market

Focusing on the IPO market, we examine the influence of corporate hedging on firm valuation. Consistent with the argument that hedging reduces information asymmetry, we find that hedging IPO firms are associated with lower price revisions and underwriting fees. More important, hedging reduces IPO underpricing, especially for informationally opaque firms. This provides strong evidence that corporate hedging increases firm valuation. We also show that corporate hedging lowers aftermarket idiosyncratic volatility, enhances aftermarket liquidity, and improves the long-term performance of IPO firms. We use both an instrumental variable approach and a regulation change on derivatives supply to address endogeneity concerns.     

Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion

The paper presents some security market pricing results in the setting of a security market equilibrium in continuous time. The theme of the paper is financial valuation theory when the primitive assets pay out real dividends represented by processes of unbounded variation. In continuous time, when the models are also continuous, this is the most general representation of real dividends, and it can be of practical interest to analyze such models.
Taking as the starting point an extension to continuous time of the Lucas consumption-based model, we derive the equilibrium short-term interest rate, present a new derivation of the consumption-based capital asset pricing model, demonstrate how equilibrium forward and futures prices can be derived, including several examples, and finally we derive the equilibrium price of a European call option in a situation where the underlying asset pays dividends according to an Itô process of unbounded variation. In the latter case we demonstrate how this pricing formula simplifies to known results in special cases, among them the famous Black–Scholes formula and the Merton formula for a special dividend rate process.     

Factors Associated with Strategic Corporate Decisions in Family Firms: Evidence from Sweden

By using detailed ownership data from Sweden, we investigate the factors associated with corporate investment decisions in family firms compared to nonfamily firms. We find that the family owner's portfolio diversification level is to some extent, and the use of dual‐class share mechanism by the family owner is strongly, associated with reduced corporate investment. We further demonstrate where entrenched family owners, holding dual‐class shares, canalize their firm free cash flows to: they prefer to distribute it as dividends with catering motivations. They opt to pay higher dividends over increasing corporate investment, which indicates some evidence of private benefits of control.     

OPTIMAL DIVIDEND POLICY WITH MEAN-REVERTING CASH RESERVOIR

Motivated by empirical evidence and economic arguments, we assume that the cash reservoir of a financial corporation follows a mean reverting process. The firm must decide the optimal dividend strategy, which consists of the optimal times and the optimal amounts to pay as dividends. We model this as a stochastic impulse control problem, and succeed in finding an analytical solution. We also find a formula for the expected time between dividend payments. A crucial and surprising economic result of our paper is that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments. This results in a reduction of the probability of default of the firm.     

INDIFFERENCE VALUATION OF MORTGAGE‐BACKED SECURITIES IN THE PRESENCE OF PREPAYMENT RISK

We present a utility‐based methodology for the valuation and the risk management of mortgage‐backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded prepayment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools.     

Valuation and firm investment and financing policies with personal tax biases

In this paper we examine firm financial policies in the presence of personal tax biases (e.g., favoring capital gains relative to interest and dividends). A form of the value additivity principle (VAP) for the tax bias case is established and applied to the firm's merger, investment, financial structure, and dividend decisions. As with the neutral tax VAP, the revised VAP requires transaction costless capital markets but does not require capital market completeness or competitiveness. Share value maximization is found not to be the proper goal for a firm that seeks to maximize the shareholders' current expected utility; however, it is found that share value maximization is generally a good approximate objective. Firm investment policy with financial structure irrelevance (owing to offsetting personal and corporate taxes) is examined assuming that the revised VAP holds.     

Estimates of the cost of equity for public utilities, 1961–1976

Using a simple version of the dividend cash flow (DCF) model of stock valuation, the cost of equity for public utilities is often inferred to be equal to the sum of the dividend yield and the expected rate of growth in dividends. Witnesses who employ this approach generally extrapolate past growth patterns into the future and then assume that investors expect these trends to continue; no effort is made to actually assess the expectations of investors. This approach to estimating the cost of equity for public utilities is criticized for the failure to develop testable hypotheses as an inferential basis for testing the statistical reliability of estimates of the cost of equity. This article demonstrates an alternative to the traditional approach, based on the premise that reliable estimates of the cost of equity are derived only within a methodological framework that produces testable hypotheses. The Gordon model of share valuation is formulated in such a way as to show that there is a systematic and predictable relationship between the ratio of market price to book value of common stock and a firm's normal or expected return on equity. This relationship suggests an econometric model that not only tests the Gordon model of share valuation but produces at the same time, inferences concerning the cost of equity. Using this approach, year-end estimates of the cost of equity for electric utilities are determined for the 16-yr period from 1961 to 1976.     

Incorporating price elasticity in financial forecasting models: From theory to practice and implementation

The authors use a capital budgeting example to show students how to incorporate price elasticity into financial analysis as an application of what students learn in their microeconomics course. They present simple as well as more advanced price-quantity relationships, and using various “what-if” scenarios; the authors show how risk analysis can be used to improve revenue projections and valuation models. A project analysis example is employed to illustrate results for negative predictive value and IRR based on three models of price elasticities across a range of potential product pricing. Students are then encouraged to replicate and create similar models, helping them improve their vital Excel and financial modeling skills.     

二叉树方法在风险投资决策中的应用

在过去的20年中,许多学者开始应用期权定价方法去估计实物资产价值,并在此基础上对公司的最优投资决策进行了大量研究。利用二叉树方法,通过对一个欧式期权与一个美式期权构成的复合期权进行定价,完成对风险投资问题的估价。主要有两个方面的内容:用实例说明怎样用二叉树方法对投资期权进行估价;把从期权模型获得的价值与用净现值方法得到的价值相关联,从而获得风险投资的最终的价值。     

The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims

We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applied to a wide range of valuation problems including complicated contingent claims associated with the term structure of interest rates. We illustrate our method by giving two examples: the valuation problems of swaptions and average (Asian) options for interest rates. Our method gives some explicit formulas for solutions, which are sufficiently numerically accurate for practical purposes in most cases. The continuous stochastic processes for spot interest rates and forward interest rates are not necessarily Markovian nor diffusion processes in the usual sense; nevertheless our approach can be rigorously justified by the Malliavin–Watanabe Calculus in stochastic analysis.     

Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example

The paper represents a model for financial valuation of a firm which has control of the dividend payment stream and its risk as well as potential profit by choosing different business activities among those available to it. This model extends the classical Miller–Modigliani theory of firm valuation to the situation of controllable business activities in a stochastic environment. We associate the value of the company with the expected present value of the net dividend distributions (under the optimal policy). The example we consider is a large corporation, such as an insurance company, whose liquid assets in the absence of control fluctuate as a Brownian motion with a constant positive drift and a constant diffusion coefficient. We interpret the diffusion coefficient as risk exposure, and drift is understood as potential profit. At each moment of time there is an option to reduce risk exposure while simultaneously reducing the potential profit—for example, by using proportional reinsurance with another carrier for an insurance company. Management of a company controls the dividends paid out to the shareholders, and the objective is to find a policy that maximizes the expected total discounted dividends paid out until the time of bankruptcy. Two cases are considered: one in which the rate of dividend payout is bounded by some positive constant M, and one in which there is no restriction on the rate of dividend payout. We use recently developed techniques of mathematical finance to obtain an easy understandable closed form solution. We show that there are two levels u₀ and u₁ with u₀≤u₁. As a function of currently available reserve, the risk exposure monotonically increases on (0,u₀) from 0 to the maximum possible. When the reserve exceeds u₁ the dividends are paid at the maximal rate in the first case and in the second case every excess above u₁ is distributed as dividend. We also show that for M small enough u₀=u₁ and the optimal risk exposure is always less than the maximal.     

股权分置、公司治理结构与现金股利分配

文章以2004-2007年中国上市公司为样本,从代理理论视角对股权分置改革前后我国公司治理与现金股利分配关系进行了理论与实证分析.研究结果表明,我国上市公司第一大股东倾向于现金股利分配,但这种情况在股权分置改革完成后有所改变;第二大股东持股比例、流通股比例以及独立董事人数等与现金股利支付率无关.同时,股改哑变量、盈利能力、成长性、偿债能力、公司规模与现金股利分配的关系可以用代理理论加以解释.     

TAKEOVERS OF DIFFUSELY HELD FIRMS: A NONSTANDARD APPROACH

A common theme in the literature on corporate control is that, when share ownership is diffuse, the free-rider problem prevents raiders from making acquisitions at tender prices below the postacquisition share price. In this paper, we address this question by formulating a nonstandard model of takeovers of diffusely held firms. It is demonstrated that, even when individual shareholdings are infinitesimal relative to firm size, takeovers succeed with positive probability and equilibria exist in which the raider earns substantial per share profits. Further, the Nash equilibria of the game are characterized with regard to raider profit, the aggregate fraction of shares tendered, and the relation between raider profit and the degree of randomization exhibited by shareholder tendering strategies.     

A Generalized Oligopoly Model

This paper generalizes and unifies the traditional quantity competition oligopoly models of Cournot and Stackelberg. Traditional oligopoly models predict that, under constant marginal costs, there will only be one market share (Cournot) or a single firm with a large market share and all others with the same market share (Stackelberg). Without altering the basic assumption set, in particular the assumptions of common marginal cost functions, perfect information and linear demand, the paper presents a general model that may be useful to explain many real‐life situations of oligopoly competition, where many different market shares may coexist. Finally, it is shown that certain existing social welfare results are robust to the generalization.     

Arbitrage‐free XVA

We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no‐arbitrage arguments, we derive backward stochastic differential equations associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no‐arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the unique XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. In the general case of asymmetric funding, repo, and collateral rates, we study the semilinear partial differential equations characterizing buyer's and seller's XVA and show the existence of a unique classical solution to it. To illustrate our results, we conduct a numerical study demonstrating how funding costs, repo rates, and counterparty risk contribute to determine the total valuation adjustment.     

TAX BASIS AND NONLINEARITY IN CASH STREAM VALUATION

The value of a future cash stream is often taken to be its net present value with respect to some term structure. This means that a linear formula is used in which each future payment is discounted by a factor deemed appropriate for the date on which the payment will be made. In a money market with taxes and shorting costs, however, there is no theoretical support for the existence of a universal term structure for this purpose. What is worse, reliance on linear formulas can be seriously inaccurate relative to true worth and can lead to paradoxes of disequilibrium. A consistent no-arbitrage theory of valuation in such a market requires instead that taxed and untaxed investors be grouped in separate classes with different valuation operators. Such operators are linear to scale but nonlinear with respect to addition. Here it is established that although these valuation operators provide general bounds applicable across an entire class, individual investors within a tax class can have more special operators because of the influence of existing holdings. These customized valuation operators have the feature of not even being linear to scale. In consequence of this nonlinearity, investors from the same or different tax classes can undertake advantageous trades even when the market is in a no-arbitrage state, but such trade opportunities are limited. Some degree of activity in financial markets can thereby be understood without appeal to differences in utility functions or temporary disequilibrium due to random disturbances.     

Consumer deliberation and quality signaling

Consumers are often uncertain about their product valuation before purchase. They may bear the uncertainty and purchase the product without deliberation. Alternatively, consumers can incur a deliberation cost to find out their true valuation and then make their purchase decision. This paper proposes that consumer deliberation about product valuation can be an endogenous mechanism to enable credible quality signaling. We demonstrate this point in a simple setup in which product quality influences the probability that the product has high valuation. We show that with endogenous deliberation there may exist a unique separating equilibrium in which the high-quality firm induces consumer deliberation by setting a high price whereas the low-quality firm prevents deliberation by charging a low price. Compared to the case of complete information, the price of the high-quality firm can be distorted upward to facilitate consumer deliberation, or distorted downward to avoid the low-quality firm’s imitation. In an extension we show that dissipative advertising can facilitate quality signaling. The high-quality firm can utilize advertising spending to avert imitation from the low-quality firm without distorting price downward, earning a higher profit than that without advertising. However, advertising mitigates the distortion at the expense of consumer surplus and social welfare.     

Pricing of New Securities in an Incomplete Market: the Catch 22 of No-Arbitrage Pricing

There are two distinctly different approaches to the valuation of a new security in an incomplete market. The first approach takes the prices of the existing securities as fixed and uses no-arbitrage arguments to derive the set of equivalent martingale measures that are consistent with the initial prices of the traded securities. The price of the new security is then obtained by appealing to certain criteria or on the basis of some preference assumption. The second method prices the new security within a general equilibrium framework. This paper clarifies the distinction between the two approaches and provides a simple proof that the introduction of the new security will typically change the prices of all the existing securities. We are left with the paradox that a genuinely new derivative security is not redundant, but the dominant pricing paradigm in derivative security pricing is the no-arbitrage approach, which requires the redundancy of the security. Given the widespread practice of using the no-arbitrage approach to price (or bound the price of) a new security, we also comment on some justifications for this approach.