two bidder all pay auctions with interdependent valuations including the highly competitive case abstract we analyze symmetric two bidder all pay auctions with interdependent valuations and discrete type spaces relaxing previous restrictions on the distribution of types and the valuation structure we present a construction that characterizes all symmetric equilibria we show how the search problem this construction faces can be complex in equilibrium randomization can take place over disjoint intervals of bids equilibrium supports can have a rich structure and non monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common particular attention is paid to the case in which an increase in a bidder s posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder such environments are highly competitive in the sense that the bidder s higher valuation also signals that the other bidder has an incentive to bid aggressively

private versus complete information in auctions abstract we show that in several but not all standard auctions i private independent values and ii complete information are payoff equivalent the first price auction generates the same revenue under i and ii the all pay auction has lower revenue under ii

warrant exercise and bond conversion in competitive markets abstract we develop a theory of warrants held by competitive warrantholders not constrained to exercise their warrants as one block the theory also applies to convertible bonds held by competitive bondholders not constrained to convert their bonds as one block we prove that the warrant bond price in each of the competitive equilibria is less than or equal to the price in an economy with the block constraint and for at least one competitive equilibrium the warrant bond price equals the warrant bond price in the block constrained economy we illustrate the paths of competitive warrant exercise and bond conversion and conclude that under realistic assumptions they can be long

asymmetric all pay auctions with incomplete information the two player case abstract we prove existence and uniqueness of bayesian equilibrium for a class of generally asymmetric all pay auctions with incomplete information due to its importance in applications some prominence is given to the first price all pay auction for which a detailed characterization of equilibrium and an approximation to equilibrium of its well studied complete information version are supplied furthermore we relate our uniqueness result to the well known multiplicity of equilibria in the war of attrition second price all pay auction which emerges as a limit point of the class of two player auction games considered journalof economic literature classification numbers d44 c62 c72

warrant valuation and exercise strategy abstract this paper demonstrates that warrant valuation and exercise strategy differ fundamentally from call option valuation simultaneous exercise of warrants is shown to be suboptimal and a monopolist owning all warrants can achieve a higher value unless warrants are perfectly divisible no satisfactory equilibrium exists for the valuation and exercise of widely held warrants the problems encountered appear to be quite general and stem from necessary assumptions about future corporate dividend policy and capital structure such assumptions are necessary for any model of corporate security valuation

a strategic analysis of sinking fund bonds abstract unlike most securities the pricing of sinking fund bonds is influenced by the distribution of ownership which summarizes the extent to which the market is cornered the effect of the distribution of ownership on the pricing of sinking fund bonds is examined by an explicit game in which the price obtained for bonds sold can depend upon the size of the investor s position this framework is used to contrast the valuation of sinking fund bonds with the valuation of amortizing bonds and straight debt we show that it is generally incorrect to view sinking fund bonds as being equivalent to serial bonds

pricing warrants an empirical study of the black scholes model and its alternatives this paper uses a sample of over 25 000 daily warrant prices to empirically investigate potential problems with the commonly used warrant pricing model proposed by black and scholes as an extension of their call option model one problem seems to be especially important the constant variance assumption of the dilution adjusted blackscholes model appears to cause biases in model prices for almost all warrants and over the entire sample period we show that more accurate price forecasts are obtained with a specific form of the constant elasticity of variance model since the derivation of the black scholes model financial economists have speculated on its usefulness for warrant valuation in their pathbreaking paper black and scholes 1973 claim that in many cases their model can be used as an approximation to give an estimate of the warrant value however black and scholes 1973 warn that

information revelation through option exercise in many real world situations agents must formulate option exercise strategies with imperfect information in such a setting agents may infer the private signals of other agents through their observed exercise strategies the building of an office building the drilling of an exploratory oil well and the commitment of a pharmaceutical company toward the research of a new drug all convey private information to other market participants this article develops an equilibrium framework for option exercise games with asymmetric private information many interesting aspects of the patterns of equilibrium exercise are analyzed in particular informational cascades where agents ignore their private information and jump on the exercise bandwagon may arise endogenously article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

all equilibria of the vickrey auction abstract this paper characterizes the set of nash equilibria in the second price sealed bid auction with independent private values and three or more bidders in addition we show that any effective reserve price implies uniqueness

stock index futures implications for international capital taxation abstract this paper develops a model of corporate capital structure and investor portfolio choice in an international setting the model s key feature is the stock index futures contract investors and companies specialize in securities based on tax and currency appreciation rates despite this specialization investors achieve complete diversification through futures positions nations should tax interest and capital gains equally and should not tax corporate income this contrasts with the result when futures do not exist in which foreigners desire for diversification provides countries with an incentive to use tax policy to reduce foreign ownership of domestic equity to acquire monopoly rents

disclosure policy in a multi prize all pay auction with stochastic abilities this paper investigates whether a contest organizer should disclose private information about bidders abilities in a multi prize all pay auction bidders abilities are randomly distributed and observed by the contest organizer the organizer decides whether to disclose this information publicly we find that concealing the information elicits higher expected total effort regardless of the distribution of abilities in addition we find that the rent dissipation rate of the contest does not depend on the disclosure policy

convertible debt valuation and conversion in complex capital structures abstract the impact of conversion strategies on the value of convertible debt is examined it is shown that for capital structures comprised of multiple classes of convertible debt the optimal conversion policy for a given bond class is affected by the decisions of other bond classes using this optimal conversion strategy closed form solutions for bond prices are derived

disclosure policies in research contests with stochastic entry abstract this paper models research contests as an all pay auction with stochastic entry and analyzes the effect of disclosing the actual number of participants on the expected winning bid i find that the classic disclosure irrelevance principle on expected revenue does not extend to the ranking on expected winning bid the ranking on expected winning bid crucially depends on the number of potential bidders participation probabilities and the distribution of bidders valuations when there are more than two potential bidders fully concealing the actual number of participants elicits a higher expected winning bid if potential bidders have low participation probabilities whereas the rank reverses if bidders have high participation probabilities and high chances of being high types

taxation of asset income in the presence of a world securities market abstract this paper examines a capm model of world security prices in which governments recognize their ability to influence international security prices via their tax treatment of foreign and domestic investors in this model governments have the incentive to set tax rates such that investors tend to specialize in domestic securities and to restrict net capital flows between countries each country does this to increase the utility of domestic residents taking as given the tax policies of other governments but the net outcome is a reduction in world efficiency and likely a reduction in the utility of all investors

the interaction between the financial and investment decisions of the firm the case of issuing warrants in a levered firm abstract in this paper we analyze the value of warrants and stock in a firm that has both equity and debt in its capital structure and assume that the proceeds from exercising the warrants are reinvested in the firm the effect of potential future scale investment on the firm s stock debt and warrants are investigated the warrants in our analysis are european in this framework there are two sources for the nonstationarity of the rate of return on any kind of financial claim the first stems from changes in the firm s capital structure and the second is due to the potential scale increase in the value of the firm should the warrants be exercised the effect of a potential transfer of wealth from equity holders to debt holders at time of exercise is analyzed when warrants are exercised and the proceeds are reinvested in a scale expansion project the probability of default may decrease it follows therefore that ceteris paribus debt is likely to appreciate in value at the expense of equity the method of pricing by arbitrage as proposed by harrison and kreps is used to derive values for claims on the firm problems associated with measuring the volatility of equity are discussed

employee stock options as warrants abstract previous studies ignore the fact that employee stock options are warrants because these options have been an insignificant component of firms capital structures i show that this assumption is no longer correct for example for more than 36 of my sample firms employee stock options represent a more significant claim on firm value than the firm s debt and preferred stock combined moreover in contrast to the suggestions of previous research i show that employee stock options are a significant claim on firms throughout the economy including larger firms older firms and firms in old economy industries finally i show that the presumption in prior studies that employee stock options are not warrants causes a potential misunderstanding of the risk shifting interests of securityholders and biases the analysis of capital structure issues

information in conflicts abstract we consider two player contests for a prize of common but uncertain value for settings where one player knows the value of the prize while the other only knows its prior distribution we give conditions for when the uninformed agent is ex ante strictly more likely to win the prize than is the informed agent in the special case of a lottery contest equilibrium expenditures are lower under asymmetric information than if either both agents are informed or neither agent is informed

multidimensional private value auctions we consider parametric examples of symmetric two bidder private value auctions in which each bidder observes her own private valuation as well as noisy signals about her opponent s private valuation we show that in such environments the revenue equivalence between the first and second price auctions spas breaks down and there is no definite revenue ranking while the spa is always efficient allocatively the first price auction fpa may be inefficient equilibria may fail to exist for the fpa we also show that auction mechanisms provide different incentives for bidders to acquire costly information about opponents valuation

option exercise games an application to the equilibrium investment strategies of firms under the standard real options approach to investment under uncertainty agents formulate optimal exercise strategies in isolation and ignore competitive interactions however in many real world asset markets exercise strategies cannot be determined separately but must be formed as part of a strategic equilibrium this article provides a tractable approach for deriving equilibrium investment strategies in a continuous time cournot nash framework the impact of competition on exercise strategies is dramatic for example while standard real options models emphasize that a valuable option to wait leads firms to invest only at large positive net present values the impact of competition drastically erodes the value of the option to wait and leads to investment at very near the zero net present value threshold copyright 2002 oxford university press

robustness of option like warrant valuation abstract this paper presents a methodology for arriving at the unobserved asset value and its volatility of a firm with outstanding warrants this enables us to price warrants correctly and to examine the robustness of option like warrant valuation where the dilution that occurs when warrants are exercised is ignored our analysis helps to justify the frequent simplifying option like warrant valuation furthermore we examine 50 960 daily prices for 37 american type warrants written on 16 german stocks over the period 1979 1990 the empirical results confirm our theoretical analysis there is virtually no dilution related pricing bias of the american constant variance diffusion model with the stock price as the state variable

employee stock options equity valuation and the valuation of option grants using a warrant pricing model we investigate the use of a warrant pricing approach to incorporate employee stock options esos into equity valuation and to account for the dilutive effect of esos in the valuation of option grants for financial reporting purposes our valuation approach accounts for the jointly determined nature of eso and shareholder values the empirical results show that our stock price estimate exhibits lower prediction errors and higher explanatory powers for actual share price than does the traditional stock price estimate we use our valuation approach to assess the implications of dilution on the fair value estimates of eso grants we find that the fair value is overstated by 6 if we ignore the dilutive feature of esos furthermore this bias is larger for firms that are heavy users of esos small and r d intensive and for firms that have a broad based eso compensation plan

all equilibria in a class of bidding games abstract we consider a class of bidding games under complete information and construct a continuum of pure and mixed strategy equilibria as corollaries of our results we obtain a continuum of equilibria for the n bidder first price auction and the n firm bertrand game

voluntary conversion of convertible securities and the optimal call strategy abstract we provide an explanation of why convertibles are called long after the conversion value exceeds the call price delaying the call benefits the firm if enough investors are expected to delay their voluntary conversions consistent with this theory we document that a substantial number of investors do not voluntarily convert when the common dividend exceeds the convertible s dividend plus its premium over conversion value we find that firms would not have increased common stock returns by switching to the strategy of calling to force conversion as soon as possible surprisingly we find that convertible preferreds frequently sell below conversion value

equilibrium warrant pricing models and accounting for executive stock options under apb opinion no 25 compensation expense arising from executive stock options consists of the excess of the market value of the stock over the exercise price of the options on their grant dates if the exercise price equals the market value of the stock on the grant date which is typically the case no compensation expense is recognized this accounting treatment has been frequently criticized for its bias toward underestimating the cost of an option to the issuing firm and a number of alternative valuation models have been suggested in the accounting literature by and large these valuation models have been borrowed from the finance literature where they were developed to explain the pricing of warrants and traded options the purpose of this paper is to assess empirically how well two of these valuation models perform in providing estimates of the value of traded securities warrants that are similar in many respects to executive stock options 2 this evidence should help calibrate the magnitude of the errors

warrant exercise dividends and reinvestment policy in this paper we examine sequential exercise strategies by warrantholders and the gain from hoarding warrants we analyze several obstacles to acquiring large blocks in order to exploit sequential strategies first we identify several reinvestment policies for which sequential exercise is not advantageous thereby eliminating the gain from hoarding however sequential exercise strategies may be advantageous for monopoly or oligopoly warrantholders even absent dividends because using exercise proceeds to repurchase stock or to expand the firm s scale increases the riskiness of an equity share second oligopoly warrantholders can receive a smaller warrant value than perfectly competitive warrantholders suggesting a potential cost to unsuccessful hoarding

warrant pricing jump diffusion vs black scholes this paper investigates the warrant pricing abilities of dilution adjusted versions of the black scholes and jump diffusion option pricing models because of the typically long lives of warrants their pricing is hypothesized to benefit from use of the jump diffusion model which relaxes the black scholes restriction against stock price jumps empirical results indicate that while the black scholes model almost uniformly provides more efficient estimates the jump diffusion model generally provides less biased estimates of market value particularly for the valuation of out of the money warrants and warrants on stocks with a history of large and or frequent jumps the jump diffusion model may be preferred

the generalized war of attrition abstract we model a war of attrition with n k firms competing for n prizes in a natural oligopoly context the k 1 lowest value firms drop out instantaneously even though each firm s value is private information to itself in a standard setting context in which every competitor suffers losses until a standard is chosen even after giving up on its own preferred alternative each firm s exit time is independent both of k and of other players actions our results explain how long it takes to form a winning coalition in politics solving the model is facilitated by the revenue equivalence theorem jel d43 d44 l13 o30

pricing options with extendible maturities analysis and applications many common types of financial contracts incorporate options with extendible maturities this paper derives closed form expressions for options that can be extended by the optionholder and presents a number of applications including the valuation of american options with stochastic dividends junk bonds and shared equity mortgages we also derive closed form expressions for writer extendible options and discuss the writer s economic incentives for extending an out of the money option we apply these results to show that corporate debtholders have a strong incentive to extend the maturity of defaulting debt if there are liquidation costs we model and solve the debtholders optimal extension problem and show that the possibility of an extension can induce shareholders in highly levered firms to accept negative npv projects many common types of financial contracts and contingent claims incorporate options with extendible maturities for example a growing number of firms in many cases firms involved in leveraged buyouts are issuing bonds with maturities that can be extended at the firm s option options on real estate often allow the optionholder to extend the expiration date by paying an additional fixed amount to the option writer corporate warrants frequently give the issuing firm the right to unilaterally extend the life of the warrants a right that is often exercised in general any financial contract that could involve a rescheduling of payments a renegotiation of terms an early call or exercise provision or some similar type of flexibility over the timing of cash flows could be viewed as including an option with an extendible maturity this paper derives valuation expressions for extendible options examines the analytical properties of these prices and presents a wide variety of applications and examples in this analysis we distinguish between options that can be extended by the optionholder and options that are extended by the option writer since they differ fundamentally in their pricing implications focusing on the

the relation between forward prices and futures prices abstract this paper consolidates the results of some recent work on the relation between forward prices and futures prices it develops a number of propositions characterizing the two prices these propositions contain several testable implications about the difference between forward and futures prices many of the propositions show that equilibrium forward and futures prices are equal to the values of particular assets even though they are not in themselves asset prices the paper then illustrates these results in the context of two valuation models and discusses the effects of taxes and other institutional factors

taxation of investment and savings in a world economy the equilibrium of capital and equilibrium market prices are derived for a world economy with a unified securities market mobile capital no uncertainty and varying tax rates on different sources of income in each country the paper then characterizes optimal tax rates for a small country in this setting focusing on the peculiar incentives created when the before tax rate of return differs among securities due to differences in their typical tax treatment copyright 1986 by american economic association

ranking disclosure policies in all pay auctions in this paper we study information disclosure policies in all pay auctions with incomplete information two symmetric players have either high or low private value the contest organizer observes players values ex post and can commit ex ante to four different symmetric information policies exhaustively she can fully disclose or conceal the players types and she can disclose their types if and only if when both are high or if and only if when both are low we characterize the unique equilibriums and completely rank the four policies by various criteria we find the full concealment policy extracts highest aggregate expected effort followed by the policy of disclosing types if and only if when both are high the policy of disclosing types if and only if when both are low induces least aggregate expected effort players enjoy highest expected payoffs under the policy of disclosing types if and only if when both are low the other three policies yield the same expected payoffs to players in terms of prize allocation efficiency the full concealment policy is ranked highest and the full disclosure policy is ranked lowest in between the other two policies rankings depend on the probability of high type jel c72 d44 d82 d83 j48

an analysis of the war of attrition and the all pay auction we study the war of attrition and the all pay auction when players signals are affiliated and symmetrically distributed we a find sufficient conditions for the existence of symmetric monotonic equilibrium bidding strategies and b examine the performance of these auction forms in terms of the expected revenue accruing to the seller under our conditions the war of attrition raises greater expected revenue than all other known sealed bid auction forms journal of economic literature classification numbers d44 d82 1997 academic press

strategic analysis of the competitive exercise of certain financial options abstract warrants and convertible bonds are claims on the firm which change the outstanding number of common stock shares when exercised or converted exercise of such claims in competitive circumstances is modeled here as a noncooperative game played by a continuum of players first equilibria of the game are shown to exist by applying results of schmeidler second the game s equilibria are compared to outcomes that come about when one individual controls the exercise of all the claims but is constrained to exercise them in one block the results are analogues of earlier results by one of the authors on the competitive pricing of such claims

derivative pricing 60 years before black scholes evidence from the johannesburg stock exchange we obtain daily data for warrants traded on the johannesburg stock exchange between 1909 and 1922 and for a broker s call option quotes on stocks from 1908 to 1911 we use this new data set to test how close derivative prices are to black scholes 1973 prices and to compute profits for investors using a simple trading rule for call options we examine whether investors exercised warrants optimally and how they reacted to extensions of the warrants durations we show that long before the development of the formal theory investors had an intuitive grasp of the determinants of derivative pricing