signaling quality with a money back guarantee the role of transaction costs direct marketing is witnessing explosive growth as consumers increasingly purchase products from their homes their ability to judge the quality of products they buy is significantly reduced in this paper we study how money back guarantees can signal product quality in such environments we interpret product quality broadly to mean both the level of attributes promised as well as the firm s consistency in delivering on those promises key aspects of our formulation are the explicit consideration of transaction costs and alternative signals of product quality transaction costs are the costs the seller or buyer faces when redeeming a money back guarantee we show that money back guarantees signal quality by exploiting the higher probability of returns for a lower quality product and the attendant higher transaction costs however if the seller s transaction costs are very large then there are less costly ways to signal namely charging a high price we compare the signaling performance of 1 price 2 price with uninformative advertising and 3 price with a money back guarantee whereas uninformative advertising does not work at all in our model under certain conditions a money back guarantee is necessary to signal and under other conditions a money back guarantee is a useful supplement to price

pricing credit derivatives with rating transitions we present a model for pricing risky debt and valuing credit derivatives that is easily calibrated to existing variables our approach expands a classical term structure model to allow for multiple rating classes of debt the framework has two salient features 1 it uses a rating transition matrix as the driver for the default process and 2 the entire set of rating categories is calibrated jointly which allows arbitrage free restrictions across rating classes as a bond migrates among them we illustrate the approach by applying it to price credit sensitive notes that have coupon payments linked to the rating of the underlying credit

bond pricing and the term structure of interest rates a new methodology for contingent claims valuation this paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates the methodology based on the equivalent martingale measure technique takes as given an initial forward rate curve and a family of potential stochastic processee for its subsequent movements a no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk examples are provided to illustrate the key results in relation to the term structure of interest rates arbitrage pricing theory has two purposes the first is to price all zero coupon default free bonds of varying maturities from a finite number of economic fundamentals called state variables the second is to price all interest rate sensitive contingent claims taking as given the prices of the zero coupon bonds this paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context of which all existing arbitrage pricing models are special cases in particular vasicek 1977 brennan and schwartz 1979 langetieg 1980 ball and torous 1983 ho and lee 1986 schaefer and schwartz 1987 and artzner and delbaen 1988 the primary contribution of this paper however is a new methodology for solving the second problem i e the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds the methodology is new because i it imposes its stochastic structure directly on the evolution of the forward rate curve ii it does not require an inversion of the term structure to eliminate the market prices of risk from contingent claim values and iii it has a stochastic spot rate process with multiple stochastic factors influencing the term structure the model can be used to consistently price and hedge all contingent claims american or european on the term structure and it is derived from necessary and more importantly sufficient conditions for the absence of arbitrage the arbitrage pricing models of vasicek 1977 brennan and schwartz 1979 langetieg 1980 and artzner and delbaen 1988 all require an iformerly titled bond pricing and the term structure of interest rates a new methodology

a model of credit risk optimal policies and asset prices this article studies an economy with borrowers firms or individuals under costly default borrowers defaulting under adverse economic conditions may despite incurring default costs emerge as wealthier than nonborrowers asset substitution is generally not pronounced although a larger risk exposure by borrowers may also occur and then binary options emerge as useful credit derivatives the asset value dynamics are endogenously determined and shown to exhibit stochastic mean and volatility in contrast to many credit risk models in equilibrium the market level is increased decreased in economic downturns upturns by the presence of credit risk

valuing investment projects under interest rate risk empirical evidence from european firms abstractin this article we perform an empirical investigation of the effect of the interest rate uncertainty on the valuation of investment projects the analysis is carried out by employing a real option approach and by considering a set of firms that operate in various production sectors in the euro area in particular the revenues generated by the investment projects are modelled using a geometric brownian motion whereas the interest rate is specified as a stochastic process of vasicek type moreover using the volatility of the equity return as a proxy the volatility of the revenues is calibrated to real firm data while the parameters of the interest rate model are estimated by fitting the euribor time series to this aim an ad hoc calibration procedure is developed which is based on the maximum likelihood principle and thus has the merit of being simple fast and suitable for practical purposes our study reveals that the interest rate uncertainty reduces the valuation of investment projects h

valuing risky fixed rate debt an extension this paper develops a corporate bond valuation model that takes into account both early default and interest rate risk it corrects a defect of recent contributions where pricing equations do not assure that the payment to bondholders upon bankruptcy is no greater than firm value the bankruptcy triggering mechanism is directly related to the payoff received by bondholders when early bankruptcy is forced upon the firm more specifically the default barrier is defined simply as a fixed quantity discounted at the riskless rate up to the maturity date of the risky corporate bond as soon as this threshold is crossed bondholders receive an exogenously specified fraction ofthe remaining assets deviations from the absolute priority rule also are captured because it accounts for gaussian interest rate uncertainty default risk and deviations from the absolute priority rule this model is capable of producing quite diverse shapes for the term structure of yield spreads

high and declining prices signal product quality high and declining prices signal a high quality product high prices are the efficient means of signaling because the consequent loss of sales volume is most damaging for lower cost lower quality products as time passes and the number of informed consumers increases the signaling distortion lessens resulting in a declining price profile the prediction of high and declining prices is robust across a variety of dynamic models and is consistent with recent empirical findings copyright 1991 by american economic association

the default risk of swaps we characterize the exchange of financial claims from risky swaps these transfers are among three groups shareholders debtholders and the swap counterparty from this analysis we derive equilibrium swap rates and relate them to debt market spreads we then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders in a simplified case we obtain closed form solutions for the value of the default risk in the swap for interest rate swaps we obtain numerical solutions for the equilibrium swap rate including default risk we compare these with equilibrium debt market default risk spreads swaps have been one of the most explosive and important innovations in international capital markets in the last 10 years in its simplest form a swap consists of an agreement hetween two entities called counterparties to exchange in the future two streams of cash flows in a currency swap these streams of cash flows consist of a stream of interest and principal payments in one cvtrrency exchanged for a stream of interest and principal payments of the same maturity in another currency in an interest rate swap they consist of streams of interest payments of one type fixed or floating exchanged for streams of interest payments of the other type in the same currency the two types of swap are shown in appendix 1 the economic importance of swap transactions is the fact that they can he comhined with deht issues to change the nature of the liahility for the borrower the sum of a hond issue and a currency swap gives a net liability stream which is equivalent to transforming the bond liability into a different currency a floating rate note combined with an interest rate swap results in a liability equivalent to fixed rate debt two issues have dominated the academic literature on swaps the first concerns the reasons for their use arbitrage of imperfections in capital markets was the original cause of their appearance price and henderson 1984 turnbull 1987 shows that lowering borrowing costs by a synthetic transaction involving a swap is not possible in a complete integrated capital market subsequent authors wall and pringle 1988 arak estrella groodman and silver 1988 smith smithson and wakeman 1987 observe

the impact of default risk on the prices of options and other derivative securities abstract this paper presents a model for valuing derivative securities when there is default risk the holder of a security is assumed to recover a proportion of its no default value in the event of a default by the counterparty both the probability of default and the size of the proportional recovery are random the paper shows how data on bonds issued by the counterparty can be used to provide information about model parameters

an integrated model for hybrid securities we develop a model for pricing securities whose value may depend simultaneously on equity interest rate and default risks the framework may also be used to extract probabilities of default pd functions from market data our approach is entirely based on observables such as equity prices and interest rates rather than on unobservable processes such as firm value the model stitches together in an arbitrage free setting a constant elasticity of variance cev equity model to represent the behavior of equity prices prior to default a default intensity process and a heath jarrow morton hjm model for the evolution of riskless interest rates the model captures several stylized features such as a negative relation between equity prices and equity volatility a negative relation between default intensity and equity prices and a positive relationship between default intensity and equity volatility we embed the model on a discrete time recombining lattice making implementation feasible with polynomial complexity we demonstrate the simplicity of calibrating the model to market data and of using it to extract default information the framework is extensible to handling correlated default risk and may be used to value distressed convertible bonds debt equity swaps and credit portfolio products such as collateralized debt obligations cdos applied to the cdx indu credit default index industrials index we find the s p 500 index explains credit premia

a two factor hazard rate model for pricing risky debt and the term structure of credit spreads this paper proposes a two factor hazard rate model in closed form to price risky debt the likelihood of default is captured by the firm s non interest sensitive assets and defaultfree interest rates the distinguishing features of the model are threefold first the impact of capital structure changes on credit spreads can be analyzed second the model allows stochastic interest rates to impact current asset values as well as their evolution finally the proposed model is in closed form enabling us to undertake comparative statics analysis compute parameter deltas of the model calibrate empirical credit spreads and determine hedge positions credit spreads generated by our model are consistent with empirical observations

the design of an optimal insurance policy almost every phase of economic behavior is affected by uncertainty the economic system has adapted to uncertainty by developing methods that facilitate the reallocation of risk among individuals and firms the most apparent and familiar form for shifting risks is the ordinary insurance policy previous insurance decision analyses can be divided into those in which the insurance policy was exogenously specified see john gould jan mossin and vernon smith and those in which it was not see karl borch 1960 and kenneth arrow 1971 1973 in this paper the pioneering work of borch and arrow the derivation of the optimal insurance contract form from the model is synthesized and extended

risk sharing in the adjustable rate loan market are existing contracts efficient abstract a previous paper arvan and brueckner 1986 showed that in an optimal loan contract interest rate risk should be shared between lender and borrower with the slope of the loan rate function which relates the loan interest rate to the lender s uncertain cost of funds lying between zero and one existing adjustable rate mortgage arm contracts violate this rule since they require complete risk absorption by the borrower when interest rate caps are not binding the present paper shows that when the earlier model is modified by adding a second type of borrower efficient loan contracts look more like existing arms

pricing derivatives on financial securities subject to credit risk this article provides a new methodology for pricing and hedging derivative securities involving credit risk two types of credit risks are considered the first is where the asset underlying the derivative security may default the second is where the writer of the derivative security may default we apply the foreign currency analogy of jarrow and turnbull 1991 to decompose the dollar payoff from a risky security into a certain payoff and a spot exchange rate arbitrage free valuation techniques are then employed this methodology can be applied to corporate debt and over the counter derivatives such as swaps and caps the purpose of this article is to provide a new theory for pricing and hedging derivative securities involving credit risk two sources of credit risk are identified and analyzed the first is where the asset underlying the derivative security may default paying off less than promised this is the case for example with imbedded options on corporate debt the second is the credit risk introduced by the writer of the derivative security who may also default examples include over the counter writers of options on eurodollar futures swaps and swaptions for pricing derivative securities involving credit risk there are currently two approaches the first views these derivatives as contingent claims not on the financial securities themselves but as compound options on the assets underlying the financial securities this is the case for example with the pricing of imbedded options on corporate debt see merton 1974 1977 black and cox 1976 ho and singer 1982 chance 1990 and kim ramaswamy and sundaresan 1993 or the pricing of vulnerable options see johnson and stulz 1987 in practice however this valuation methodology is difficult to use first the assets underlying the financial security are often not tradeable and therefore their values are not observable this makes application of the theory and estimation of the relevant parameters problematic second as in the case of corporate debt all of the other liabilities of the firm senior to the corporate debt must first and simultaneously be valued this generates significant computational difficulties as a result this approach has not

pricing the risk of recovery in default with absolute priority rule violation abstract this paper proposes a simple approach to infer the risk neutral density of recovery rates implied by the prices of the debt securities of a firm the proposed approach is independent of modeling default arrival rates and allows for the violation of absolute priority rule the paper demonstrates that a new statistic the adjusted relative spread captures risk neutral recovery information in debt prices interest rates and firm tangible assets are shown to be significant determinants of the price of recovery an application illustrates the pricing of credit derivatives written on the realized recovery rate

warranties durability and maintenance two sided moral hazard in a continuous time model double moral hazard in continuous time generates the familiar warranty pattern with full coverage for an initial block of time the more complete the warranty the better the producer s durability incentives and the worse the consumer s maintenance incentives using continuous time highlights the need for some warranty bound to avoid reaching the first best as an unreasonable limit early in the paper an exogenous bound is used while later the bound arises endogenously from the possibility of abuse and repair a quadratic example shows that the warranty s duration depends on the relative severity of the two moral hazard problems

product warranties and double moral hazard this article explores a model of warranties in which moral hazard problems play a key role the goal is to understand the important characteristics of warranties including their provision of incomplete insurance and the relationship between product quality and coverage we analyze a model in which buyers and sellers take actions that affect a product s performance since these actions are not cooperatively determined an incentives problem arises we characterize the optimal warranty contract and undertake comparative statics to determine the predicted correlation of warranty coverage and product quality

an exact bond option formula this paper derives a closed form solution for european options on pure discount bonds assuming a mean reverting gaussian interest rate model as in vasicek 8 the formula is extended to european options on discount bond portfolios

term structures of credit spreads with incomplete accounting information we study the implications of imperfect information for term structures of credit spreads on corporate bonds we suppose that bond investors cannot observe the issuer s assets directly and receive instead only periodic and imperfect accounting reports for a setting in which the assets of the firm are a geometric brownian motion until informed equityholders optimally liquidate we derive the conditional distribution of the assets given accounting data and survivorship contrary to the perfect information case there exists a default arrival intensity process that intensity is calculated in terms of the conditional distribution of assets credit yield spreads are characterized in terms of accounting information generalizations are provided

warranties as signals under consumer moral hazard this article examines the use of prices and warranties as signals of product quality to consumers who choose how to maintain their purchases the seller s incentives are strongly affected by the interaction of quality and maintenance in determining product reliability two different assumptions about this interaction are made a separating equilibrium in which high quality is signalled with a low warranty and low price is shown to be possible in both cases

multiple market entry cost signalling and entry deterrence a low cost incumbent may limit price to informatively signal her cost to an uncertain potential entrant and therefore deter entry we enrich this model by investigating the strategic pricing behavior of the incumbent when she operates in multiple markets we demonstrate that the low cost incumbent s ability to separate from a ghost high cost type is enhanced when she combines her signalling effort across markets instead of independent signalling in each market we show that in the combined least cost signalling the low cost incumbent limit prices in each market in an attempt to minimize dissipative but informative signalling costs the low cost incumbent may enter unprofitable markets but exit after credible separation

efficient contracts in credit markets subject to interest rate risk an application of raviv s insurance model interest rate risk borne by financial institutions has increased markedly as the credit markets have become more unstable in recent years the burden of this new instability has been especially severe for lending institutions whose balance sheets show the greatest mismatch between the maturities of assets and liabilities the savings and loan industry for example which borrows short and lends long suffered serious losses in recent years as income from its portfolio of old mortgages failed to keep pace with the escalating cost of short term funds the specter of such losses has led to the emergence of adjustable rate mortgages arms as well as other types of variable rate contracts these contracts often specify a complex functional relationship between the future loan interest rate and the lender s uncertain future cost of funds in view of the growing popularity of variable rate loans it is important to know what features an efficient contract of this type would possess to answer this question the present paper derives the form of the optimal variable rate contract focusing especially on the contractual relationship between the loan rate and the future cost of funds the framework used in the analysis is very similar to artur raviv s 1979 optimal insurance model section i derives the form of the optimal loan contract and evaluates the risk sharing efficiency of arms in light of the results subsequent sections discuss extensions of the model and offer conclusions 1 i analysis

advertising and limit pricing we enrich milgrom and roberts 1982 limit pricing model to allow an incumbent to signal his costs with both price and advertisements our fundamental result is that a cost reducing distortion occurs in that the incumbent behaves as if there were complete information but his costs were lower than they are preentry price is therefore distorted downward and demand enhancing advertising is distorted upward as a consequence of signalling if advertising is a purely dissipative signal it is not used nor therefore distorted recent refinements of the sequential equilibrium concept are featured