a condition guaranteeing that the nash allocation is walrasian abstract consider the set of net trades attainable by an economic agent when he varies his strategy and all other agents stick to their strategies if all attainable sets for all agents are star shaped with respect to the origin then every pareto efficient nash allocation is walrasian this result bears upon the question whether it is possible to implement redistributive goals without impairing efficiency

does adding up of economic capital for market and credit risk amount to conservative risk assessment there is a tradition in the banking industry of dividing risk into market risk and credit risk both categories are treated independently in the calculation of risk capital but many financial positions depend simultaneously on both market risk and credit risk factors in this case an approximation of the portfolio value function separating value changes into a pure market risk plus pure credit risk component can result not only in an overestimation but also in an underestimation of risk we discuss this compounding effect in the context of foreign currency loans and argue that a separate calculation of economic capital for market risk and for credit risk may significantly underestimate true risk

intertemporally consistent shadow prices in an open economy estimates for cyprus abstract in the practical estimation of shadow prices the assumption that the economy is on a steady state growth path is often invoked usually implicitly most developing countries are far from this trajectory we derive shadow prices where the dynamic evolution of the economy is endogenously determined important influences being initial conditions and the constraints on foreign borrowing hence the resulting dated shadow prices of tradeables nontradeables labor and the accounting rate of interest ari are mutually consistent estimates for the republic of cyprus show that derivations from steady state growth can be significant leading to large fluctuations in the ari and thereby making the timing of investment projects crucial

risk neutral parameter shifts and derivatives pricing in discrete time we obtain a large class of discrete time risk neutral valuation relationships or preference free derivatives pricing models by imposing a simple restriction on the state price density process the risk neutral stock return and forward rate dynamics are obtained by changing only a location parameter which can be determined independent of the preference and true location parameters the gaussian models of rubinstein 1976 brennan 1979 and c mera 2003 and the gamma model of heston 1993 are all special cases the model provides simple relationships between expected returns and state price density parameters analogous to the diffusion case

credit risk measurement developments over the last 20 years abstract this paper traces developments in the credit risk measurement literature over the last 20 years the paper is essentially divided into two parts in the first part the evolution of the literature on the credit risk measurement of individual loans and portfolios of loans is traced by way of reference to articles appearing in relevant issues of the journal of banking and finance and other publications in the second part a new approach built around a mortality risk framework to measuring the risk and returns on loans and bonds is presented this model is shown to offer some promise in analyzing the risk return structures of portfolios of credit risk exposed debt instruments

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

modeling correlated market and credit risk in fixed income portfolios abstract current risk assessment methodologies separate the analysis of market and credit risk and thus misestimate security and portfolio risk levels we propose a new approach that relates financial market volatility to firm specific credit risk and integrates interest rate interest rate spread and foreign exchange rate risk into one overall fixed income portfolio risk assessment accounting for the correlation between these significant risk factors as well as portfolio diversification results in improved risk measurement and management the methodology is shown to produce reasonable credit transition probabilities prices for bonds with credit risk and portfolio value at risk measures

distributional and revenue raising arguments for tariffs this paper presents and analyses distributional and revenue raising arguments in favor of tariffs and other trade taxes it shows that such an argument depends crucially on the domestic tax powers that are available to the government conditions that must be satisfied by optimal tariffs are obtained and interpreted these conditions are then applied to a simplified model in order to gain greater insight into the determinants of the optimal tariffs finally the arguments are illustrated by some numerical examples which show that these tariffs can be far from negligible and demonstrate their sensitivity to various parameter changes

nonlinear mean reversion in the short term interest rate using a new bayesian method for the analysis of diffusion processes this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative the assumption of stationarity which is common in the literature represents a nontrivial prior belief about the shape of the drift function this belief and the use of flat priors contribute strongly to the finding of nonlinear mean reversion implementation of an approximate jeffreys prior results in virtually no evidence for mean reversion in interest rates unless stationarity is assumed finally the article documents that nonlinear drift is primarily a feature of daily rather than monthly data and that these data contain a transitory element that is not reflected in the volatility of longermaturity yields the drift of the short term interest rate is an important determinant of a wide variety of asset prices both inside and outside the boundaries of what is often called fixed income while volatilities may be estimated relatively accurately using high frequency observations of the short rate the short rate s extreme persistence makes identifying the true shape of the drift function a particularly elusive goal if our goal is merely to fit prices then the difficulty in estimating a drift function can be avoided by backing out implied drifts using a no arbitrage approach such as hull and white 1990 or heath jarrow and morton 1992 these methods bypass the true distribution entirely focusing on solving for the risk neutral drift function that is consistent with the cross section of bond prices if our goal however is to learn from prices and to be able to assess theories such as the expectations hypothesis that link short and long rates then estimating the drift function under the true measure is unavoidable in several recent articles a variety of sophisticated econometric techniques have been brought to bear on the problem in particular

equilibria and efficiency in the fixprice setting abstract the aim of this paper is to study efficiency under fixed price constraints and to define an equilibrium concept that extends to some degree the standard welfare analysis of general equilibrium theory this paper contains a description of the fixprice setting a study of the set of relatively pareto efficient allocations a definition of coupon equilibria the proof of their existence and an investigation into the structure of the set of coupon equilibria and of the set of economies admitting efficient coupon equilibria

a unified approach to bermudan and barrier options under stochastic volatility models with jumps abstract many financial assets such as currencies commodities and equity stocks exhibit both jumps and stochastic volatility which are especially prominent in the market after the financial crisis some strategic decision making problems also involve american style options in this paper we develop a novel fast and accurate method for pricing american and barrier options in regime switching jump diffusion models by blending regime switching models and markov chain approximation techniques in the fourier domain we provide a unified approach to price bermudan american options and barrier options under general stochastic volatility models with jumps the models considered include heston hull white stein stein scott the 3 2 model and the recently proposed 4 2 model and the hypergeometric model with general jump amplitude distributions in the return process applications include the valuation of discretely monitored contracts as well as continuously monitored contracts common in the foreign exchange markets numerical results are provided to demonstrate the accuracy and efficiency of the proposed method

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

an equilibrium model of bond pricing and a test of market efficiency in two previous and related papers 3 4 the authors have reported the results of estimating a particular equilibrium model of bond pricing using quarterly data on canadian government bonds for the period 1964 to 1979 this paper reports the results of applying a similar model to the pricing of u s government bonds for the period 1958 1979 using data from the crsp government bond file the paper also extends the previous empirical analysis by evaluating the ability of the pricing model to detect underpriced and overpriced bonds the data reveal a strong relation between price prediction errors and subsequent bond returns

a dynamic programming approach for pricing options embedded in bonds abstract we propose a dynamic programming dp approach for pricing options embedded in bonds the focus being on call and put options with advance notice an efficient procedure is developed for the cases where the interest rate process follows the vasicek cox ingersoll ross cir or generalized vasicek models our dp methodology uses the exact joint distribution of the interest rate and integrated interest rate at a future date conditional on the current value of the interest rate we provide numerical illustrations for the vasicek and cir models comparing our dp method with finite difference methods our procedure compares quite favorably in terms of both efficiency and accuracy an important advantage of the our dp approach is that it can be applied to more general models calibrated to capture the term structure of interest rates e g the generalized vasicek model

a consistent stochastic model of the term structure of interest rates for multiple tenors abstract starting from the observation that single currency swap basis spreads contradict classical arbitrage arguments we construct a framework where this basis arises due to the presence of roll over risk this risk consists of two components 1 facing a higher credit spread e g due to a credit downgrade when rolling over short term borrowing 2 heightened borrowing costs due to an absence of market liquidity the model simultaneously fits ois interest rate swap and basis swap market quotes including cds market quotes allows the two components of roll over risk to be explicitly separated this is highly relevant to the current libor transition illustrating why alternative benchmarks are fundamentally different from the rates they may be replacing

restricted redistributive taxation shadow prices and trade policy abstract this paper reports on the use of an algorithm to compute optimal policies in the areas of commodity taxation international trade and public shadow pricing for a government which is interested in redistributing income but has limited powers of taxation the algorithm is applied to selected ldc data using a highly simplified general equilibrium model some insight into the relationships between constraints on taxation and other areas of government policy is provided by analyzing models where domestic tax restrictions can make inefficient public production or tariffs on international trade desirable

a tractable interest rate model with explicit monetary policy rates abstract this paper proposes a novel interest rate model that presents simple analytical pricing formulas for interest rate based derivatives including swaps futures swaptions caps and floors exploring the regime switching feature of markov chains the proposed model focuses on discrete changes in the central bank policy rates the main driver of short term rate fluctuations an empirical analysis shows that the proposed model generally outperforms other standard short term rate models in fitting cross sections of options prices moreover the explicit nature of policy rates to some extent enables the model to infer risk neutral probabilities of the central bank rate decisions

a nonlinear general equilibrium model of the term structure of interest rates abstract we derive and test an alternative closed form general equilibrium model of the term structure within the cox ingersoll and ross theoretical framework in which yields are nonlinear functions of the risk free rate we show that equilibrium bond prices and the risk free rate are not always inversely related and that bond risk need not be strictly increasing in maturity using hansen s generalized method of moments to obtain parameter estimates this nonlinear model outperforms the cox ingersoll and ross square root model in describing actual treasury bill yields for the 1964 1986 period

continuous time methods in finance a review and an assessment i survey and assess the development of continuous time methods in finance during the last 30 years the subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing term structure theory asset pricing and optimal consumption and portfolio choices during the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance this latter subperiod has seen significant progress in econometric theory computational and estimation methods to test and implement continuous time models capital market frictions and bargaining issues are being increasingly incorporated in continuous time theory the roots of modern continuous time methods in finance can be traced back to the seminal contributions of merton 1969 1971 1973b in the late 1960s and early 1970s merton 1969 pioneered the use of continuous time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting merton 1973b also showed how such a framework can be used to develop equilibrium asset pricing implications thereby significantly extending the asset pricing theory to richer dynamic settings and expanding the scope of applications of continuous time methods to study problems in financial economics 1 within a span of about 30 years from the publication of merton s inf luential papers continuous time methods have become an integral part of financial economics indeed in certain core areas in finance such as e g asset pricing derivatives valuation term structure theory and portfolio selection continuoustime methods have proved to be the most attractive way to conduct research and gain economic intuition the continuous time approach in these areas has produced models with a rich variety of testable implications the econometric theory for testing continuous time models has made rapid strides in the last decade and has thus kept pace with the impressive progress on the theoretical front one hopes that the actual empirical investigations and estimation using the new procedures will follow suit soon

voluntariness and efficiency in the provision of public goods abstract this paper presents a characterization of lindahl allocations which makes no reference to personalized prices lindahl equilibria are characterized here by two conditions pareto efficiency and a voluntariness condition voluntariness requires that no consumer may benefit from a reduction in his contribution if this means that the vector of public goods must be reduced in the same proportion the intersection of the large set of voluntary allocations and that of efficient ones turns out to be under differentiability the set of lindahl allocations

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

optimal taxation and public production in an open dual economy abstract this paper analyses the determinants of optimal tax policy trade policy and shadow prices for cost benefit analysis in a dual economy it breaks new ground by combining in one model the tax and public investment policies considered in the public economics literature with the notion of labor market imperfection central to contributions on the dual economy optimal policies are first derived analytically providing rules for organizing production setting taxes and off setting labor market distortions production efficiency is shown to obtain for the taxable part of the economy a generalized ramsey rule derived for producing cumconsuming households in the directly non taxable sector of the economy and new characterizations of optimal rural urban migration established in the presence of distortionary taxation a simple general equilibrium model is then numerically implemented on data for a particular developing country the optimal policies analytically derived before are computed in the model under alternative assumptions about government revenue requirements the degree to which different sectors of the economy are directly taxable the nature of property rights and technological substitution possibilities the results of these computations provide further insight into the theoretical results as well as clarifying their quantitative significance

unspanned stochastic volatility and fixed income derivatives pricing we propose a parsimonious unspanned stochastic volatility model of the term structure and study its implications for fixed income option prices the drift and quadratic variation of the short rate are affine in three state variables the short rate its long term mean and variance which follow a joint markov vector process yet bond prices are exponential affine functions of only two state variables independent of the current interest rate volatility level because this result holds for an arbitrary volatility process such a process can be calibrated to match fixed income derivative prices furthermore this model can be extended by relaxing the time homogeneity to fit any arbitrary term structure in its hjm form this model nests the analogous stochastic equity volatility model of heston 190 heston s l 1993 a closed form solution for options with stochastic volatility review of financial studies 6 327 343 in particular if the volatility process is specified to be affine closed form solutions for interest rate options obtain we propose an efficient algorithm to compute these prices an application using data on caps and floors shows that the model can capture very well the implied black spot volatility surface while simultaneously fitting the observed term structure c 2005 elsevier b v all rights reserved

pricing and hedging interest rate options evidence from cap floor markets we examine the pricing and hedging performance of interest rate option pricing models using dailydata on us dollar cap and floor prices across both strike rates and maturities our results show that fitting the skew of the underlying interest rate probability distribution provides accurate pricing results within a one factor framework however for hedging performance introducing a second stochastic factor is more important than fitting the skew of the underlying distribution this constitutes evidence against claims in the literature that correctly specified and calibrated one factor models could replace multi factor models for consistent pricing and hedging of interest rate contingent claims 2004 elsevier b v all rights reserved

directly unproductive profit seeking dup activities this paper propses directly unproductive profit seeking dup activities as a general concept that embraces a wide range of recently analyzed economic activities including the subset of rent seeking activities considered by krueger it then proceeds to provide a synthesis and generalization of the welfare theoretic analysis of such activities by developing a fourfold categorization of cases depending on the levels of distortions before and after the dup activity thus a unification and overview of the subject are achieved

an economic capital model integrating credit and interest rate risk in the banking book banks often measure credit and interest rate risk in the banking book separately and then add the risk measures to determine economic capital this approach misses complex interactions between the two risk types we develop a framework where these risks are analysed jointly since banking book positions are generally not marked to market our model is based on book value accounting our simulations show that interactions matter and that ignoring them leads to risk overstatement the magnitude of the errors depends on the structure of the balance sheet and on the repricing characteristics of assets and liabilities

a simple approach to interest rate option pricing a simple introduction to contingent claim valuation of risky assets in a discrete time stochastic interest rate economy is provided taking the term structure of interest rates as exogenous closed form solutions are derived for european options written on 1 treasury bills 2 interest rate forward contracts 3 interest rate futures contracts 4 treasury bonds 5 interest rate caps 6 stock options 7 equity forward contracts 8 equity futures contracts 9 eurodollar liabilities and 10 foreign exchange contracts article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

a dynamic model for the forward curve this article develops and estimates a dynamic arbitrage free model of the current forward curve as the sum of i an unconditional component ii a maturity specific component and iii a date specific component the model combines features of the preferred habitat model the expectations hypothesis et and affine yield curve models it permits a class of low parameter multiple state variable dynamic models for the forward curve we show how to construct alternative parametric examples of the three components from a sum of exponential functions verify that the resulting forward curves satisfy the heath jarrow morton hjm conditions and derive the risk neutral dynamics for the purpose of pricing interest rate derivatives we select a model from alternative affine examples that are fitted to the fama bliss treasury data over an initial training period and use it to generate out of sample forecasts for forward rates and yields for forecast horizons of 6 months or longer the forecasts of this model significantly outperform those from common benchmark models jel c53 e43 e47 the structure of forward rates for fixed maturity loans to begin at various dates in the future can be inferred from the prices of treasury securities or directly observed from the extremely active eurodollar futures market the constellation of these rates or of the related yields plays a central role intheallocationofcapital therandombehaviorofthis yieldcurve or the relationship between the yields and the term to maturity is a subject of considerable theoretical and empirical study

throwing away a billion dollars the cost of suboptimal exercise strategies in the swaptions market abstract this paper studies the costs of applying single factor exercise strategies to american swap options when the term structure is actually driven by multiple factors using a multifactor string market model of the term structure we find that even when single factor models are recalibrated to match the market at every exercise date the exercise strategies they imply can be suboptimal based on estimates of notional amounts outstanding the total present value costs of following single factor strategies could be several billion dollars these results illustrate the importance of using well specified term structure models

pricing and hedging in incomplete markets abstract we present a new approach for positioning pricing and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable by assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure we derive a counterpart to the first fundamental theorem of asset pricing we also derive a counterpart to the second fundamental theorem which leads to unique derivative security pricing and hedging even though markets are incomplete for products that are not spanned by the liquid assets of the economy we show how our methodology provides more realistic bid ask spreads

firm specific information and the correlation between individual stocks and bonds abstract this paper examines the correlation between the returns on individual stocks and the yield changes of individual bonds issued by the same firm and finds that they are negatively and contemporaneously correlated this suggests that individual stocks and bonds are driven by firm specific information that is predominantly related to the mean rather than the variance of the firm s underlying assets furthermore i find that lagged stock returns have explanatory power for current bond yield changes while current stock returns are unrelated to lagged bond yield changes this shows that stocks lead bonds in reflecting firm specific information

a one factor model of interest rates and its application to treasury bond options 1990 a one factor model of interest rates and its application to treasury bond options financial analysts journal vol 46 no 1 pp 33 39

from the static to the dynamic some problems in the theory of taxation abstract this paper considers problems and issues that arise when we attempt to extend the static theory of taxation and production planning to a dynamic context and to combine that theory with theories of growth the reasons dynamic theory is less developed include problems with the analytical tractability of even those dynamic models which attempt to retain the basic structure of the static model furthermore difficult and interesting issues arise in a dynamic context which are either not present or are much less severe in the static theory special attention is paid to these new issues and the difficulties they pose

small dimension pde for discrete asian options abstract this paper presents an efficient method for pricing discrete asian options in presence of smile and non proportional dividends using an homogeneity property we show how to reduce an n 0 dimensional problem to a one or two dimensional one we examine different numerical specifications of our dimension reduced pde using a crank nicholson method interpolation method grid boundaries time and space steps as well as the extension to the case of non proportional discrete dividends using a jump condition we benchmark our results with quasi monte carlo simulation and a multi dimensional pde

an interest rate risk management model for commercial banks abstract this paper develops a goal programming model to assist a commercial bank in managing its exposure to interest rate risk the bank s objective is to immunize its equity position against innovations in interest rates while maximizing its market value to accomplish this task a duration gap framework is developed that does not require interest rate forecasts as decision variables the model includes assets liabilities and off balance sheet derivative securities the focus is on a protective put strategy that uses options on interest rate futures but to provide contrast a short interest rate futures position is examined as well application of the model to an illustrative environment indicates that for larger interest rate changes the option strategy provides better protection against interest rate risk than the short futures position

undominated prices in the three good model abstract any movement away from walrasian prices will make somebody worse off we ask which other prices share this property the paper characterizes the set of such prices called undominated prices for the three good economy output labor and a nonproduced good that is now well known from the work of barro grossman benassy and malinvaud we consider two groups of consumers workers and shareholders we show that under some conditions there exist prices and wages that generate unemployment and are undominated this requires that a workers be poorly endowed with the nonproduced good b there be little substitution in consumption between the produced and the nonproduced good and c the market for the produced good be balanced i e prices equal marginal costs

term structure movements and pricing interest rate contingent claims this paper derives an arbitrage free interest rate movements model ar model this model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free we then show that the ar model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates this paper also studies the behavior and the economics of the model our approach can be used to price a broad range of interest rate contingent claims including bond options and callable bonds

investment and shadow pricing in a growing economy with tax restrictions abstract this paper analyses the evolution of investment and shadow prices in a growing economy where government investment must be financed by distortionary taxation it pays particular attention to the sensitivity of this evolution to the sort of shocks that have affected developing countries recently increased debt service and an increased price for energy the analysis is conducted with the help of a numerical model of a dual economy the main policy implications are that it is inappropriate to use time invariant shadow prices in cost benefit analysis that the response of shadow prices to changes in the economic environment may not be unidirectional and that the accounting rate of interest cannot simply be seen as a regulator of investment that responds to shortages of investment finance in addition the paper develops a new approach to the valuation of terminal capital stock in a finite horizon model and shows how the non convexity of second best models can lead to discontinuities in investment

the pricing of options on default free bonds recent developments in the finance literature dealing with the valuation of contingent claims have been triggered by black and scholes 2 with their valuation of european options on corporate stocks the type of valuation model derived by black and scholes is attractive because it is independent of preferences this independence is possible due to the fact that the contingent claims are usually assumed to be contingent on traded assets or traded state variables for example a european call option is a claim contingent on the value of the corresponding stock to maintain the independence of the claim from preferences however some variables have to be discarded and considered as constants for example the rate of interest which is not a traded state variable is considered a constant in most of the literature see black and scholes 2 merton 11 and ingersoll 9 though this approximation might not cause important discrepancies in the case of corporate liabilities and options on corporate liabilities the effect of such an approximation on the value of default free bonds and options on default free bonds is more important since these liabilities depend only on the rate of interest

discount rates and shadow prices for public investment abstract this paper extends the harberger sandmo dreze model for public discount rates to a many good economy it derives a formula for discount rates which are specific to each public enterprise or agency and used by them to discount future outputs and inputs evaluated at market prices such an approach is shown to be more efficient than that of simply using a single rate for all public projects it is also more practical than asking each public firm to use second best shadow prices in their analyses of investment projects the general results are first provided then simple cases are considered and numerical examples presented to help interpret our formula and analyse its main determinants

commodity taxation with administered and free market prices theory and an application to china abstract this paper analyses commodity taxes in an economy where some production is centrally planned and subject to price controls and some is market determined it shows that backward shifting of taxes can lead to significant distributional effects and demonstrates how these lead to the modification of tax rules the implications of these modifications are analysed using a numerical model based on chinese data significant non uniformity of tax rates is shown to be desirable in a case where standard tax rules imply uniformity the sensitivity of optimal taxes to concern for inequality revenue requirements and food rations are also demonstrated

on alternative interest rate processes abstract in this paper alternative interest rate processes are estimated for denmark germany sweden and the uk using the generalized method of moments gmm in line with the study by chan karolyi longstaff and sanders 1992 on us data there seems to be a positive relation between interest rate level and volatility for some countries in contrast to their study it is found that mean reversion plays an important role for the specification of the interest rate dynamics the results seem to be robust to the use of different moment conditions and simulations of the estimated models reveal that they are fairly able to capture non fitted moments as well in addition there is evidence of a structural change in the danish interest rate process in august 1985 which may be due to a change in monetary policy the small sample properties of the gmm estimators are also studied through simulations

one factor interest rate models and the valuation of interest rate derivative securities this paper compares different approaches to developing arbitrage free models of the term structure it presents a numerical procedure that can be used to construct a wide range of one factor models of the short rate that are both markov and consistent with the initial term structure of interest rates

dynamic asset allocation in a mean variance framework the aim of this article is to analyze the portfolio strategies that are mean variance efficient when continuous rebalancing is allowed between the current date 0 and the horizon t under very general assumptions when a zero coupon bond of maturity t exists the dynamic efficient frontier is a straight line the slope of which is explicitly characterized every dynamic mean variance efficient strategy can be viewed as buy and hold combinations of two funds the zero coupon bond of maturity t and a continuously rebalanced portfolio an appropriate dynamic strategy defining the latter is explicitly derived for two particular price processes and comparisons of the efficient frontiers static versus dynamic are provided in these cases

the declining credit quality of u s corporate debt myth or reality in recent years the number of downgrades in corporate bond ratings has exceeded the number of upgrades leading some to conclude that the credit quality of u s corporate debt has declined however an alternative explanation of this apparent decline in credit quality is that the rating agencies are now using more stringent standards in assigning ratings an ordered probit analysis of a panel of firms from 1978 through 1995 suggests that rating standards have indeed become more stringent implying that at least part of the downward trend in ratings is the result of changing standards bond ratings play a key role in corporate financing and investment decisions a corporation that can issue higher rated bonds usually receives better terms than one that can issue only lower rated bonds by law or policy some investors can purchase only bonds with an investment grade rating a restriction which in some asset pricing models would affect the relative prices of financial assets numerous articles in the popular press have presumed that the credit quality of the debt of u s corporations has been declining over the last couple of decades the comprehensive study by lucas and lonski 1992 of moody s rating changes of corporate debt is consistent with this presumption to cite their statistics in 1970 moody s downgraded 21 issues and upgraded 23 issues but over the following years the number of bonds downgraded began to exceed by substantial margins the number of bonds upgraded and by 1990 moody s downgraded 301 issues and upgraded only 61 their study includes both investment and noninvestment grade bonds but internal data from donaldson lufkin jenrette confirm that this trend also applies to investment grade bonds alone in a somewhat different context grundy 1997 documents similar trends in the ratings of preferred shares over the 1965 to 1990 period as the credit quality of a firm s corporate debt decreases that firm will face a greater probability of financial distress which at the extreme translates into bankruptcy there is some debate as to the effect of financial dis

an empirical comparison of forward rate and spot rate models for valuing interest rate options our main goal is to investigate the question of which interest rate options valuation models are better suited to support the management of interest rate risk we use the german market to test seven spot and forward rate models with one and two factors for interest rate warrants for the period from 1990 to 1993 we identify a one factor forward rate model and two spot rate models with two factors that are not significantly outperformed by any of the other four models further rankings are possible if additional criteria are applied

voluntary and efficient allocations are walrasian let f be a private ownership economy call an allocation w voluntary for a price vector p if no agent can benefit by trading less at p we prove that under differentiability and interiority if w is voluntary and pareto efficient it is a competitive equilibrium for w perhaps surprisingly production economies where some agents receive profit income require a stronger voluntariness condition than the one sufficient for exchange economies the stronger condition singles out a commodity as a medium of exchange

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

single factor heath jarrow morton term structure models based on markov spot interest rate dynamics this paper considers the class of heath jarrow morton term structure models where the spot interest rate is markov and the term structure at time t is a function of time maturity and the spot interest rate at time t a representation for this class of models is derived and i show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen i provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable i also derive a partial differential equation representation of the term structure dynamics that does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process using the analysis presented in this paper a class of intertemporal term structure models is derived

dynamic models of the term structure in the past 25 years tremendous progress has been made in modeling the dynamics of the term structure of interest rates which play an instrumental role in determining prices and hedging portfolios of fixed income derivative securities this article reviews the theoretical development of the dynamic models of the default free term structure and their applications in pricing interest rate options classic models sometimes termed equilibrium models and their multifactor extensions are outlined these models provide clear economic intuitions connecting the term structure with economic fundamentals they also lay a foundation for the framework of the arbitrage models that price interest rate derivatives on the basis of the market prices of bonds this framework has been expanded and enriched by recent advances in directly modeling observable market rates through the market models and in incorporating an internally consistent correlation structure through the infinite dimensional models

a cyclical square root model for the term structure of interest rates this paper presents a cyclical square root model for the term structure of interest rates assuming that the spot rate converges to a certain time dependent long term level this model incorporates the fact that the interest rate volatility depends on the interest rate level and specifies the mean reversion level and the interest rate volatility using harmonic oscillators in this way we incorporate a good deal of flexibility and provide a high analytical tractability under these assumptions we compute closed form expressions for the values of different fixed income and interest rate derivatives finally we analyze the empirical performance of the cyclical model versus that proposed in cox et al 1985 and show that it outperforms this benchmark providing a better fitting to market data

importance sampling for integrated market and credit portfolio models a sophisticated approach for computing the total economic capital needed for various stochastically dependent risk types is the bottom up approach in this approach usually market and credit risks of financial instruments are modeled simultaneously as integrating market risk factors into standard credit portfolio models increases the computational burden of calculating risk measures it is analyzed to which extent importance sampling techniques previously developed either for pure market portfolio models or for pure credit portfolio models can be successfully applied to integrated market and credit portfolio models specific problems which arise in this context are discussed the effectiveness of these techniques is tested by numerical experiments for linear and non linear portfolios

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

pricing of long dated commodity derivatives do stochastic interest rates matter abstract does modelling stochastic interest rates beyond stochastic volatility improve pricing performance on long dated commodity derivatives to answer this question we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables we examine the empirical pricing performance of these models on pricing long dated crude oil derivatives estimating the model parameters from historical crude oil futures prices and option prices we find that stochastic interest rate models improve pricing performance on long dated crude oil derivatives when the interest rate volatility is relatively high furthermore increasing the model dimensionality does not tend to improve the pricing performance on long dated crude oil option prices but it matters for long dated futures prices we also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long dated crude oil option prices

fixprice analysis in productive economies abstract the paper compares the definitions of fixprice equilibrium for productive convex economies due to dreze benassy and malinvaud younes it turns out that dreze s resp malinvaud younes notion is the strictest resp least strict one the three notions are however equivalent under smoothness and absence of intermediate goods they are in particular equivalent for the familiar fixprice model with three goods money labor and output studied among others by barro grossman benassy and malinvaud

optimal trade taxes on agriculture in developing countries subsistence foodcrops and incomes are hard to tax in developing countries it is easy and common to tax agricultural imports and exports if domestic transactions cannot be taxed how should agricultural trade taxes be set and how should indirect taxes on nonagricultural consumer goods be set this paper derives and quantifies formulas for the optimal export tax on a nonfood agricultural product ghanaian cocoa in which the country has market power and the level of indirect taxes on taxable consumer goods it asks whether starting from free trade on cereals there should be import tariffs or subsidies copyright 1990 by royal economic society

the valuation of options on coupon bonds abstract we derive simple closed form expressions for european options on coupon bonds using the general equilibrium term structure framework of cox ingersoll and ross the properties of these options are very different from those implied by the black scholes model for example bond call and put values can move in the same direction as the value of the underlying bond changes this has important implications for hedging interest rate risk with bond options furthermore bond option values can be decreasing functions of interest rate volatility as well as their time to expiration we also examine the properties of american bond options

hedging demands in hedging contingent claims minimum variance hedging of a contingent claim in discrete time is suboptimal when the contingent claim is hedged for multiple periods and the objective is to maximize the expected utility of cumulative hedging errors this is because the hedging errors are not independent the difference between a minimum variance hedge and the optimal multiperiod hedge is called the hedging demand and depends on the hedger s preferences the characteristics of the contingent claim the trading frequency and horizon and most importantly the joint distribution of the contingent claim and the underlying security prices since modeling this joint distribution is empirically controversial i examine nonparametrically the economic importance of hedging demands in the case of hedging standard poor s 500 index options

a model for hedging load and price risk in the texas electricity market energy companies with commitments to meet customers daily electricity demands face the problem of hedging load and price risk we propose a joint model for load and price dynamics which is motivated by the goal of facilitating optimal hedging decisions while also intuitively capturing the key features of the electricity market driven by three stochastic factors including the load process our power price model allows for the calculation of closed form pricing formulas for forwards and some options products often used for hedging purposes making use of these results we illustrate in a simple example the hedging benefit of these instruments while also evaluating the performance of the model when fitted to the texas electricity market

taxing the informal economy the current state of knowledge and agendas for future research abstractthis paper reviews the literature on taxation of the informal economy taking stock of key debates and drawing attention to recent innovations conventionally the debate on whether to tax has frequently focused on the limited revenue potential high cost of collection and potentially adverse impact on small firms recent arguments have increasingly emphasised the more indirect benefits of informal taxation in relation to economic growth broader tax compliance and governance more research is needed we argue into the relevant costs and benefits for all including quasi voluntary compliance political and administrative incentives for reform and citizen state bargaining over taxation

discounting the distant future how much does model selection affect the certainty equivalent rate evaluating investment with long term consequences using discount rates that decline with the time horizon declining discount rates of ddrs means that future welfare changes are of greater consequence in present value terms recent work in this area has turned towards operationalising the theory and establishing a schedule of ddrs for use in cost benefit analysis using us data we make the following points concerning this transition i model selectionhas important implications for operationalising a theory of ddrs that depends upon uncertainty ii misspecification testing naturally leads to employing models that account for changes in the interest reat generating medanism lastly we provide an analysis of the policy implications of ddrs in the context of climate change for the us and show that the use of a state space model can increase valuations by 150 compared to conventional constant discounting

pricing interest rate derivatives a general approach the relationship between affine stochastic processes and bond pricing equations in exponential term structure models has been well established we connect this result to the pricing of interest rate derivatives if the term structure model is exponential affine then there is a linkage between the bond pricing solution and the prices of many widely traded interest rate derivative securities our results apply to m factor processes with n diffusions and l jump processes the pricing solutions require at most a single numerical integral making the model easy to implement we discuss many options that yield solutions using the methods of the article

interaction of market and credit risk abstract experience during the financial crisis illustrates that the integrated measurement and management of different forms of risk remains a challenge for industry practitioners researchers and financial supervisors alike in the context of related literature this article summarizes new research on the interaction of market and credit risk and implications for risk management that is presented in this special issue the research covered highlights in particular the errors that can occur in the aggregation of the two types of risk and the strong relationships between them that suggest caution in the use of pragmatic distinctions between them the article also touches on some research based lessons for supervisory policies and suggests some directions for future research

pricing interest rate derivative securities this article shows that the one state variableinterest rate models of vasicek 1977 and cox ingersoll and ross 1985b can be extended sothat they are consistent with both the current termstructure of interest rates and either the currentvolatilities of all spot interest rates or the currentvolatilities of all forward interest rates theextended vasicek model is shown to be very tracta ble analytically the article compares option pricesobtained using the extended vasicek model withthose obtained using a number of other models