lp modeling for asset liability management a survey of choices and simplifications dynamic linear programming lp models for asset liability management alm are quite powerful and flexible but face two challenges 1 many modeling choices not all consistent with one another or with finance theory and 2 solution difficulties due to the large number of scenarios obtained from standard interest rate models we first survey these modeling choices with a view to help researchers make self consistent choices next we review how the dynamic lp model for alm and the representation of uncertainty therein have been simplified in the past to motivate new or hybrid models emphasizing tractability to this end we review existing static lp models as extreme modeling simplifications and aggregation as a simplification of uncertainty

interest rate volatility and the term structure a two factor general equilibrium model we develop a two factor general equilibrium model of the term structure the factors are the short term interest rate and the volatility of the short term interest rate we derive closed form expressions for discount bonds and study the properties of the term structure implied by the model the dependence of yields on volatility allows the model to capture many observed properties of the term structure we also derive closed form expressions for discount bond options we use hansen s generalized method of moments framework to test the cross sectional restrictions imposed by the model the tests support the two factor model there are essentially two approaches to the modeling of the term structure of interest rates in continuous time the equilibrium approach pioneered by

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

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

robust optimization models for managing callable bond portfolios abstract a major sector of the bond markets is currently represented by instruments with embedded call options the complexity of bonds with call features coupled with the recent increase in volatility has raised the risks as well as the potential rewards for bond holders these complexities however make it difficult for the portfolio manager to evaluate individual securities and their associated risks in order to successfully construct bond portfolios traditional bond portfolio management methods are inadequate particularly when interest rate dependent cashflows are involved in this paper we integrate traditional simulation models for bond pricing with recent developments in robust optimization to develop tools for the management of portfolios of callable bonds two models are developed a single period model that imposes robustness by penalizing downside tracking error and a multi stage stochastic program with recourse both models are applied to create a portfolio to track a callable bond index the models are backtested using ex poste market data over the period from january 1992 to march 1993 and they perform constistently well

paying not to go to the gym how do consumers choose from a menu of contracts we analyze a novel dataset from three u s health clubs with information on both the contractual choice and the day to day attendance decisions of 7 752 members over three years the observed consumer behavior is difficult to reconcile with standard preferences and beliefs first members who choose a contract with a flat monthly fee of over 70 attend on average 4 3 times per month they pay a price per expected visit of more than 17 even though they could pay 10 per visit using a 10 visit pass on average these users forgo savings of 600 during their membership second consumers who choose a monthly contract are 17 percent more likely to stay enrolled beyond one year than users committing for a year this is surprising because monthly members pay higher fees for the option to cancel each month we also document cancellation delays and attendance expectations among other findings leading explanations for our findings are overconfidence about future self control or about future efficiency overconfident agents overestimate attendance as well as the cancellation probability of automatically renewed contracts our results suggest that making inferences from observed contract choice under the rational expectation hypothesis can lead to biases in the estimation of consumer preferences

the valuation of american options on bonds abstract we value american options on bonds using a generalization of the geske johnson geske r johnson h 1984 journal of finance 39 1151 1542 gj technique the method requires the valuation of european options and options with multiple exercise dates it is shown that a risk neutral valuation relationship rnvr along the lines of black scholes black f scholes m 1973 journal of political economy 81 637 659 model holds for options exercisable on multiple dates even under stochastic interest rates when the price of the underlying asset is lognormally distributed the proposed computational procedure uses the maximized value of these options where the maximization is over all possible exercise dates the value of the american option is then computed by richardson extrapolation the volatility of the underlying default free bond is modeled using a two factor model with a short term and a long term interest rate factor we report the results of simulations of american option values using our method and show how they vary with the key parameter inputs such as the maturity of the bond its volatility and the option strike price

market failure in incentive based regulation the case of emissions trading abstract among the existing evaluations of the us epa s emissions trading program a consensus has emerged while the program has resulted in significant cost savings it has not even approximately achieved a cost effective allocation of the control responsibility the cost savings have been smaller and the trades fewer than might have been expected at the outset of the program in this article we explore one hypothesis which purports to explain the divergence between the cost minimizing and the observed pattern of trades for nonuniformly mixed pollutants the trading process hypothesis attributes some significant proportion of this divergence to the nature of the process by which emission reduction credits are traded under the bubble policy an examination of actual bubble trades reveals that the actual trading process is sequential and bilateral and hence differs considerably from the implicit process modeled in the existing empirical studies simulations of this more realistic trading process suggest that the resulting equilibria deviate considerably from cost effective allocations of the control responsibility

a discrete time approach to arbitrage free pricing of credit derivatives this paper develops a framework for modelling risky debt and valuing credit derivatives that is flexible and simple to implement and that is to the maximum extent possible based on observables our approach is based on expanding the heath jarrow morton term structure model to allow for defaultable debt rather than follow the procedure of implying out the behavior of spreads from assumptions concerning the default process we work directly with the evolution of spreads the risk neutral drifts in the resulting model possess a recursive representation that facilitates implementation and makes it possible to handle path dependence and early exercise features without difficulty the framework permits embedding a variety of specifications for default we present an empirical example of a default structure which provides promising calibration results

trading sulphur emissions in europe guided bilateral trade in this paper a system of guided permit trading is developed for so2emissions reduction which considers permit trading as a bilateral andsequential process this implies that in order to meet the deposition targetsat the end of the trading process not every single trade transaction hasto meet the deposition targets to ensure that the target is ultimately met the number of permits traded should be controlled by a trade coordinatinginstitution a simulation of the system of guided bilateral trading ofso2 permits among european countries on the basis of the secondso2 protocol indicates that some non profitable trade transactionstake place this prevents the cost effective emission allocation from beingfully achieved however the calculations show that guided bilateral permittrading may generate substantial cost savings while contributing toenvironmental protection

dynamic models for fixed income portfolio management under uncertainty abstract we develop multi period dynamic models for fixed income portfolio management under uncertainty using multi stage stochastic programming with recourse the models integrate the prescriptive stochastic programs with descriptive monte carlo simulation models of the term structure of interest rates extensive validation experiments are carried out to establish the effectiveness of the models in hedging against uncertainty and to assess their performance vis a vis single period models an application to tracking the salomon brothers mortgage index is reported with very encouraging results results that establish the efficacy of the models in hedging against out of sample scenarios are also reported for an application from money management the multi period models outperform classical models based on portfolio immunization and single period models

we like to see you in the gym a field experiment on financial incentives for short and long term gym attendance abstract this paper presents a field experiment to analyze whether financial incentives conditional on attending the gym can increase gym attendance of members of an off campus gym both in the short run two quarters of a year and in the long run the next two quarters of the year the incentivized subjects received a rebate of approximately 10 of the average membership fee conditional on attending the gym at least once per week in 11 of the 13 weeks of the first quarter of 2010 in the second quarter of 2010 the incentive was repeated allowing subjects a second chance to earn a rebate in both quarters they received a rebate of 25 instead of 15 conditional on attending the gym at least twice a week in 11 of the 13 weeks gym attendance was recorded both during the intervention period and during the two quarters after we compared the conditional incentive to attend the gym with an unconditional incentive where subjects would receive the 10 rebate per quarter merely for staying a member of the gym the conditional incentive to attend the gym had a positive yet non persistent impact on gym attendance we conclude that gym attendance can be improved through incentives but that smarter non financial incentives and nudges need to be explored as well to obtain more persistent improvements in gym attendance

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

using the black derman toy interest rate model for portfolio optimization abstract no arbitrage interest rate models are designed to be consistent with the current term structure of interest rates the diffusion of the interest rates is often approximated with a tree in which the scenario dependent fair price of any security is calculated as the present value of the risk neutral expectation by backward induction to use this tree in a portfolio optimization context it is necessary to account for the so called market price of risk in this paper we present a method to change the conditional probabilities in the black derman toy model to the physical or real measure including the market price of risk and explore the economic implications for expected spot rates and for expected bond returns

the dynamics of the forward interest rate curve a formulation with state variables the objective of this paper is twofold first the paper develops a class of models of the term structure of interest rates in the heath jarrow and morton 1992 framework with dynamics characterized by the evolution of a small set of state variables second the paper exploits this characterization of the dynamics of the term structure in an estimation exercise that makes use of both the time series and cross section of bond prices in this way our class of models bridges the gap between traditional models such as cox ingersoll and ross 1985 and vasicek 1977 that emphasize the dynamics of interest rates and the models of heath jarrow and morton 1992 that stress fitting the cross section of bond prices

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

the term structure of interest rates with housing abstract this paper develops a general equilibrium model to study the link between the amount of capital invested in housing assets and the term structure of interest rates in the model the production of housing assets is irreversible and housing assets can be used as collateral for borrowing funds agents decisions about consumption and investments in housing and non housing assets generate a time varying market price of risk that drives the dynamics of the term structure the calibration to u s data using the simulated method of moments technique captures the dynamics of consumption and the short and long term interest rates

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

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

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

discretized reality and spurious profits in stochastic programming models for asset liability management in the literature on stochastic programming models for practical portfolio investment problems relatively little attention has been devoted to the question how the necessarily approximate description of the asset price uncertainty in these models influences the optimal solution in this paper we will show that it is important that asset prices in such a description are arbitrage free descriptions which have been suggested in the literature are often inconsistent with observed market prices and or use sampling to obtain a set of scenarios about the future we will show that this effectively introduces arbitrage opportunities in the optimization model for an investor who cannot exploit arbitrage opportunities directly because of market imperfections and trading restrictions we will illustrate that the presence of such arbitrage opportunities may cause substantial biases in the optimal investment strategy

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

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

economic prescriptions for environmental problems how the patient followed the doctor s orders o ne of the dangers with ivory tower theorizing is that it is easy to lose sight of the actual set of problems which need to be solved and the range of potential solutions as one who frequently engages in this exercise i can attest to this fact in my view this loss of sight has become increasingly evident in the theoretical structure underlying environmental economics which often emphasizes elegance at the expense of realism in this paper i will argue that both normative and positive theorizing could greatly benefit from a careful examination of the results of recent innovative approaches to environmental management the particular set of policies examined here involves two tools which have received widespread support from the economics community marketable permits and emission charges pigou 1932 dales 1968 kneese and schultze 1975 both tools represent ways to induce businesses to search for lower cost methods of achieving environmental standards they stand in stark contrast to the predominant command and control approach in which a regulator specifies the technology a firm must use to comply with regulations under highly restrictive conditions it can be shown that both of the economic approaches share the desirable feature that any gains in environmental quality will be obtained at the lowest possible cost baumol and oates 1975 until the 1960s these tools only existed on blackboards and in academic journals as products of the fertile imaginations of academics however some countries have recently begun to explore using these tools as part of a broader strategy for managing environmental problems

arbitrage opportunities in arbitrage free models of bond pricing mathematical models of bond pricing are used by both academics and wall street practitioners with practitioners introducing time dependent parameters to fit arbitrage free models to selected asset prices we show in a simple one factor setting that the ability of such models to reproduce a subset of security prices need not extend to state contingent claims more generally we argue that the additional parameters of arbitrage free models should be complemented by close attention to fundamentals which might include mean reversion multiple factors stochastic volatility and or nonnormal interest rate distributions

convertible bonds model value attribution and analytics convertible bonds provide investors an option to convert the bond into the underlying equity for this reason a convertible bond is exposed to both equity and interest rate risk incorporating these two sources of risk into the model is particularly important for callable issues in this study a two factor model is used to analyze a sample of bonds the model shows that the correlation of stock risk and interest rate risk may affect convertible bond prices significantly the bond pricing model also provides portfolio analytics and can decompose a convertible bond into its basic components the stock and bonds with different maturities this approach enables an investor to implement a more precise hedging strategy than is possible using only delta

empirical tests of two state variable heath jarrow morton models models for pricing interest rate claims developed under the heath jarrow morton paradigm differ according to the volatility structure imposed on forward rates for most general hjm structures the resultant path dependence creates implementation problems ritchken and sankarasubramanian have recently identified necessary and sufficient conditions on the class of volatility structures of forward rates that enable the term structure dynamics to be captured by a finite set of state variables the class is quite rich the instantaneous spot rate volatility may be quite general but the model curtails the structure of forward rate volatilities relative to this spot rate volatility this article provides empirical tests for this class of volatility structures unlike other studies the volatility structure is examined over a broad section of maturities in the yield curve using treasury data over the period 1982 94 we find support for this class furthermore unlike other studies no evidence of a volatility hump is identified copyright 1996 by ohio state university press

improving efficiency in bilateral emission trading when environmental damages from emissions are spatially nonuniform permit trading has been modeled most often as a pollution offset program in which emission permits are traded between agents subject to constraints on ambient air quality to date the institution envisioned to implement such a program involves trading on a bilateral and sequential basis however simulation studies indicate that the sequence of trades may alter the outcome and undermine the cost savings from a pollution offset program this paper identifies a design for the trading institution that tends to overcome this phenomenon and improve the efficiency of equilibria obtained in a simulation model we model a bilateral trading process for the reduction of sulfur dioxide emissions with a stochastic description of the sequence of trades within groups of nations in europe when trading takes place between disaggregated stylistic representations of economic enterprises rather than between national governments a significantly greater portion of potential savings is achieved in fact under most sets of assumptions approximate first order stochastic dominance is achieved wherein the more decentralized the trading agents the greater the expected savings from a trading program

nonparametric modeling of u s interest rate term structure dynamics and implications on the prices of derivative securities this paper develops a nonparametric model of interest rate term structure dynamics based on a spot rate process that permits only positive interest rates and a market price of interest rate risk that precludes arbitrage opportunities both the spot rate process and the mar ket price of interest rate risk are nonparametrically specified so that the model allows for maximal flexibility in fitting into the data marginal density of interest rates and historical term structure data are exploited to provide robust estimation of the nonparametric term structure model the model is implemented using u s data and the estimation results are compared to those in the available literature empirical results not only provide strong evidence that most traditional spot rate models and market prices of interest rate risk are misspecified but also confirm that the nonparametric model generates significantly differ ent term structures and prices of common derivatives

the analysis and valuation of interest rate options abstract this paper provides a simple alternative model for the valuation of european style interest rate options the assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two state process later this assumption is made more specific by postulating that the discount on a zero coupon bond follows a multiplicative binomial process in contrast to the black scholes assumption applied to zero coupon bonds the limiting distribution of this process has the attractive features that the zero bond price has a natural barrier at unity thus precluding negative interest rates and that the bond price is negatively skewed the model is used to price interest rate options in general and interest rate caps and floors in particular the model is then generalized and applied to european style options on bonds a relationship is established between options on swaps and options on coupon bonds the generalized model then provides a computationally simple formula closely related to the black scholes formula for the valuation of european style options on swaps

a model for designing callable bonds and its solution using tabu search abstract we formulate the problem of designing callable bonds as a non linear global optimization problem the data of the model are obtained from simulations of holding period returns of a given bond design which are used to compute a certainty equivalent return viz some target assets the design specifications of the callable bond are then adjusted so that the certainty equivalent return is maximized the resulting problem is multi modal and a tabu search procedure implemented on a distributed network of workstations is used to optimize the bond design the model is compared with the classical portfolio immunization model and the tabu search solution technique is compared with simulated annealing for solving the global optimization program it is shown that the global optimization model yields higher returns than portfolio immunization it is also shown that tabu search is computationally more efficient than simulated annealing in solving the model and it produces better solutions

on the suboptimality of single factor exercise strategies for bermudan swaptions abstract this paper resolves the disagreement between longstaff et al 2001 journal of finance economics 62 39 66 and andersen and andreasen 2001 journal of financial economics 62 3 37 over the effectiveness of the common business practice of using best fit single factor term structure models to deduce exercise strategies of bermudan swaptions i examine the cost of using recalibrated single factor models to determine the exercise strategy for bermudan swaptions in a multifactor world i show that single factor exercise strategies applied in a multifactor world only give rise to economically insignificant losses furthermore i find that the conditional model risk as defined in longstaff et al 2001 journal of finance economics 62 39 66 is statistically insignificant given the number of observations additional tests using the primal dual algorithm of andersen and broadie 2004 management science 50 9 indicate that losses found in longstaff et al 2001 journal of finance economics 62 39 66 cannot as claimed be ascribed to the number of factors

a comparison of yield curve estimation techniques using uk data abstract i compare different methods of estimating the term structure of interest rates on a daily uk treasury bill and gilt data that spans the period from january 1995 to january 1999 in sample and out of sample statistics reveal the superior pricing ability of certain methods characterised by an exponential functional form in addition to these standard goodness of fit statistics model performance is judged in terms of two trading strategies based on model residuals both strategies reveal that parsimonious representations of the term structure perform better than their spline counterparts characterised by a linear functional form this is valid even when abnormal returns are adjusted for market movements linear splines overfit the data and are likely to give misleading results

a theory of the nominal term structure of interest rates a model of the nominal term structure of interest rates is developed that has a positive and stationary process for the interest rate and delivers closed form expressions for the prices of discount bonds and european options on bonds unlike the one state variable version of the cox ingersoll and ross 1985 model this model even in its one state variable version allows the term premium to change sign as a function of the state and the term to maturity and also allows for shapes of the yield curve that are observed in the u s data but that are disallowed in the cox ingersoll and ross model article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

from data to model and back to data a bond portfolio management problem abstract the bond portfolio management problem is formulated as a multiperiod stochastic program using interest rate scenarios the scenarios are sampled from the binomial lattice from a black derman toy model the paper analyzes the sensitivity of the solution of the resulting large scale mathematical program with respect to the model inputs the numerical results are for the italian bond market

the empirical properties of two classes of designs for transferable discharge permit markets abstract previous work by atkinson and lewis j environ econ manag 1 237 250 1974 and anderson et al an analysis of alternative policies for attaining and maintaining a short term no2 standard mathtech inc princeton n j 1979 has indicated the tremendous cost advantages to be achieved by moving from a policy based on emission standards to one based on marketable emission permits as tietenberg land econ 56 391 416 1980 points out however neither of the major permit designs treated in the literature are optimal from all points of view this has triggered a search for alternative permit designs which while they may not minimize compliance costs have sufficient other virtues as to make them attractive on other grounds the purpose of this paper is to examine within the context of an empirical mathematical programming model the air quality emission and cost consequences of two classes of the permit designs which can be implemented in the absence of information on control costs this case study involves particulate control in st louis

can financial incentives help people trying to establish new habits experimental evidence with new gym members can financial incentives aid habit formation in people attempting to establish a positive health behavior we provide evidence on this question from a randomized controlled trial of modest sized incentives to attend the gym among new members of a fitness facility our experiment randomized 690 participants into a control group that received a 30 payment unconditionally or one of 3 incentive groups that received a payment for attending the gym at least 9 times over the first 6 weeks of membership two incentive treatment arms offered monetary payments of 30 and 60 the third incentive treatment motivated by the endowment effect offered a physical item worth 30 all three incentives had only small impacts on attendance during members first 6 weeks and no effect on their post incentive visit trajectories we document substantial overconfidence among new members about their likely visits and discuss how overconfidence may undermine the effectiveness of incentive programs

modeling the stochastic behavior of short term interest rates pricing implications for discount bonds abstract this paper models the stochastic behavior of short term interest rates and determines the correct specification of the drift and diffusion functions of the spot rate process a wide variety of one factor diffusion and two factor stochastic volatility models is compared in terms of their ability to capture the dynamics of interest rate volatility the empirical evidence on the one three and six month eurodollar deposit rates indicates that a new class of models with stochastic volatility is better than the single factor diffusion models in forecasting the future volatility of interest rate changes the paper extends the one factor bdt term structure model to a two factor setting and presents the pricing implications for discount bonds monte carlo simulation results for the implied yields of three and six month zero coupon bonds imply that incorporating the so called level and garch effects in volatility improves the pricing performance of the interest rate models

bond and option pricing when short rates are lognormal this article describes a one factor model for bond and option pricing that is based on the short term interest rate and that allows the target rate mean reversion and local volatility to vary deterministically through time for any horizon the distribution of possible short rates is lognormal so the rate neither falls below zero nor reflects off a barrier at zero a model like this allows one to match the yield curve the volatility curve and the cap curve surprisingly adding to future local volatility lowers the volatility curve a conventional binary tree with probabilities of 0 5 but variable time spacing is used to value bonds and options when the inputs are constant the slope of the yield curve starts out positive and ends up negative while its curvature shifts from negative to positive even when mean reversion is zero the volatility curve has a negative slope the differential cap curve rises steeply through the effects of volatility and then falls steeply through the effects of discounting and a falling forward rate used as the strike price

integrated simulation and optimization models for tracking indices of fixed income securities increasing performance pressures on fixed income managers have led to a search for new and creative ways to add to portfolio returns the largest pension plan sponsors insurance companies foundations and money management firms are using indexed portfolios as their fixed income assets management strategies since the late 1970s tracking a fixed income index is a difficult task due to transaction costs portfolio size and diversification restrictions liquidity requirements bid ask spreads etc this paper develops an integrated simulation and optimization approach for tracking fixed income indices the model was implemented at metropolitan life insurance company we introduce a simulation model for generating scenarios of holding period returns of the securities in the index then we develop optimization models to select a portfolio that tracks the index the models penalize downside deviations of the portfolio return from the index the developed framework is used to track the salomon brothers mortgag

an integrated pricing model for defaultable loans and bonds abstract in recent years credit risk has played a key role in risk management issues practitioners academics and regulators have been fully involved in the process of developing studying and analysing credit risk models in order to find the elements which characterize a sound risk management system in this paper we present an integrated model based on a reduced pricing approach for market and credit risk its main features are those of being mark to market and that the spread term structure by rating class is contingent on the seniority of debt within an arbitrage free framework we introduce issues such as the integration of market and credit risk the use of stochastic recovery rates and recovery by seniority moreover we will characterize default risk by estimating migration risk through a mortality rate actuarial based approach the resultant probabilities will be the base for determining multi period risk neutral transition probability that allow pricing of risky debt in the trading and banking book

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

the intersection of market and credit risk abstract economic theory tells us that market and credit risks are intrinsically related to each other and not separable we describe the two main approaches to pricing credit risky instruments the structural approach and the reduced form approach it is argued that the standard approaches to credit risk management creditmetrics creditrisk and kmv are of limited value when applied to portfolios of interest rate sensitive instruments and in measuring market and credit risk empirically returns on high yield bonds have a higher correlation with equity index returns and a lower correlation with treasury bond index returns than do low yield bonds also macro economic variables appear to influence the aggregate rate of business failures the creditmetrics creditrisk and kmv methodologies cannot reproduce these empirical observations given their constant interest rate assumption however we can incorporate these empirical observations into the reduced form of jarrow and turnbull 1995b drawing the analogy risk 5 63 70 model here default probabilities are correlated due to their dependence on common economic factors default risk and recovery rate uncertainty may not be the sole determinants of the credit spread we show how to incorporate a convenience yield as one of the determinants of the credit spread for credit risk management the time horizon is typically one year or longer this has two important implications since the standard approximations do not apply over a one year horizon first we must use pricing models for risk management some practitioners have taken a different approach than academics in the pricing of credit risky bonds in the event of default a bond holder is legally entitled to accrued interest plus principal we discuss the implications of this fact for pricing second it is necessary to keep track of two probability measures the martingale probability for pricing and the natural probability for value at risk we discuss the benefits of keeping track of these two measures

stochastic volatility movements in short term interest rates and bond option values abstract two classes of models for pricing interest rate contingent claims are compared the first contains standard single factor models while the second includes stochastic volatility variants of these it is demonstrated that incorporating stochastic volatility significantly improves the ability of the models to fit movements in short term interest rates the fundamental reason for this is that standard univariate models do not generate enough conditional heteroskedasticity the models are also compared on the basis of bond option prices when each is constrained to fit a particular yield curve the results suggest that stochastic volatility models will typically produce lower option values than corresponding single factor models particularly for near the money to deep out of the money options this is because estimated historical volatilities are significantly lower under stochastic volatility when single factor models are constrained to the same level of volatility as implied by stochastic volatility models in most cases the pricing differences become minor

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

lattice models for pricing american interest rate claims this article establishes efficient lattice algorithms for pricing american interest sensitive claims in the heath jarrow and morton paradigm under the assumption that the volatility structure of forward rates is restricted to a class that permits a markovian representation of the term structure the class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility the algorithm exploits the markovian property of the term structure and permits the efficient computation of all types of interest rate claims specific examples are provided

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

the valuation of complex derivatives by major investment firms empirical evidence this article examines the auction of a portfolio of collateralized mortgage obligations cmos to major broker dealers and institutional investors the unique data set allows us to analyze a number of important empirical questions related to the valuation of cmos by the bidders and the elasticity of demand for the securities the results reveal that the valuations differ substantially implying a significant elasticity of demand this article is designed to shed light on two related questions first it extends the work of bagwell 1991 1992 brown and ryngaert 1990 and bradley desai and kim 1988 among others on shareholder heterogeneity and the elasticity of the demand for financial assets to date the empirical research on investor heterogeneity has focused on common stock this article supplements previous work by examining an auction of another class of securities complex collateralized mortgage obligations cmos to major securities dealers and institutional investors second it provides perspective on fixed income valuation models in the spirit of cox ingersoll and ross 1985 and black derman and toy 1990 virtually all of these models even those that specify relatively complex interest rate processes assume homogeneous beliefs this implies that within the constraints imposed by estimation error sophisticated investors should place equal values on fixed income securities bagwell observes that investors can be heterogeneous along several dimensions first heterogeneity can be induced by tax rules to the extent that different investors are taxed in different ways their demand for securities will be affected second transaction costs can cause heterogeneity by driving a wedge between buyers sellers and owners of a security third investors can differ in their assessments of the value of a security either because they possess different information or because they analyze that information in different ways fourth investors can face different nontradeable risks and thus can have different assessments of the value of a security depending on how it interacts with these risks finally it has been suggested by lee shleifer and thaler 1991 among others that investors may differ for idio

a stochastic programming model for money management abstract portfolio managers in the new fixed income securities have to cope with various forms of uncertainty in addition to the usual interest rate changes uncertainy in the timing and amount of cashflows changes in the default and other risk premia and so on complicate the portfolio manager s problem we develop here a multi period dynamic portfolio optimization model to address this problem the model specifies a sequence of investment decisions over time that maximize the expected utility of return at the end of the planning horizon the model is a two stage stochastic program with recourse the dynamics of interest rates cashflow uncertainty and liquidity default and other risk premia are explicitly modeled through postulated scenarios simulation procedures are developed to generate these scenarios the optimization models are then integrated with the simulation procedures extensive validation experiments are carried out to establish the effectiveness of the model in dealing with uncertainty in particular the model is compared against the popular portfolio immunization strategy and against a portfolio based on mean absolute deviation optimization

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 multifactor spot rate model for the pricing of interest rate derivatives we propose a multifactor model in which the spot rate libor follows a lognormal process with a stochastic conditional mean under the risk neutral measure in addition to the spot rate factor the second factor is related to the premium of the first futures rate over the spot libor similarly the third factor is related to the premium of the second futures rate over the first futures rate we calibrate the model to the initial term structure of futures rates and to the implied volatilities of interest rate caplets we then apply the model to price interest rate derivatives such as european and bermudan style swaptions and yieldspread options the model can be employed to price more complex interest rate derivatives such as path dependent derivatives or multi currency dependent derivatives because of its markovian property

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

black merton and scholes their central contributions to economics i will briefly summarize the central contributions to economics of fisher black robert c merton and myron s scholes of course the contribution that first comes to mind is the black scholes option pricing formula for which robert merton and myron scholes were awarded the alfred nobel memorial prize in economic sciences in 1997 i have no doubt that because of his key role in that far reaching formula fischer black would have shared in that prize but for his recent untimely death so i will depart from the usual convention for essays that appear in this journal on these occasions and address the contributions of all three of these exceptional economists simultaneously rather than giving separate treatment to fischer black my goal is to give an objective and concise account of their path breaking research and what it has offered to the theory and practice of economics

risk management implications of time inconsistency model updating and recalibration of no arbitrage models a widespread approach in the implementation of asset pricing models is based on the periodic recalibration of its parameters and initial conditions to eliminate any conflict between model implied and market prices modern no arbitrage market models facilitate this procedure since their solution can usually be written in terms of the entire initial yield curve as a result the model fits by construction the interest rate term structure this procedure is however generally time inconsistent since the model at time t 0 completely specifies the set of possible term structures for any t 0 in this paper we analyze the pros and cons of this widespread approach in pricing and hedging both theoretically and empirically the theoretical section of the paper shows a under which conditions recalibration improves the hedging errors by limiting the propagation of an initial error b that recalibration introduces timeinconsistent errors that violate the self financing argument of the standard replication strategy the empirical section of the paper quantifies the trade off between a and b under several scenarios first we compare this trade off for two economies with and without model specification error then we discuss the trade off when the underlying economy is not markovian 2005 elsevier b v all rights reserved

a methodology for assessing model risk and its application to the implied volatility function model we propose a methodology for assessing model risk and apply it to the implied volatility function ivf model this is a popular model among traders for valuing exotic options our research is different from other tests of the ivf model in that we reflect the traders practice of using the model for the relative pricing of exotic and plain vanilla options at one point in time we find little evidence of model risk when the ivf model is used to price and hedge compound options however there is significant model risk when it is used to price and hedge some barrier options

on the optimality of path dependent structured funds the cost of standardization abstract this paper examines the suitability of an important class of standard financial structured products namely those whose performances are based on smoothing the return of a given risky underlying asset while providing a guarantee at maturity using various assumptions about the customers attitudes towards risk we show that such standardized products are not optimal even if the financial market volatility is constant as a by product we provide in particular the optimal portfolio value in the regret rejoice framework to go further with the notion of aversion of getting a return smaller than the risk free one using the notion of compensating variation we determine for the first time the monetary losses of providing these standardized products instead of the optimal ones to the customers we show that these monetary losses can be very significant when the volatility of the risky asset is stochastic from the operational point of view such results highly suggest to trade on the volatility index vix and or to introduce derivatives written on it when selling standardized funds in order to better meet investors needs and preferences

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

inflation risk premia and the expectations hypothesis abstract we study the properties of the nominal and real risk premia of the term structure of interest rates we develop and solve the bond pricing implications of a structural monetary version of a real business cycle model with taxes and endogenous monetary policy we show the relation of this model with the class of essentially affine models that incorporate an endogenous state dependent market price of risk we characterize and estimate the inflation risk premium and find that over the last 40 years the ten year inflation risk premium has been has averaged 70 basis points it is time varying ranging from 20 to 140 basis points over the business cycle and its term structure is sharply upward sloping the inflation risk premium explains 23 42 of the time variation in the five ten year forward risk premium and it plays an important role in help explain deviations from the expectations hypothesis of interest rates

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

another look at models of the short term interest rate the short term rate of interest is fundamental to much of theoretical and empirical finance yet no consensus has emerged on the dynamics of its volatility we show that models which parameterize volatility only as a function of interest rate levels tend to over emphasize the sensitivity of volatility to levels and fail to model adequately the serial correlation in condi tional variances on the other hand serial correlation based models like garch models fail to capture adequately the relationship between interest rate levels and volatility we introduce and test a new class of models for the dynamics of short term interest rate volatility which allows volatility to depend on both interest rate levels and information shocks two important conclusions emerge first the sensitivity of interest rate volatility to interest rate levels has been overstated in the literature while this relationship is important adequately modeling volatility as a function of unexpected information shocks is also important sec ond we conclude that the volatility processes in many existing theoretical models of interest rates are misspecified and suggest new paths toward improving the theory

pricing interest rate options in a two factor cox ingersoll ross model of the term structure solutions are presented for prices on interest rate options in a two factor version of the cox ingersoll ross model of the term structure specific solutions are developed for caps on floating interest rates and for european options on discount bonds coupon bonds coupon bond futures and euro dollar futures the solutions for the options are expressed as multivariate integrals and we show how to reduce the calculations to univariate numerical integrations which can be calculated very quickly the two factor model provides more flexibility in fitting observed term structures and the fixed parameters of the model can be set to capture the variability of the term structure over time article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

capturing the correlations of fixed income instruments this paper develops a framework for managing portfolios of fixed income instruments based on traditional principles from the equities market i e based on diversification it shows through an analysis of the high yield bond market over the period 1987 to 1991 that fixed income prices could be highly correlated these correlations can be quantified and integrated in a systematic way in an asset liability management framework for vanishing fixed income securities however we cannot resort to statistical analysis of historical data in order to quantify correlations the paper develops a forward looking simulation procedure for capturing correlations applications are illustrated for examples from high yield bonds and mortgage backed securities the superiority of the proposed approach over the traditional portfolio immunization techniques is demonstrated in the context of funding an insurance liability stream with mortgage instruments

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

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