the valuation of american options with stochastic interest rates a generalization of the geske johnson technique the geske johnson approach provides an efficient and intuitively appealing technique for the valuation and hedging of american style contingent claims here we generalize their approach to a stochastic interest rate economy the method is implemented using options exercisable on one of a finite number of dates we illustrate how the value of an american style option increases with interest rate volatility the magnitude of this effect depends on the extent to which the option is in the money the volatilities of the underlying asset and the interest rates as well as the correlation between them

a reevaluation of the macroeconomic effects of positive trend inflation abstract to date most of the papers which have examined the effects of trend inflation on the properties of new keynesian model were based on relatively simple sticky prices dsge models and whose realism was sometimes questionable in this paper we re evaluate the macroeconomic effects of non zero trend inflation building on the model of ascari 2004 as one of the most cited papers in the literature on the effects of trend inflation we show that the omission of some important theoretical ingredients significantly distorts the results obtained to date we propose a refinement of this model by introducing two theoretical important ingredients namely investment adjustment costs and a roundabout production structure once we add these features to make the model more realistic as commonly for medium scale models we find that the standard new keynesian model without real frictions overestimates the short term macroeconomic effects of a positive trend inflation rate and underestimates those of the long term

income dispersion and counter cyclical markups recent advances in measuring cyclical changes in the income distribution raise new questions how might these distributional changes affect the business cycle itself we show how counter cyclical income dispersion can generate counter cyclical markups in the goods market without any preference shocks or price setting frictions in recessions idiosyncratic labor productivity shocks raise income dispersion lower the price elasticity of demand and increase imperfectly competitive firms optimal markups the calibrated model explains not only many cyclical features of markups but also cyclical and long run patterns of standard business cycle aggregates

bank market power and the risk channel of monetary policy abstract do banks lend to riskier borrowers after a monetary expansion we modify the classic costly state verification problem by introducing a risk neutral monopolistic bank which maximizes profits subject to borrowers participation while the bank can diversify idiosyncratic default risk it bears the aggregate risk in partial equilibrium the bank prefers a higher leverage ratio of the borrower when the profitability of lending increases e g after a monetary expansion this risk channel persists in a new keynesian dsge model that replicates the conditional comovement in response to a monetary policy shock and the unconditional cross correlations of bank related variables in the data

can we explain inflation persistence in a way that is consistent with the microevidence on nominal rigidity this paper adopts the impulse response methodology to under stand inflation persistence it has often been argued that existing models of pricing fail to explain the persistence that we observe we adopt a common general framework which allows for an explicit modelling of the distribution of contract lengths and for different types of price setting we also evaluate how far the theories are consistent with recent evidence on price and wage rigidity we find that allowing for a distribution of durations can take us a long way to solving the puzzle of inflation persistence but not all the way yet

the quantitative analytics of the basic neomonetarist model this paper constructs a dynamic macroeconomic model with less than perfect price flexibility which has a classical side consistent with real business cycle theory augmented by investment adjustment costs increasing returns to scale and a new flexible formalization of imperfect competition something akin to the classical dichotomy is justified by a mode of approximation appropriate for a model in which one state variable adjusts quickly while another state variable adjusts slowly even with investment adjustment costs monetary expansions are found to raise the real interest rate the determinants of real rigidity and the macroeconomic rate of price adjustment are investigated copyright 1995 by ohio state university press

state dependent pricing and the dynamics of money and output standard macroeconomic models of price stickiness assume that each firm leaves its price unchanged for a fixed amount of time we present an alternative model in which the pricing decision depends on the state of the economy we find a method of aggregating individual price changes that allows a simple characterization of macroeconomic variables the model produces a positive money output correlation and an empirical phillips curve in addition the impact of monetary shocks depends crucially on the current level of output which points to a natural connection between state dependent microeconomics and state dependent macroeconomics i introduction there is a long tradition in macroeconomics of attributing the real effects of nominal demand shocks to nominal price stickiness in this view if there is no change in prices when nominal demand rises then quantities must bear the burden of adjustment hence nominal price rigidity provides the friction needed for nominal demand shocks to be transmitted to the real economy standard models of this transmission mechanism such as fischer 1977 and taylor 1980 are based on the assumption that each firm leaves its price unchanged for a fixed amount of time the main reason for considering such time dependent pricing rules is their analytic tractability constraining firms to adjust their prices at prespecified times both simplifies the derivation of equilibrium strategies and allows the use of powerful time series techniques to analyze aggregate dynamics the main disadvantage of the timedependent approach is that between price adjustments firms are not allowed to respond even to extreme changes of circumstance this makes it difficult to know whether the qualitative effects of money in these models are the result of nominal rigidities per se or of the exogenously imposed pattern of price changes an alternative approach to modeling price stickiness is to allow the price setting decision to depend on the actual state of the

how robust are popular models of nominal frictions this paper analyzes three popular models of nominal price and wage frictions to determine which best ts post war u s data we construct a dynamic stochastic general equilibrium dsge model and use maximum likelihood to estimate each model s parameters because previous research nds that the conduct of monetary policy and the behavior of in ation changed in the early 1980s we examine two distinct sample periods using a bayesian pseudo odds measure as a means for comparison a sticky price and wage model with dynamic indexation best ts the data in the early sample period whereas either a sticky price and wage model with static indexation or a sticky information model best ts the data in the late sample period our results suggest that price and wage setting behavior may be sensitive to changes in the monetary policy regime if true the evaluation of alternative monetary policy rules may be even more complicated than previously believed

real rigidities and the non neutrality of money rigidities in real prices are not sufficient to create rigidities in nominal prices and real effects of nominal shocks and by themselves small frictions in nominal adjustment such as costs of changing prices create only small non neutralities but this paper shows that substantial nominal rigidity can arise from a combination of real rigidities and small nominal frictions the paper shows the connection between real and nominal rigidity given the presence of nominal frictions both in general and for two specific sources of real rigidity one arising from goods market imperfections and the other from labour market imperfections

business cycles with staggered prices and international trade in intermediate inputs abstract international trade in intermediate inputs and increasingly in goods produced at multiple stages of processing has been widely studied in the real trade literature we assess the role of this feature of modern world trade in accounting for some stylized facts about international business cycles our model with staggered prices and trade in intermediates across four stages of processing does well in explaining the observed international correlations in aggregate quantities and it performs much better than a single stage model with no trade in intermediates the model in itself does not provide a full account of the cyclical behavior of the real exchange rate but compared to the single stage model it moves in the right direction

pricing american options under stochastic volatility and stochastic interest rates we introduce a new analytical approach to price american options using an explicit and intuitive proxy for the exercise rule we derive tractable pricing formulas using a short maturity asymptotic expansion depending on model parameters this method can accurately price options with time to maturity up to several years the main advantage of our approach over existing methods lies in its straightforward extension to models with stochastic volatility and stochastic interest rates we exploit this advantage by providing an analysis of the impact of volatility mean reversion volatility of volatility and correlations on the american put price

the american put option valued analytically an analytic solution to the american put problem is derived herein the hedge ratio and other derivatives of the solution are presented the formula derived implies an exact duplicating portfolio for the american put consisting of discount bonds and stock sold short the formula is extended to consider put options on stocks paying cash dividends a polynomial expression is developed for evaluating these formulae values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated tabulated and compared with values derived by numerical integration and binomial approximation as with european options evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods finally applications of this american put solution are discussed

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

the accelerated binomial option pricing model this paper describes the application of a convergence acceleration technique to the binomial option pricing model the resulting model termed the accelerated binomial option pricing model also can be viewed as an approximation to the geske johnson model for the value of the american put the new model is accurate and faster than the conventional binomial model it is applicable to a wide range of option pricing problems

inside debt aggregate demand and the cambridge theory of distribution this paper presents a kaleckian model of aggregate demand with inside debt and a generational structure the model shows how worker borrowing and population growth affect the level of aggregate demand it also reexamines the cambridge theorem and shows that the introduction of inside debt arising from worker borrowing means that the rate of profit and profit share are no longer independent of worker consumption behavior because increased worker borrowing increases capitalists debt service income this necessitates a decline in profits to maintain the balance between capitalists savings and their investment funding requirement c 1996 academic press limited copyright 1996 by oxford university press

unfunded liabilities and uncertain fiscal financing we develop a rational expectations framework to study the consequences of alternative means to resolve the unfunded liabilities problem the projected exponential growth in federal social security medicare and medicaid spending with no known plan for financing the transfers resolution requires specifying a probability distribution for how and when monetary and fiscal policies will change as the economy evolves through the 21st century beliefs based on that distribution determine the existence of and the nature of equilibrium we consider policies that in expectation combine reaching a fiscal limit some distorting taxation modest inflation and some reneging on the government s promised transfers in the equilibrium inflation targeting monetary policy and debt targeting tax policy cannot anchor expectations on those target variables expectational effects are always present but need not have large impacts on inflation and interest rates in the short and medium runs in the economy s stationary distribution the capital stock may grow or shrink and substantial probability falls on little or no reneging

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

on the consistency of the black scholes model with a general equilibrium framework we construct a simple economy with consumption only at the final date in which we endogenize the stochastic behavior of prices assumed in the black scholes model certain preferences constant proportional risk aversion and beliefs are shown to be sufficient and necessary in certain respects for the existence of such an equilibrium the analysis is then generalized to a continuous consumption framework in which we embed the merton proportional dividend model

the fiscal multiplier in a liquidity constrained new keynesian economy we study the effects of fiscal policy on the macroeconomy using a liquidity constrained new keynesian model in which government bonds are liquid and private financial assets are only partially liquid we find that the fiscal multipliers in this economic environment are large enough for fiscal policy to be highly effective in this model a bond financed fiscal expansion can stimulate output because higher public borrowing improves liquidity by increasing the proportion of liquid assets in private sector wealth

time consistent monetary policy with endogenous price rigidity abstract i characterize time consistent equilibrium in an economy with price rigidity and an optimizing monetary authority operating under discretion firms have the option to increase their frequency of price change at a cost in response to higher inflation previous studies which assume a constant degree of price rigidity across inflation regimes find two time consistent equilibria one with low inflation the other with high inflation in contrast when price rigidity is endogenous the high inflation equilibrium ceases to exist hence time consistent equilibrium is unique this result depends on two features of the analysis 1 a plausible quantitative specification of the fixed cost of price change and 2 the presence of an arbitrarily small cost of inflation that is independent of price rigidity

nominal price rigidity money supply endogeneity and business cycles abstract this paper investigates the ability of nominal price rigidity to explain the co movement of inflation with the cyclical component of output observed in the post war u s data a dynamic general equilibrium model is constructed with the introduction of monopolistic competition and nominal price rigidity in a standard real business cycle model allowing for an endogenous money supply rule it is then demonstrated that sticky price models can explain the observed associations between movements in inflation and output much better than flexible price models this result depends little on whether money supply is assumed to be endogenous or not

predetermined prices and the persistent effects of money on output this note illustrates a model of predetermined pricing where firms set a fixed schedule of nominal prices at the time of price readjustment based on the work of fischer 1977 this contrasts with the model of fixed pricing the specification underlying most recent dynamic sticky price models it is well known that predetermined pricing cannot generate substantial persistence in the real effects of monetary shocks when prices are set via fixed duration contracts unless the contracts are of long duration however we show that with a probabilistic model of price adjustment a predetermined pricing specification can produce almost as much persistence as the more conventional model of fixed prices without the assumption of long average contract duration

are prices too sticky nominal price rigidity has a negative externality rigidity in one firm s price increases the variability of aggregate real spending which harms all firms this paper investigates whether this externality is large which would imply that stabilization policy can be highly beneficial even if the costs of making prices flexible are small there are three conclusions first both the private cost of price rigidity and the externality are second order in the size of fluctuations second the externality can nonetheless be arbitrarily large third in a simple model the externality is small for plausible parameter values

the phillips curve under state dependent pricing abstract we derive a phillips curve equation from the dynamic stochastic general equilibrium dsge model with state dependent pricing developed by dotsey et al 1999 state dependent pricing and the general equilibrium dynamics of money and output quarterly journal of economics 114 655 690 this state dependent phillips curve encompasses the new keynesian phillips curve nkpc based on calvo type price setting as a special case we analyze the effect of the state dependent terms that is the variations in the distributions of price vintages on inflation persistence and we examine whether the hybrid nkpc that is the nkpc extended by a lagged inflation term can adequately describe inflation dynamics generated in a calibrated state dependent pricing economy

price elasticities and demand side real rigidities in micro data and in macro models abstract high degrees of demand side real rigidities are able to generate the large monetary non neutrality found in aggregate data this paper provides micro based evidence on the key parameters governing this rigidity using european homescan data we find strong evidence for demand side real rigidity which is however significantly lower than that normally assumed in macro models in a menu cost model calibrated to our estimates we show that these estimates are associated with reasonable values for production side parameters but they are not able to generate the degree of monetary non neutrality observed in macro data

sticky price models of the business cycle can the contract multiplier solve the persistence problem we construct a quantitative equilibrium model with firms setting prices in a staggered fashion and use it to ask whether monetary shocks can generate business cycle fluctuations these fluctuations include persistent movements in output along with the other defining features of business cycles like volatile investment and smooth consumption we assume that prices are exogenously sticky for a short time persistent output fluctuations require endogenous price stickiness in the sense that firms choose not to change prices much when they can do so we find that for a wide range of parameter values the amount of endogenous stickiness is small thus we find that in a standard quantitative model staggered price setting alone does not generate business cycle fluctuations

the financial system and the pasinetti theorem palley inside debt aggregate demand and the cambridge theory of distribution cambridge journal of economics vol 20 no 4 465 74 1996 financial institutions and the cambridge theory of distribution cambridge journal of economics vol 26 no 2 275 7 2002 considers the pasinetti theorem in the context of the credit money system where banks generate debts endogenously and claims that the theorem ceases to hold in such a system being valid only in the loanable funds system this paper traces the root of palley s claim to his assumption regarding the ownership of banks sets out an alternative more realistic ownership arrangement and thereby restores the pasinetti theorem unscathed in the credit money system at least in the kind palley must have considered the paper however uncovers the case where the theorem indeed collapses and discusses the reason for it the hoarding of a non interest bearing asset copyright 2006 oxford university press

selection and monetary non neutrality in time dependent pricing models for a given frequency of price adjustment monetary non neutrality is smaller if older prices are disproportionately more likely to change selection for the age of prices provides a complete characterization of price setting frictions in time dependent models selection for older prices is weaker and non neutralities are larger if the hazard function of price adjustment is less strongly increasing selection is weaker if there is heterogeneity in price stickiness finally selection is weaker if durations of price spells are more variable in particular the taylor 1979 model exhibits maximal selection for older prices whereas the calvo 1983 model exhibits no selection

returns to scale market power and the nature of price rigidity in new keynesian models with self fulfilling expectations increasing returns to scale and firms market power are two potential sources of sunspot expectations in neoclassical models we show that in new keynesian models returns to scale and market power can have fundamentally different implications for broad macroeconomic issues including self fulfilling expectations depending on the nature of price rigidity our findings suggest that the design of stabilization monetary policy can depend on precise knowledge about the economy s real and nominal features therefore a clear understanding of the specific economic environment and its relevance to monetary policymaking for ensuring macroeconomic stability can be an integrated part of monetary policy practice

alternative views of the money transmission mechanism what difference do they make for monetary policy this paper examines how alternative views of the monetary transmission mechanism affect the choice of a monetary policy rule the main finding is that many different structural models indicate that the same simple monetary policy rule one in which the central bank s target short term interest rate reacts to inflation and to real output would perform well such rules work well even in models where the monetary transmission mechanism has a relatively strong exchange rate channel the models differ however in their implications for more complex monetary rules prepared for the oxford review of economic policy this paper is an updated revised and shortened version of an earlier paper entitled the monetary transmission mechanism and the evaluation of monetary policy rules presented at the central bank of chile in september 20 21 1999 i am grateful to david vines for very helpful comments

optimal monetary policy with international trade in intermediate inputs abstract this paper examines optimal monetary policy in a two country new keynesian model with international trade in intermediate inputs we derive the loss function of a cooperative monetary policymaker and find that the optimal monetary policy must target intermediate goods price inflation rates final goods price inflation rates final goods output gaps and relative price gaps we use the welfare loss under the optimal monetary policy as a benchmark to evaluate the welfare implications of three taylor type monetary policy rules a main finding is that the degree of price stickiness at the stage of intermediate goods production is a key factor to determine which policy rule should be followed specifically when the degree of price stickiness at the stage of intermediate goods production is high the policymaker should follow intermediate goods ppi based taylor rule whereas cpi based taylor rule should be followed when the degree of price stickiness at the stage of intermediate goods production is intermediate or low

monte carlo valuation of american options through computation of the optimal exercise frontier this paper introduces a monte carlo simulation method for pricing multidimensional american options based on the computation of the optimal exercise frontier we consider bermudan options that can be exercised at a finite number of times and compute the optimal exercise frontier recursively we show that for every date of possible exercise any single point of the optimal exercise frontier is a fixed point of a simple algorithm once the frontier is computed we use plain vanilla monte carlo simulation to price the option and obtain a low biased estimator we illustrate the method with applications to several types of options

money demand and the effects of fiscal policies this paper reexamines the choice of the scale variable in the money demand function a variety of evidence suggests that consumer spending is a better scale variable than gnp changing the money demand specification along these lines can profoundly affect the standard keynesian analysis of a tax cut copyright 1986 by ohio state university press

menu costs and the neutrality of money a model of endogenous price adjustment under money growth is presented firms follow s s pricing policies and price revisions are imperfectly synchronized in the aggregate price stickiness disappears and money is neutral the connection between firm price adjustment and relative price variability in the presence of monetary growth is also investigated the results contrast with those obtained in models with exogenous fixed timing of price adjustment

comparing dsge var forecasting models how big are the differences abstract i generate priors for a vector autoregression var from a standard real business cycle rbc model an rbc model with capital adjustment costs and habit formation and a sticky price model with an unaccommodating monetary authority the response of hours worked to a tfp shock differs sharply across these models i compare the accuracy of forecasts made from each of the resulting dynamic stochastic general equilibrium vector autoregression dsge var models despite having different structural characteristics the dsge vars are comparable in terms of forecasting performance as in previous work dsge vars compare favorably with atheoretical vars

how well does sticky information explain the dynamics of inflation output and real wages abstract this paper finds that a model with sticky information is less successful than a standard model featuring nominal rigidities inflation indexation and habits in generating the dynamics triggered by technology shocks as estimated by a vector autoregression using u s macroeconomic data the real wage responses after a permanent increase in productivity clearly favor the standard model the sticky information model fails to replicate the observed inertial response in the real wage whereas the standard model relies on inflation indexation in wage setting to achieve a better fit the two models are however statistically equivalent after a shock in monetary policy

real and nominal propagation of nominal shocks the role of real and nominal propagation mechanisms in generating persistent real effects of nominal shocks is analysed analytically in a fully specified intertemporal general equilibrium model while neither a real propagation mechanism capital acccumulation with one period nominal contracts nor nominal propagation staggered nominal contracts in the absence of any real propagation can generate plausible impulse responses with strong persistence it is shown that the two mechanisms interact so as to strengthen persistence possibly unit roots and generate more plausible impulse responses

monetary fiscal policy interactions and fiscal stimulus abstract increases in government spending trigger substitution effects both inter and intra temporal and a wealth effect the ultimate impacts on the economy hinge on current and expected monetary and fiscal policy behavior studies that impose active monetary policy and passive fiscal policy typically find that government consumption crowds out private consumption higher future taxes create a strong negative wealth effect while the active monetary response increases the real interest rate this paper estimates markov switching policy rules for the united states and finds that monetary and fiscal policies fluctuate between active and passive behavior when the estimated joint policy process is imposed on a conventional new keynesian model government spending generates positive consumption multipliers in some policy regimes and in simulated data in which all policy regimes are realized the paper reports the model s predictions of the macroeconomic impacts of the american recovery and reinvestment act s implied path for government spending under alternative monetary fiscal policy combinations

a note on the convergence of binomial pricing and compound option models the binomial pricing model of cox ross and rubinstein 2 and the compound option model of geske 3 are both elegant and self contained frameworks for the valuation of american options and related contingent claims each providing us with a distinctive valuation procedure flexible enough to be adapted to a wide variety of problems for american type options on assets with a prices following a lognormal diffusion process and b a continuous time exercise policy such as put options on individual stocks calls and puts on foreign exchange and calls and puts on futures contracts the binomial pricing model approximates both the stochastic process and the exercise opportunity set the latter by restricting exercise to a discrete set of dates the compound option model on the other hand approximates only the exercise opportunity set however it pays for this with a high price in computational requirements specifically with n exercise dates allowed multivariate normal probabilities of every order up to and including n must be evaluated in their article on the valuation of put options geske and johnson 4 provide an ingenious solution to this problem by applying acceleration techniques common in numerical analysis but new to the finance literature letting t be the time to expiration of the option and p the value of a compound option with exercise permitted at the n uniformly spaced dates t n 2t n t they generate the sequence of compound option values p1 p2 pn polynomial extrapolation is then used to estimate p lim n x oo pn they found this procedure to be very accurate over a limited sample of put options with low values of n though not discussed by geske and johnson the reasons for the effectiveness of acceleration techniques in a compound option model are apparent from a cursory examination an acceleration technique will perform best when the approximating sequence converges uniformly on the true value of the contingent claim and worst when convergence includes complex and unpredictable oscilla

the valuation of multivariate contingent claims in discrete time models there are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables familiar cases of such claims include options on a portfolio of options options whose exercise price is stochastic and options to exchange one asset for another this paper derives risk neutral valuation relationships rnvrs in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors and joint normally distributed underlying variables and constant absolute risk aversion preferences respectively this methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds multicurrency option bonds and investment options

prices output and hours an empirical analysis based on a sticky price model abstract i show that a simple sticky price model based on rotemberg 1982 is consistent with a variety of facts concerning the correlation of prices hours and output it is consistent with the negative correlation between forecastable movements in prices and output as well as the smaller negative correlation between forecastable movements in prices and hours it is also consistent with the positive correlations of unexpected movements in prices output and hours these patterns are harder to reconcile with the flexible price version of the model in particular they require that money respond differently to forecastable and to unforecastable real shocks

a sunspot paradox abstract this paper shows that the local stability properties of dynamic general equilibrium macroeconomic models may depend on the length of a period in the model economy this leads to the following paradoxical situation the economy may be driven by sunspots for some decision frequencies while sunspots can have no impact at other decision frequencies

interactions of commitment and discretion in monetary and fiscal policies we consider monetary scal interactions when the monetary authority is more conservative than the scal with both policies discretionary 1 nash equilibrium yields lower output and higher price than the ideal points of both authorities 2 of the two leadership possibilities scal leadership is generally better with scal discretion monetary commitment yields the same outcome as discretionary monetary leadership for all realizations of shocks but scal commitment is not similarly negated by monetary discretion second best outcomes require either joint commitment or identical targets for both authorities output socially optimal and price level appropriately conservative or complete separation of tasks jel e61 e63

the economic crisis from a neoclassical perspective abstract this paper assesses the 2007 2009 recession using neoclassical business cycle theory i find that the 2007 2009 u s recession differs substantially from other postwar u s recessions and also from the 2008 recession in other countries in that lower labor input accounts for virtually all of the decline in income and output in the united states while lower productivity accounts for much of other u s recessions and the 2007 2009 recession in other countries i also find that existing classes of models including financial market imperfections models do not explain the u s recession this is because the 2007 2009 recession is almost exclusively related to what appear to be labor market distortions that drive a wedge between the marginal product of labor and the marginal rate of substitution between consumption and leisure a topic about which current classes of financial imperfection models are largely silent i discuss future avenues for developing this class of models and i consider alterna

sticky price models and the natural rate hypothesis abstract a major criticism of standard specifications of price adjustment in models for monetary policy analysis is that they violate the natural rate hypothesis by allowing output to differ from potential in steady state in this paper we estimate a dynamic optimizing business cycle model whose price setting behavior satisfies the natural rate hypothesis the price adjustment specifications we consider are the sticky information specification of mankiw and reis sticky information versus sticky prices a proposal to replace the new keynesian phillips curve quarterly journal of economics 117 1295 1328 and the indexed contracts of christiano et al nominal rigidities and the dynamic effects of a shock to monetary policy journal of political economy 113 1 45 our empirical estimates of the real side of the economy are similar whichever price adjustment specification is chosen consequently the alternative model specifications deliver similar estimates of the u s output gap series but the empirical behavior of the gap series differs substantially from standard gap estimates

the american put option and its critical stock price we derive an expression for the critical stock price for the american put we start by expressing the put price as an integral involving first passage probabilities this approach yields intuition for merton s result for the perpetual put we then consider the finite lived case using 1 the fact that the put value ceases to depend on time when the critical stock price is reached and 2 the result that an american put equals a european put plus an early exercise premium we derive the critical stock price we approximate the critical stock price function to compute accurate put prices kim 1990 jacka 1991 and carr jarrow and myneni 1992 showed that the american put price is equal to the corresponding european put price plus an integral representing the early exercise premium however to use their approach one needs to know the critical stock price which may be defined in three equivalent ways 1 it is the value of the stock price at which one is indifferent between exercising and not exercising the put

monopolistic competition and the effects of aggregate demand how important is monopolistic competition to an understanding of the effects of aggregate demand on output we ask the question at three levels can monopolistic competition by itself explain why aggregate demand movements affect output can it together with other imperfections generate effects of aggregate demand in a way that perfect competition cannot if so can it give an accurate account of the response of the economy to aggregate demand movements the answers are no yes and yes

money prices interest rates and the business cycle the mechanisms governing the relationship of money prices and interest rates to the business cycle are the most studied and most disputed topics in macroeconomics in this paper we first document key empirical aspects of this relationship we then ask how well three benchmark rational expectations macroeconomic models a real business cycle model a sticky price model and a liquidity effect model account for these central facts while the models have diverse successses and failures none can account for the fact that real and nom inal interest rates are inverted leading indicators of real economic activity that is none of the models captures the post war u s business cycle fact that a high real or nominal interest rate in the current quarter predicts a low level of real economic activity two to four quarters in the future i introduction the positive correlation of monetary aggregates and real economic activity over the course of many business cycles is a key empirical fact about the u s economy indeed the dynamic dimension of this covariation is so strong and stable that a monetary variable has long been included in the commerce department s index of leading economic indica tors while this pattern of cyclical comovement is widely agreed upon its interpretation is not some macroeconomists view money as purely passive with a positive response to varying levels of economic activity producing the positive correlation others view changes in the quantity of money as an important perhaps dominant source of economic fluctua tions frequently the real effects of monetary changes are suggested to arise from frictions in commodity labor or financial markets in economic theories that describe the influence of these frictions the transmission mechanism from monetary changes to real activity is typically viewed as involving interest rates and the price level the primary goal of this paper is to evaluate three models that explain the link between money prices interest rates and the business cycle we do this in three steps first we docu ment the cyclical behavior of these variables in the united states over the postwar period second we construct three quantitative rational expectations models of macroeconomic activity i a real business cycle model with endogenous money ii a model of commodity market frictions with mon etary non neutralities arising from gradual adjustment of goods prices and iii a model of financial market frictions with monetary non neutralities arising from gradual adjust ments of portfolios finally we compare the models predic tion for the business cycle behavior of money prices and interest rates with the data in exploring the predictions of these models we take the stock of money to be one of several exogenous variables in the system all of our models are capable of generating a forecasting role for money relative to real economic activity similar to that found in the u s data in the real business model monetary changes can forecast real activity because productivity is related to many underlying sources of shocks and because these real shocks also affect the money stock in the models with sticky prices and liquidity effects short hand names for the models with frictions in the com modity and financial markets monetary changes have an additional direct positive effect on aggregate output the outline of the paper is as follows section ii describes the data and documents its business cycle characteristics section iii outlines the three macroeconomic models and develops the particular quantitative versions of the models used in our analysis our main empirical results are pre sented in section iv and section v summarizes our results and concludes

constrained labor supply and risk aversion abstract this paper extends previous work by showing that consumption constraints typically increase individuals risk aversion even if the illiquid good e g leisure has good substitutes calibrations indicate time use constraints may raise risk aversion considerably under many common scenarios

the valuation of american barrier options using the decomposition technique in this paper we propose an alternative approach for pricing and hedging american barrier options speci cally we obtain an analytic representation for the value and hedge parameters of barrier options using the decomposition technique of separating the european option value from the early exercise premium this allows us to identify some new put call symmetry relations and the homogeneity in price parameters of the optimal exercise boundary these properties can be utilized to increase the computational e ciency of our method in pricing and hedging american options our implementation of the obtained solution indicates that the proposed approach is both e cient and accurate in computing option values and option hedge parameters our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and e ciency in particular the method is free of the di culty that existing

sticky price models and durable goods the inclusion of a durable goods sector in sticky price models has strong and unexpected implications even if most prices are flexible a small durable goods sector with sticky prices may be sufficient to make aggregate output react to monetary policy as though most prices were sticky in contrast flexibly priced durables with sufficiently long service lives can undo the implications of standard sticky price models in a limiting case flexibly priced durables cause monetary policy to have no effect on aggregate output our analysis suggests that durable goods prices are the most relevant data for calibrating price rigidity jel e21 e23 e31 e52

imperfect credibility and inflation persistence in this paper we formulate a dynamic general equilibrium model with staggered nominal contracts in which households and rms use optimal ltering to disentangle persistent and transitory shifts in the monetary policy rule the calibrated model accounts quite well for the dynamics of output and insation during the volcker disinsation and implies a sacri ce ratio very close to the estimated value our approach indicates that insation persistence and substantial costs of disinsation can be generated in an optimizing agent framework without relaxing the assumption of rational expectations or relying on arbitrary modi cations to the aggregate supply relation jel classi cation e31 e32 e52

financial institutions and the cambridge theory of distribution this paper shows how the cambridge theory of distribution is affected by the nature of financial intermediation when credit markets are akin to loanable funds markets in which lenders transfer resources to borrowers the cambridge theory holds and steady state income distribution is independent of workers saving behaviour however when credit markets embody endogenously generated bank money the cambridge theory does not hold financial institutions and endogenous money therefore matter for long run steady state outcomes just as they do for short run macroeconomic outcomes copyright 2002 oxford university press

a monte carlo approach for the american put under stochastic interest rates abstract this paper presents a new approach for the valuation of an american put option under stochastic interest rates the paper combines a monte carlo simulation approach for the valuation of bermudan options and the valuation technique for american options proposed by geske and johnson 1984 the american put option valued analytically journal of finance 39 5 1511 1524 numerical results show that the price estimates are accurate with very low standard errors the simulation algorithm used to generate the price estimates is fast and easy to implement the effect of stochastic interest rates is clearly reflected in the option prices especially under regimes where interest rate volatility is high this effect can be important to incorporate also for long lived options this can be an important extension

output persistence from monetary shocks with staggered prices or wages under a taylor rule we analytically examine output persistence from monetary shocks in a dsge model with staggered prices or wages under a taylor rule surprisingly while taylor style staggering never yields persistence calvo style staggering of wages does generate persistence under decreasing returns to labour c 2009 elsevier b v all rights reserved

the new open economy macroeconomics a survey since the 1995 publication of obsteld and rogoff s redux model there has been an outpouring of research on open economy dynamic general equilibrium models that incorporate imperfect competition and nominal rigidities this paper offers an interim survey of this recent literature 2001 elsevier science b v all rights reserved

imperfect common knowledge staggered price setting and the effects of monetary policy this paper studies the consequences of a lack of common knowledge in the transmission of monetary policy by integrating the woodford 2003a imperfect common knowledge model with taylor calvo staggered price setting models the average price set by monopolistically competitive firms depends on their higher order expectations about not only the current state of the economy but also about the states in the future periods in which prices are to be fixed this integrated model provides a plausible explanation for the observed effects of monetary policy it shows analytically how price adjustments are delayed and how the response of output to monetary disturbances is amplified

is there a fiscal free lunch in a liquidity trap this paper uses a dsge model to examine the eects of an expansion in government spending in a liquidity trap the spending multiplier can be much larger than in the normal situation if the liquidity trap is very persistent and scal stimulus can be rapidly implemented moreover the budgetary costs may be minimal as the large response of output boosts tax revenues allowing for something close to a scal free lunch however we caution that the multiplier may be much smaller under plausible implementation lags for many types of public spending and or if the liquidity trap lasts less than two years in addition because the marginal impact of scal expansion decreases in the scale of the outlay it is crucial to distinguish between average and marginal multipliers

the compound option approach to american options on jump diffusions abstract we derive analytical valuation formulas for compound options when the underlying asset follows a jump diffusion process we then apply these results to value extendible options american call options on stocks that pay discrete dividends and american options on assets that pay continuous proportional dividends numerical results are provided

fiscal shocks and their consequences this paper investigates the response of hours worked and real wages to fiscal policy shocks in the post world war ii us we identify these shocks with exogenous changes in military purchases and argue that they lead to a persistent increase in government purchases and tax rates on capital and labor income and a persistent rise in aggregate hours worked as well as declines in real wages the shocks are also associated with short lived rises in aggregate investment and small movements in private consumption we describe and implement a methodology for assessing whether standard neoclassical models can account for the consequences of a fiscal policy shock simple versions of the neoclassical model can account for the qualitative effects of a fiscal shock once we allow for habit formation and investment adjustment costs the model can also account reasonably well for the quantitative effects of a fiscal shock

endogenous capacity utilization and macroeconomic persistence abstract this paper presents a monetary dynamic general equilibrium model featuring a strong internal propagation mechanism limited short run factor substitutability and idiosyncratic demand uncertainty play a prominent role in the results firms are ex post heterogeneous and a well defined distribution of capacity utilization rates characterizes the equilibrium of the model the economy responds gradually to aggregate shocks since firms with excess capacity can raise production without experiencing large increases in their marginal costs the modeling framework presented in this paper offers a plausible microeconomic interpretation for reduced form mark up shocks typically considered in the new keynesian literature

on the precision of calvo parameter estimates in structural nkpc models abstract we study the extent of empirical information that can be obtained from alternative structural new keynesian inflation equations concerning the average duration of prices in the united states given that such specifications may be hard to identify using four different indexation and real wage rigidity based models in conjunction with identification robust econometric methods we evaluate the precision of calvo parameter estimates while results are sensitive to calibration and instrument selection we find confidence bounds on the average duration of prices that line up with available micro founded studies statistically significant coefficients for the forcing variables and non zero estimates on the coefficient of lagged inflation

identifying the influences of nominal and real rigidities in aggregate price setting behavior we formulate a generalized price setting framework that incorporates staggered contracts of multiple durations and that enables us to directly identify the influences of nominal vs real rigidities we estimate this framework using macroeconomic data for germany 1975 1998 and for the u s 1983 2003 in each case we find that the data are well characterized by nominal contracts with an average duration of about two to three quarters we also find that new contracts exhibit very low sensitivity to marginal cost corresponding to a relatively high degree of real rigidity finally our results indicate that backward looking price setting behavior such as indexation to lagged inflation is not needed in explaining the aggregate data at least in an environment with a stable monetary policy regime and a transparent and credible inflation objective

discrete time valuation of american options with stochastic interest rates we develop an arbitrage free discrete time model to price american style claims for which domestic term structure risk foreign term structure risk and currency risk are important this model combines a discrete version of the heath jarrow and morton 1992 term structure model with the binomial model of cox ross and rubinstein 1979 it converges weakly to the continuous time models in amin and jarrow 1991 1992 the general model is path dependent and can be implemented with arbitrary volatility functions to value claims with maturity up to five years the model is illustrated with applications to long dated american currency warrants and a cross rate swap from the quanto class article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

the valuation of american options for a class of diffusion processes we present an integral equation approach for the valuation of american style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic our contribution is fourfold first we show that the exercise region is determined by a single exercise boundary under very general conditions on the interest rate and the dividend yield second based on this result we derive a recursive integral equation for the exercise boundary and provide a parametric representation of the american option price third we apply the results to models with stochastic volatility or stochastic interest rate and to american bond options in one factor models for the cases studied explicit parametric valuation formulas are obtained finally we extend results on american capped options to general diffusion prices numerical schemes based on approximations of the optimal stopping time such as approximations based on a lower bound or on a combination of lower and upper bounds are shown to be valid in this context

pricing american options on foreign assets in a stochastic interest rate economy this paper values american options on foreign assets in a stochastic interest rate economy using a two point geske and johnson 1984 technique the method requires the valuation of just two options a european option and a twice exercisable option i first derive the risk neutral distributions of asset prices under two forward risk adjusted measures closedform solutions for european options on foreign assets are then obtained by applying these risk neutral distributions this article also provides analytic solutions for pricing twiceexercisable options that are at most two dimensional even though the valuation problem involves four risk factors at two exercise dates i report the results of numerical evaluations of american option values using my method and show how they vary with the interest rate parameters i also verify the accuracy of the proposed method by comparing with the benchmark values obtained from the least square method of longstaff and schwartz 2001