sraffa and his arguments against marginism the subtitle of sraffa s most celebrated work production of commodities by means of commodities is prelude to a critique of economic theory given that no later work was ever published by sraffa we are left to wonder what would have come after the prelude this paper suggests that the core of the critique might have been the marginal method itself by carefully distinguishing between published and unpublished work we shows that sraffa s opposition to the marginal method follows several threads some of which were developed over a period of nearly 35 years such as the belief that economic theory should use only measurable and observable magnitudes the critique of the fundamental symmetry between production and consumption and the disagreement with the marshallian concept of equilibrium although none of the arguments reached a stage that sraffa considered satisfactory enough to be worth publishing our reconstruction sheds light on his research programme and on otherwise rather obscure passages in his works

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

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

exact solutions for futures and european futures options on pure discount bonds this paper provides closed form solutions for futures and european futures options on pure discount bonds under the ornstein uhlenbeck normal process a significant difference between black s model 1976 and the model in this paper for futures options is discussed

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

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

a note on an interest rate immunization strategy abstract the mechanisms for insuring investments in stocks and bonds against depreciation have grown rapidly in the last decade insuring a portfolio entails managing it in such a way that the left hand tail of the return distribution is truncated the present paper demonstrates how this may be achieved for fixed interest securities discrete time hedging procedures are derived with the inclusion of transaction costs

a contingent claims analysis of the interest rate risk characteristics of corporate liabilities abstract this paper provides a contingent claims analysis of the interest rate risk characteristics of corporate liabilities by identifying merton s 1973 option pricing model with vasicek s 1977 mean reverting term structure model only a non zero positive range of duration values for the firms assets is shown to be consistent with the previous empirical evidence on the interest rate sensitivity of corporate stocks and bonds chance s 1990 duration measure is shown to be biased downward under empirically realistic conditions theoretical conditions are derived under which the duration of a default prone zero coupon bond can be either higher or lower than the duration of the corresponding default free bond the duration of the default prone bond of a firm with high low interest rate sensitive assets is shown to be an increasing decreasing function of the bond s default risk

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

estimation of the value and cost of government and market supplied goods a review of previous research indicates that people s valuationsof government supplied services are not closely related to theircosts raising the question of how much people know about thecosts of such goods respondents rated the value of governmentand market supplied goods and services and estimated their costsin three studies the respondents made poor estimates of the percapita costs of supplying government services and were littlebetter at estimating per capita expenditure on a range of marketsupplied goods e g expenditure on fruit but they were quiteaccurate at estimating the prices of individual market supplieditems rated values of individual market supplied itemscorrelated well with the costs of the items but rated annualvalues of both government and market supplied goods were moreweakly correlated with their annual per capita costs the resultssuggests that the inaccuracy in estimating the costs ofgovernment goods might arise because such items do not haveindividual item prices rather than because people generally donot pay for them themselves

some international evidence on the stochastic behavior of interest rates abstract this paper examines the stochastic behavior of short term interest rates in eleven countries following chan et al 1992a we consider eight stochastic models of short term interest rates all of which are nested within a discretized approximation to a differential equation we use the generalized method of moments to estimate the model the empirical results show that no single model can satisfactorily describe the stochastic structure of interest rates for all countries on balance if we classify the sample countries according to the size of the elasticity of variance of short term interest rates france holland and the usa belong to the group of high elasticity in comparison australia belgium germany and japan belong to the group of medium elasticity while canada italy switzerland and the uk belong to the group of low elasticity

piero sraffa and the true object of economics the role of the unpublished manuscripts this special issue is concerned with the work of piero sraffa and with recent developments in its interpretation occasioned by the opening of the sraffa archives in late 1993 1 it brings together some of the contributions to a workshop on this theme that was sponsored by the cambridge journal of economics and held in july 2010 on the occasion of the 50th anniversary of the publication of piero sraffa s major work production of commodities by means of commodities pcmc the original workshop on new perspectives on the work of piero sraffa was aimed at sraffa scholars who had taken the opportunity to engage with materials in the sraffa archives and who were interested in exploring their potential for revisiting and placing pcmc in the wider context of ongoing debates on economic philosophy economic theory and economic policy as is usually the case not all presentations made at the workshop were advanced for consideration in this special issue nor could all invitees attend heinz kurz as chief editor of the sraffa archives agreed to present his view on the relevance of the sraffa archives to research on sraffa and to comment on contributions at the workshop as well as on their final versions submitted for publication in this special issue kurz s contribution to this special issue was thus written in the short time available between the receipt of final versions and publication deadlines we are indebted to him for his cooperation in the preparation of this special issue we are especially grateful for his patience in the time taken to bring this project to publication this abstract was borrowed from another version of this item

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

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

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

fixed income linked life insurance policies with minimum guarantees pricing models and numerical results abstract we propose a pricing model for life insurance policies in which the benefits are linked to the performance of a portfolio of interest rate sensitive assets reference fund and a minimum guarantee provision is present the model is cast in the celebrated term structure framework developed by cox ingersoll and ross 1985 as for the behaviour of the investment component we analyse two polar cases in the first one the payments due on the reference fund when the contract is still alive are not reinvested while in the second case we propose a reinvestment policy we show how to obtain a closed form solution for the single premium in the no reinvestment case and how to implement a simulation approach to calculate numerically the single premium in the reinvestment case we illustrate our analysis with numerical results that help in understanding the comparative static properties of the models proposed

dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield the main objective of this paper is to address in an a continuous time framework the issue of using storable commodity futures as vehicles for hedging purposes when in particular the convenience yield as well as the market prices of risk evolve randomly over time following the martingale route and by operating a suitable constant relative risk aversion utility function crra specific change of numeraire we solve the investor s dynamic optimization program to obtain quasi analytical solutions for optimal demands which can be expressed in terms of two discount bonds traded and synthetic contrary to the existing literature we explicitly derive the individual optimal proportions invested in the spot commodity in a discount bond and in the futures contracts which can be computed in a simple recursive way we suggest various decompositions allowing an investor to assess the sensitivity of the optimal demands to the state variables and to specify the role played by each risky asset empirical evidence shows that the convenience yield has a strong impact on the speculation and hedging positions and the interaction among time varying risk premia determines the magnitude and the sign of these positions

currency option pricing with mean reversion and uncovered interest parity a revision of the garman kohlhagen model abstract we consider a model for the pricing of currency options where the logarithm of the exchange rate exhibits mean reversion i e follows the omstein uhlenbeck process we mention reasons why exchange rates could exhibit mean reversion the domestic and foreign short interest rates are related to the logarithm of the exchange rate through uncovered interest parity under these assumptions we derive formulas for the value of a european currency option from the point of view of both domestic and foreign investors we also derive formulas for options on forward and futures contracts we compare option values computed by means of the garman kohlhagen model with corresponding results from our model it appears that our model cannot explain all instances of mispricing of currency options by the garman kohlhagen model which have been reported by previous authors the main virtue of our paper however is that we derive a simple model which incorporates clear theoretical relationship between the exchange rate and the domestic and foreign interest rates

shifting endpoints in the term structure of interest rates abstract this paper links the term structure to perceptions of monetary policy long horizon forecasts of short rates required by no arbitrage term structure models are heavily influenced by the endpoints or limiting conditional forecasts of the short rate process common assumptions that the short rate is mean reverting or contains a unit root are shown to generate unrealistic yield predictions failures occur because these assumptions inadequately account for historical shifts in market perceptions of the policy target for inflation this paper links endpoint shifts to agent learning about shifts in long term policy goals shifting endpoints in short rate processes significantly improve yield predictions

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

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

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

dynamic asset allocation portfolio decomposition formula and applications a new decomposition of the optimal portfolio in dynamic models with von neumann morgenstern preferences and ito prices is established the formula rests on a change of numeraire that uses pure discount bonds as units of account the dynamic hedging demand has two components the first hedge insures against fluctuations in an optimally designed bond with a maturity date matching the investor s horizon the second hedge immunizes against fluctuations in the market price of risk in the bond numeraire various applications are examined new results concerning the behavior of extremely risk averse individuals the demand for bonds and its long horizon limit and the optimal portfolio in incomplete markets are derived the author 2009 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please email journals permissions oxfordjournals org oxford university press

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

on alternative notions of change and choice krishna bharadwaj s legacy krishna bharadwaj following upon the work and insights of sraffa made substantial contributions to our understanding of what is implied in the neoclassical notion of change and its related notion of choice in this respect she appears closer to the spirit of sraffa s critique of neoclassical theory than many others she also supplemented important elements in building an alternative approach based on classical political economy which is free from the need to employ marginal magnitudes and does not require hypothetical or potential changes to determine the resting positions of economic variables moreover the notion of choice is rescued from the parable of preferences and given more meaningful contents allowing for consideration of habits customs and power relationships 1 premise the consumption and production of goods is the kind of human activity to which the term economic is applied in most societies these activities are mediated through exchange and in capitalist societies exchange is performed in organised markets in the history of economic thought a range of different conceptions have been put forward to explain how individuals interact in markets and various accounts have been advanced of ways to understand which are the incentives and the constraints affecting their behaviour and decision making in neoclassical theories choices in consumption and production are conceptualised through reasoning at the margin under the ceteris paribus assumption i e that everything else remains unchanged this method provides the means to measure the effects of a small technically infinitesimal variation in quantities of selected variables such as utility and cost which are compared with the relevant prices to determine the optimum choice by individuals the optimal choice framework is in fact the basis upon which price and quantities are simultaneously determined in the neoclassical world

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

circuitous processes jigsaw puzzles and indisputable results making best use of the manuscripts of sraffa s production of commodities by means of commodities the opening of the sraffa archive has allowed the production of credible narratives of the development of sraffa s thought based on documentary evidence the archive is complex especially in the case of the papers relating to production of commodities by means of commodities pcmc but the author s paperwork helps guide us through the development of his ideas affirming the causal relationship between thought and archive the complex interrelationships between materials in the archive make a painstaking scholarly approach necessary but rewarding allowing authors to use material of high evidential value to corroborate the cases they are making the archive has primarily been used by historians of economic thought however as the material contextualises pcmc it may also be useful to those working on economic theory from a sraffian perspective copyright oxford university press

the economics of options implied inflation probability density functions recently a market in options based on cpi in ation in ation caps and oors has emerged in the us this paper uses quotes on these derivatives to construct probability densities for in ation we study how these pdfs respond to news announcements and nd that the implied odds of de ation are sensitive to certain macroeconomic news releases we compare the option implied probability densities with those obtained by time series methods and use this information to construct empirical pricing kernels the options implied densities assign considerably more mass to extreme in ation outcomes either de ation or high in ation than do their time series counterparts this yields a u shaped empirical pricing kernel with investors having high marginal utility in states of the world characterized by either de ation or high in ation

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

measuring rents and interest rate risk in imperfect financial markets the case of retail bank deposits traditional measures of interest rate risk assume that prices of financial assets and liabilities are set in perfectly competitive markets however evidence suggests that many retail financial markets do not follow the competitive paradigm in this paper we employ a general contingent claims framework to value rents earned by banks in demandable retail deposit markets our analysis provides a natural and economically meaningful measure of interest rate risk for these imperfectly competitive markets using monthly survey data on now accounts and mmdas we estimate the value of retail deposit rents and deposit durations for more than 200 commercial banks

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