futures prices on yields forward prices and implied forward prices from term structure when futures contracts are settled with respect to underlying asset prices received theory suggests that the differences between futures prices and implied forward prices from the term structure are strictly due to marking to market ceteris paribus empirical evidence appears to indicate that such differences are small for contracts with short maturities what happens when the futures contract settles to yields implied by future prices of underlying assets the eurodollar futures contract which is the most actively traded futures contract in the united states settles to yield as opposed to prices this unique settlement feature is shown to imply that the implied forward prices from the libor term structure should differ from the futures prices even in the absence of marking to market differences due to marking to market effect are small they are shown to vary between 2 to 45 basis points less than one half percent of futures prices on the other hand differences between implied forward prices and futures prices are shown to be relatively large

the valuation of options on yields abstract many contingent claims incorporate options on yield levels i derive closed form expressions for european yield option prices using a general equilibrium model in which the underlying yield is the relevant state variable the properties of these options differ markedly from those of conventional options on traded assets for example yield call values can be less than their intrinsic value and can be decreasing functions of the underlying yield these features have important hedging implications i examine the empirical implications of the model using price data for the 13 week t bill options traded on the chicago board options exchange

on the valuation of an option to exchange one interest rate for another abstract this paper studies the problem of pricing a european option on the difference of two interest rates which is analogous to an option to exchange one asset for another studied in margrabe 1978 it is first shown that such option may be valued as exchanging two interest rates implied in relevant futures prices through an extended black 1976 model and then by a two factor heath jarrow morton hjm model which shows that introduction of imperfect interest rates movements is essential for pricing such options for which a one factor model such as ho and lee 1986 should not be applied

computing the constant elasticity of variance option pricing formula this paper expresses the constant elasticity of variance option pricing formula in terms of the noncentral chi square distribution this allows the application of well known approximation formulas and the derivation of a whole class of closed form solutions in addition a simple and efficient algorithm for computing this distribution is presented this paper shows that the constant elasticity of variance cev formula can be expressed as a function of the noncentral chi square distribution a simple and efficient algorithm for computing this distribution is presented approximations to this distribution can be used to estimate accurately the cev formula when the computation of the exact solution is problematic section i discusses theories and some evidence on the association between volatility and price level section ii presents the particular kind of relationship assumed by the cev model and reviews empirical evidence on the model section iii shows that the cev formula can be expressed in terms of the noncentral chisquare distribution a simple algorithm for computing this distribution is derived in section iv section v presents some special closed form solutions to this distribution finally section vi shows that an approximation to the cev formula can be used when the exact solution converges slowly i relationship between volatility and price level several theoretical arguments imply an association between stock price and volatility geske 11 black 3 and christie 5 consider the effects of financial leverage on the variance of the stock an increase in the stock price reduces the debt equity ratio of the firm and therefore reduces the variance of the stock s returns black hypothesizes that price changes may also affect volatility through their impact on operating leverage in addition he proposes a reverse causal relationship whereby an increase in the volatility of stocks causes prices to fall in rubinstein s 171 displaced diffusion model the relation between price and volatility of returns depends on the firm s asset mix and debt equity ratio empirical evidence supports the hypothesis that volatility changes with stock price schmalensee and trippi 19 examining just over a year of weekly data on six stocks find a strong negative relationship between stock price changes and changes in implied volatility black 3 using over ten years of data on thirty stocks finds that a given proportional increase decrease in stock price is

married women s allocation of time to employment and care of elderly parents married women who have been shown in past research to exhibit relatively elastic labor supply constitute a group of particular interest with respect to decisions concerning time spent in parental care and time spent in market work this paper presents estimates of a simultaneousequations model of employment hours of work and the provision of care to an older parent the results provide no evidence of reduced propensities to be employed or of reduced conditional hours of work due to the provision of parent care these findings are consistent with other research on women s allocation of time to competing productive uses

the strategic bequest motive although recent research suggests that intergenerational transfers play an important role in aggregate capital accumulation our understanding of bequest motives remains incomplete we develop a simple model of strategic bequests in which a testator influences the decisions of his beneficiaries by holding wealth in bequeathable forms and by conditioning the division of bequests on the beneficiaries actions the model generates falsifiable empirical predictions that are inconsistent with other theories of intergenerational transfers we present econometric and other evidence that strongly suggests that bequests are often used as compensation for services rendered by beneficiaries

wealth inequality and intergenerational links previous work has had difficulty generating household saving behaviour that makes the distribution of wealth much more concentrated than that of labour earnings and that makes the richest households hold onto large amounts of wealth even during very old age i construct a quantitative general equilibrium overlapping generations model in which parents and children are linked by accidental and voluntary bequests and by earnings ability i show that voluntary bequests can explain the emergence of large estates while accidental bequests alone cannot and that adding earnings persistence within families increases wealth concentration even more i also show that the introduction of a bequest motive generates lifetime savings profiles more consistent with the data

the analytic pricing of asymmetric defaultable swaps swaps where both parties are exposed to credit risk still lack convincing pricing mechanisms this article presents a reduced form model where the event of default is related to structural characteristics of each party the cash flows submitted to credit risk are identified before the swap is priced analytical pricing formulas for interest rate and currency swaps are computed using a gaussian model for risky bonds currency swaps exhibit additional correlation risk the benefits from netting depend on the balance between exposures and market conditions in valuation we show that sources of credit risk asymmetries are also likely to impact on credit spreads

inter vivos transfers and intended bequests abstract empirical work on intergenerational transfers has focused on distinguishing between altruistic and exchange motivated behavior however these two models are unable to explain the strong tendency for inter vivos transfers to be negatively related to the income of the recipient while bequests bear no relationship to income this paper presents a new framework for analyzing transfers from parents to children that is more consistent with observed behavior than are the altruistic and exchange models alone in particular the model developed here predicts differing behavior with respect to inter vivos transfers and bequests due to liquidity constraints and uncertainty about the recipient s permanent income the empirical work uses data from the health and retirement study and the asset and health dynamics study the patterns observed in these data are consistent with earlier findings that inter vivos transfers go disproportionately to less well off children while bequests are divided equally across children further the results support the predictions of the model in that differences in inter vivos transfers arise from differences in current income while differences in bequests result when indicators of the children s permanent incomes differ

on pricing of credit spread options abstract this paper describes and analyses different pricing models for credit spread options such as longstaff schwartz black das sundaram and duan garch based models the first two models longstaff schwartz and black assume respectively a mean reverting dynamic and a lognormal distribution for the spread and are representative of the so called spread models such models consider the spread as a unique variable and provide closed form solutions for option pricing on the contrary das sundaram propose a recursive backward induction procedure to price credit spread options on a bivariate tree which describes the dynamic of the term structure of forward risk neutral spread and risk free rate this model belongs to the class of structural models which can be used to price a wider range of credit risk derivatives finally we consider the pricing of credit spread options assuming a discrete time garch model for the spread

an alternative valuation model for contingent claims abstract this paper studies contingent claim valuation in a lucas type exchange economy the derived fundamental valuation equation differs from its cox ingersoll ross production economy counterpart in that it is expressed in terms of the direct utility function and an exogenous output process thus offering superior tractability we apply our approach to derive closed form solutions for bond bond option individual stock and stock option prices under a more general setting than allowable in the cox ingersoll ross framework the resulting interest rate and stock price dynamics are empirically plausible moreover our stock option pricing formula with stochastic volatility and interest rates can reconcile certain puzzling empirical regularities including the volatility smile

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

measuring and modeling intergenerational links in relation to long term care long term care has profound intergenerational implications it can be costly for those who need it and onerous for loved ones who provide it we pinpoint three intergenerational aspects of long term care that require further research one concerns the link between costs of private care and intergenerational wealth transfers the second concerns the link between participation in care and the work and welfare of family providers the third relates to intergenerational tensions that these and other late in life interactions create we outline innovations in modeling and measurement that would improve understanding of intergenerational linkages and their implementation in appropriate panel data jel d91 i13 j22

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

fiscal dimensions of emu the issue of fiscal policy in a monetary union has once again become very topical as the eu deadline for emu approaches and as countries take seriously the need to meet the maastricht fiscal criteria but are by no means certain to succeed in attaining them by the time a first decision on participation is made moreover germany has thrown open the issue of whether the fiscal criteria are adequate to ensure the needed discipline and has proposed more ambitious targets and monetary sanctions for non compliance with the 3 deficit ceiling in this paper i shall discuss what i consider to be the three essential issues with respect to fiscal policy and emu i the debt and deficit criteria as conditions for qualifying for emu membership 2 the need for fiscal discipline and policy coordination in emu and the role of the criteria in achieving them and 3 the desirability of and prospects for creating a supranational fiscal authority in the eu to accompany monetary union naturally these three issues have already achieved considerable attention in the literature and i will not be able to do justice to that literature by providing a proper survey instead i will provide my own views and be selective in my discussion of those of others

bond price dynamics and options this paper provides a closed form preference free means of valuing a european call option written on a default free pure discount bond investors may not agree upon a theory of the term structure but they will necessarily agree on equilibrium option values further these equilibrium option values may be obtained without recourse to numerical approximation default free pure discount bond prices were posited to follow a non standardized transformed brownian bridge process this specification implicitly incorporates the terminal constraint that the price of a default free pure discount bond equal its face value at maturity contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities the brownian bridge specification permits an appropriate means of incorporating a number of such constraints therefore while this paper has considered only the application of the brownian bridge process to the valuation of debt options the introduction of this process may provide for many further financial applications

fiscal discipline and flexibility in emu the implementation of the stability and growth pact fiscal discipline to safeguard the credibility of the single monetary authority and fiscal flexibility to respond to country specific shocks are two core principles governing budgetary policy in emu the stability and growth pact aims at ensuring the first objective to comply with the requirements of the pact eu members need to achieve a close to balance or surplus position and change their budgetary behaviour in periods of cyclical upturns by refraining from spending the growth dividend past experience shows that fiscal laxity does not buy more effective stabilization once emu countries have achieved their medium term target their automatic stabilizers will be able to operate fully thus helping in smoothing out cyclical fluctuations the main potential problems in the implementation of the pact may arise in the early years of emu during the transition to a balanced budget in the event of a slow down in economic activity

the supply of children s time to disabled elderly parents i introduction in recent years economists have become increasingly interested in intergenerational transfers of both time and money 1 such transfers may be motivated by altruism or exchange models of altruism assume that a person s utility depends on the consumption or utility of other family members and her own consumption for example children may supply unpaid informal care to aging parents because their utility increases when their parents are happier one of the most striking predictions of models of altruism is that public subsidies tend to crowd out transfers by altruistic individuals especially if the subsidy is financed by taxing the altruistic individual becker 1974 in exchange models there is typically altruism but one family member such as a parent can induce a relative such as a child or kid 2 to provide more services or money than the relative would normally provide by threatening to withhold a bequest to the extent that this is so one would plausibly expect more care and attention to be provided to wealthy parents when there is more than one kid more care should be provided because the threat of disinheritance is more credible when there is competition between kids for bequests in a well known article bernheim shleifer and summers 1985 hereafter referred to as bss found empirical support for the strategic bequest motive based on an observed positive relationship between children s visits and telephone calls to elderly parents per child as the measure of attention and bequeathable wealth per child as the measure of the financial motivation for providing such attention one might expect this result to extend to decisions about direct provision of help informal care that kids may provide to parents the marginal benefit of such care is plausibly greater than the benefit derived from a visit or telephone call in a recent article however we found no evidence that the strategic bequest motive is an important determinant of the amount of informal care kids provide or a related decision whether or not to place the parent in a nursing home sloan hoerger and picone 1996 we focused on the distinction between cognitively aware parents who can threaten to disinherit their kids and cognitively unaware parents who cannot disinherit and examined whether this distinction had any effect on the probability that the parent entered a nursing home or on amounts of formal and informal care received if the parent remained in the community any strategic effects were swamped by the greater marginal benefit of care to the parent when the parent was cognitively unaware moreover among the cognitively aware richer parents actually received less informal care contrary to the strategic model s predictions unfortunately in past research on intergenerational transfers of time and money it was not possible to control for the wealth wage and other characteristics of kids to the extent that kid s wealth and wage were positively correlated with parent s wealth which was observed the parameter estimates on parent s wealth may be negatively biased although parent s wealth and kid s wealth and wage rates are plausibly positively correlated they have opposite effects on the supply of kid s time according to the strategic bequest model that is potential bequests from a parent may be less attractive to rich kids and therefore induce less care we test the strategic bequest model using information on elderly parents and their children from two linked surveys the 1989 national long term care survey nltcs for elderly individuals and the survey of informal caregivers sic for a subsample of the elderly s children using these data we can include explicit measures of kid s wealth and wage rates thereby avoiding the possible bias introduced by a correlation between parent s and kid s wealth and wages also the data sets provide information on several pertinent health cognitive and functional status variables which are not typically observed in surveys of financial status

dynamic wage and employment effects of elder parent care this article formulates and estimates a dynamic discrete choice model of elder parent care and work to analyze how caregiving affects a woman s current and future labor force participation and wages the model incorporates parental health changes human capital accumulation and job offer availability the estimates indicate that women face low probabilities of returning to work or increasing work hours after a caregiving spell i use the estimated model to simulate the caregiving employment and welfare effects of a longer unpaid work leave than currently available under the family and medical leave act a paid leave and a caregiver allowance

the value of life and the rise in health spending over the past half century americans spent a rising share of total economic resources on health and enjoyed substantially longer lives as a result debate on health policy often focuses on limiting the growth of health spending we investigate an issue central to this debate is the growth of health spending a rational response to changing economic conditions notably the growth of income per person we develop a model based on standard economic assumptions and argue that this is indeed the case standard preferences of the kind used widely in economics to study consumption asset pricing and labor supply imply that health spending is a superior good with an income elasticity well above one as people get richer and consumption rises the marginal utility of consumption falls rapidly spending on health to extend life allows individuals to purchase additional periods of utility the marginal utility of life extension does not decline as a result the optimal composition of total spending shifts toward health and the health share grows along with income in projections based on the quantitative analysis of our model the optimal health share of spending seems likely to exceed 30 percent by the middle of the century

strategic play among family members when making long term care decisions this paper describes a strategic model of bargaining within a family to determine how to care for an elderly parent we estimate the parameters of the model using data from the national long term care survey we find that the parameter estimates generally make sense and that the model is consistent with the data the results have strong implications for using less structural empirical models for policy analysis

parental altruism and inter vivos transfers theory and evidence this paper uses psid data on the extended family to test whether inter vivos transfers from parents to children are motivated by altruism specifically the paper tests whether an increase by one dollar in the income of parents actively making transfers to a child coupled with a one dollar reduction in that child s income results in the parents increasing their transfer to the child by one dollar this restriction on parental and child transfer income derivatives is derived for the standard altruism model augmented to include uncertainty and liquidity constraints these additional elements pin down the timing of inter vivos transfers the method used to estimate income transfer derivatives takes into account unobserved heterogeneity across families in the degree of altruism the findings strongly reject the altruism hypothesis redistributing one dollar from a recipient child to donor parents leads to less than a 13 cent increase in the parents transfer to the child far less than the one dollar increas

valuing futures and options on volatility abstract this paper presents simple closed form expressions for volatility futures and option prices and examines their implications for the characteristics of these securities we show that the properties of these volatility derivatives are fundamentally different from those of conventional option and futures contracts this analysis also provides insights into the role that volatility derivatives may play in managing and hedging volatility risk in financial markets

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

fiscal transfers and fiscal sustainability we examine whether the u s and german state governments pursue sustainable fiscal policies taking into account fiscal transfers using panel data techniques we investigate whether the debt to gdp ratio had a positive influence on the primary surplus bohn model we show that including excluding fiscal transfers changes the results if fiscal transfers are not included in the primary surplus the test results do not indicate that the u s and german state governments pursued sustainable fiscal policies our results also suggest that fiscal transfers were positively related to debt these findings indicate that intergovernmental transfers have implicitly subsidized debts

the composition and drawdown of wealth in retirement as the baby boomers approach and enter their retirement years the accumulation phase of their life cycle is nearly over thus the focus of many researchers financial services firms and public policymakers concerned with retirement saving is shifting from the accumulation of resources while working to the drawdown of resources during retirement retired households are dependent on the annuitized income streams that they have built up during their working careers and on the wealth that they have accumulated in other forms the two most common annuitized income streams are social security benefits and the payments from defined benefit pension plans these payout streams provide income for life and thus provide some protection against falling into poverty if one lives an especially long life the three most common sources of accumulated wealth are equity in an owner occupied home financial assets such as bonds and stocks and financial assets held in a personal retirement account such as an individual retirement arrangement or a 401 k plan throughout our analysis we will define retirement age households as those headed by someone between the ages of 65 and 69 in 2008 just over 80 percent of these households had some equity in their home or another property while 52 percent had assets in personal retirement accounts a much higher fraction 87 percent had some financial assets outside their retirement accounts but for many households the amount of such assets was relatively modest only 45 percent had more than 20 000 in non retirement account financial assets the median financial asset holding for this group including holdings in personal retirement accounts is 52 000 in short many households have small enough amounts of accumulated wealth that they will depend heavily on the life contingent payout streams offered by social security and if they have one a defined benefit pension this paper presents evidence on the resources available to households as they enter retirement it draws heavily on data collected by the health and retirement study which we sometimes refer to as the hrs we calculate the potential additional annuity income that households could purchase given their holdings of non annuitized financial assets at the start of retirement even if households used all of their financial assets inside and outside personal retirement accounts to purchase a life annuity only 47 percent of households between the ages of 65 and 69 in 2008 could increase their life contingent income by more than 5 000 per year at the upper end of the wealth distribution however a substantial number of households could make large annuity purchases we also consider the role of housing equity in the portfolios of retirement age households and explore the extent to which households draw down housing equity and financial assets as they age we find that many households appear to treat housing equity and non annuitized financial assets as precautionary savings tending to draw them down only when they experience a shock such as the death of a spouse or a period of substantial medical outlays because home equity is often conserved until very late in life for many households it may provide some insurance against the risk of living longer than expected a brief conclusion summarizes our findings and indicates how they bear on a number of policy issues such as the role for annuity defaults in retirement saving plans

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

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

nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active cboe option classes from august 23 1976 through august 31 1978

heterogeneity in state dependent utility evidence from strategic surveys a standard result of life cycle models under uncertainty is that optimizing individuals equate the expected marginal utility of consumption across states of the world if insurance is available at actuarially fair rates a small empirical literature has suggested that the marginal utility of consumption is lower in less healthy states we use a novel survey based measure to document significant heterogeneity in health state dependence across individuals largely orthogonal to standard controls we further show that individuals value unhealthy states of the world more when facing work limiting disabilities than when facing disabilities requiring long term care and when facing physical rather than mental disabilities jel d12 i10