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

inferring future volatility from the information in implied volatility in eurodollar options a new approach we study the information content of implied volatility from several volatility specifications of the heath jarrow morton 1992 hjm models relative to popular historical volatility models in the eurodollar options market the implied volatility from the hjm models explains much of the variation of realized interest rate volatility over both daily and monthly horizons the implied volatility dominates the garch terms the glosten et al 1993 type asymmetric volatility terms and the interest rate level however it cannot explain that the impact of interest rate shocks on the volatility is lower when interest rates are low than when they are high article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

implicit delivery options and optimal delivery strategies for financial futures contracts abstract futures contract specification usually allow the short position some variation as to when where how much and what is to be delivered in this paper we derive the optimal delivery policy for the treasury bond futures contracts and find that our policy produces profits that are positive and statistically significant this indicates that future prices are too high in that the short position can earn profits by skillfully exercising his delivery options we find the actual delivery policies of market participants depart substantially from the optimal strategy the implications of these findings for futures traders and bond dealers are discussed

rationing rules and european central bank auctions abstract theoretical analyses of multi unit auctions tend to side step the importance of rationing rules by assuming strictly decreasing aggregate demand however under european central bank rules bidders are allowed to submit no more than ten price quantity pairs so even if the underlying demand is strictly decreasing it is likely that several bidders may submit a market clearing bid if at the market clearing bid excess demand exists it is necessary to ration how much each bidder receives the effect on bidding behavior and equilibrium revenues under two distinct rationing rules is explored in this paper

pricing american interest rate claims with humped volatility models abstract some of the most recent empirical studies on interest rate derivatives have found humped shapes in the volatility structure of interest rates in this paper we propose a simple model that allows for humped volatility structures and that can be described by one state variable with the model american style claims can be priced very efficiently which is very important if the model has to be calibrated daily to market prices of standard american options furthermore the model allows for explicit formulas for european style options finally the computational efficiency of our model in the li et al 1995 framework is compared with the efficiency in a typical hull and white 1993a 1994 1996 framework in fact we can use both procedures for our model since we prove that if a deterministic volatility model can be embedded in either of these algorithms then so it does in the other one empirical evidence from option data supporting our model is provided as well

input demand under yield and revenue insurance previous studies disagree on the effects of insurance on fertilizer application rates the effect of increased fertilizer on the probability of low yields primarily determines whether fertilizer and insurance are substitutes or complements we estimate conditional distributions of corn yields to determine if the technical relationship between yields and fertilizer supports the hypothesis that insurance increases optimal application rates our results indicate no support for this hypothesis at all nitrogen fertilizer rates and reasonable levels of risk aversion nitrogen fertilizer and insurance are substitutes suggesting that those who purchase insurance are likely to decrease nitrogen fertilizer applications

bond pricing and the term structure of interest rates a new methodology for contingent claims valuation this paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates the methodology based on the equivalent martingale measure technique takes as given an initial forward rate curve and a family of potential stochastic processee for its subsequent movements a no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk examples are provided to illustrate the key results in relation to the term structure of interest rates arbitrage pricing theory has two purposes the first is to price all zero coupon default free bonds of varying maturities from a finite number of economic fundamentals called state variables the second is to price all interest rate sensitive contingent claims taking as given the prices of the zero coupon bonds this paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context of which all existing arbitrage pricing models are special cases in particular vasicek 1977 brennan and schwartz 1979 langetieg 1980 ball and torous 1983 ho and lee 1986 schaefer and schwartz 1987 and artzner and delbaen 1988 the primary contribution of this paper however is a new methodology for solving the second problem i e the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds the methodology is new because i it imposes its stochastic structure directly on the evolution of the forward rate curve ii it does not require an inversion of the term structure to eliminate the market prices of risk from contingent claim values and iii it has a stochastic spot rate process with multiple stochastic factors influencing the term structure the model can be used to consistently price and hedge all contingent claims american or european on the term structure and it is derived from necessary and more importantly sufficient conditions for the absence of arbitrage the arbitrage pricing models of vasicek 1977 brennan and schwartz 1979 langetieg 1980 and artzner and delbaen 1988 all require an iformerly titled bond pricing and the term structure of interest rates a new methodology

an analytically tractable interest rate model with humped volatility abstract some of the most recent empirical studies on interest rate derivatives have found humped shapes in the volatility structure of interest rates however this realistic feature has been hardly addressed in theoretical works in this paper we propose an interest rate model which allows for a humped volatility structure and which is analytically tractable in that it leads to explicit formulae for european options on discount bonds empirical evidence supporting the model is also provided

on optimal portfolio choice under stochastic interest rates abstract in an economy where interest rates and stock price changes follow fairly general stochastic processes we analyze the portfolio problem of an investor endowed with a non traded cash bond position he can trade on stocks the riskless asset and a futures contract written on the bond so as to maximize the expected utility of his terminal wealth when the investment opportunity set is driven by an arbitrary number of state variables the optimal portfolio strategy is known to contain a pure preference free hedge component a speculative element and merton breeden hedging terms against the fluctuations of each and every state variable while the first two components are well identified and easy to work out the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics using the martingale approach we show that the optimal strategy can be simplified to include in addition to the pure hedge and speculative components only two merton breeden type hedging elements however large is the number of state variables the first one is associated with interest rate risk and the second one with the risk brought about by the co movements of the spot interest rate and the market prices of risk the implementation of the optimal strategy is thus much easier as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous a priori unknown state variables moreover the investor s horizon is shown explicitly to play a crucial role in the optimal strategy design in sharp contrast with the traditional decomposition finally the role of interest rate risk in actual portfolio risk management is emphasized

pricing caps with hjm models the benefits of humped volatility in this paper we compare different multifactor hjm models with humped volatility structures to each other and to models with strictly decreasing volatility all the models are estimated on euribor and swap rates panel data maximizing the quasi likelihood function obtained from the kalman filter we develop the analysis in two steps first we study the in sample properties of the estimated models then we test the pricing performance on caps we find the humped volatility specification to greatly improve the model estimation and to provide sufficiently accurate cap prices although the models has been calibrated on interest rates data and not on cap prices moreover we find the two factor humped volatility model to outperform the three factor models in pricing caps

impacts of federal crop insurance on land use and environmental quality this article integrates economic and biophysical models to assess how federal crop revenue insurance programs affect land use cropping systems and environmental quality in the u s corn belt region the empirical framework includes econometric models that predict land conversion and crop choices at the parcel level based on expectation and variance of crop revenues land quality climate conditions and physical characteristics at each site the predictions are then combined with site specific environmental production functions to determine the effect of revenue insurance on nitrate runoff and leaching soil water and wind erosion and carbon sequestration results suggest that federal crop insurance has on average a small effect on conversions of non cropland to cropland and somewhat more significant impacts on crop choice and crop rotation these changes in cropping systems have on average small impacts on agricultural pollution

implications of implicit credit spread volatilities on interest rate modelling abstract we test seven term structure models in the heath jarrow and morton 1992 class in order to find the best representation of the libor rate in interest rate markets after the credit crunch of 2007 the libor rate is considered as a risky rate subject to the credit risk of a generic counterparty whose credit quality is refreshed at each fixing date we study the volatilities of the credit spreads implicitly obtained from libor time series in order to understand how assumed volatility functions affect interest rate curve modelling and asset pricing we develop a model to estimate basis swap prices through the monte carlo simulations we compare obtained results and individuate systematic relations existing between the basis spread forecast error and both the accuracy in volatility modelling and the accuracy of the monte carlo estimates we analyse and document these relations by defining appropriate pricing error measures

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

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

crop insurance acreage decisions and nonpoint source pollution the redirection of farm policy in the 1996 farm bill has generated much interest in seeking environmentally friendly and economically viable ways to protect farm income agricultural insurance has been suggested as such an instrument this article estimates the effect of crop insurance on crop mix and the resulting change in chemical use in the central nebraska basin providing corn insurance will shift land from hay and pasture to corn which will increase chemical use at the extensive margin this extensive margin effect dominates the effect of crop insurance on the application rate leading to an increase in total chemical use

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

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

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

on correlation and default clustering in credit markets we establish markovian models in the heath jarrow and morton 1992 paradigm that permit an exponential affine representation of riskless and risky bond prices while offering significant flexibility in the choice of volatility structures estimating models in our family is typically no more difficult than in the workhorse affine family besides diffusive and jump induced default correlations defaults can impact the credit spreads of surviving firms allowing for a greater clustering of defaults numerical implementations highlight the importance of incorporating interest rate credit spread correlations credit spread impact factors and the full credit spread curve when building a unified framework for pricing credit derivatives the author 2010 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please e mail journals permissions oxfordjournals org oxford university press

potential environmental impacts of increased reliance on corn based bioenergy this paper integrates economic and physical models to assess a how increases in agricultural commodity prices driven by ethanol production and other factors affect land use and cropping systems in the us midwest and b how the changes in land use and cropping systems in turn affect environmental quality in the region the empirical framework includes a set of econometric models that predict land conversion crop choices and crop rotations at the parcel level based on commodity prices land quality climate conditions and other physical characteristics at the sites the predictions are then combined with site specific environmental production functions to determine the effect of rising commodity prices on nitrate runoff and leaching soil water and wind erosion and carbon sequestration results suggest that increasing commodity prices will result in widespread conversions of non cropland to cropland fifty percent of the region s pasture and range land will be converted to cropland with 6 corn rising commodity prices will also result in dramatic changes in crop mix and rotation systems in the midwest with 6 corn the total acreage of corn will increase by 23 and 40 in the corn belt and lake states respectively the acreage of continuous corn will increase considerably in both regions as well these changes in land use and crop mix will have a large impact on agricultural pollution approaches to mitigating the environmental impacts are discussed

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

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

currency risk hedging futures vs forward abstract the objective of this paper is to address the issue of choosing between currency forward and currency futures contracts when hedging against currency risk within a stochastic interest rates environment we compare between the hedging effectiveness of the two derivative assets both within a narrow sense i e volatility minimization and within a wide sense i e risk return trade off when judging hedging effectiveness in the narrow sense forward and futures contracts give identical results even if they do not have identical prices when judging hedging effectiveness in the wide sense the choice between the two contracts is determined by the correlation between the domestic and the foreign term structures dynamics

the state contingent properties of stochastic production functions this paper develops the state contingent properties of the most frequently used representations of stochastic production in the agricultural economics literature particular attention is paid to the cases of multiplicative and additive uncertainty and to the convolution of multiplicative and additive uncertainty embodied in the just pope stochastic production function state contingent technologies and their associated cost functions are reviewed and that theory is applied to the stochastic production function a generalisation of the just pope technology that has desirable state contingent characteristics is proposed cost functions based upon state contingent technologies are compared with cost functions based on a parametrised distribution representation of production uncertainty

bond yields and the federal reserve bond yields respond to policy decisions by the federal reserve and vice versa to learn about these responses i model a high frequency policy rule based on yield curve information and an arbitrage free bond market in continuous time the fed s target is a pure jump process jump intensities depend on the state of the economy and the meeting calendar of the federal open market committee the model has closed form solutions for yields as functions of a few state variables introducing monetary policy helps to match the whole yield curve because the target is an observable state variable that pins down its short end and introduces important seasonalities around fomc meetings the volatility of yields is snake shaped which the model explains with policy inertia the policy rule crucially depends on the two year yield and describes fed policy better than taylor rules

a direct discrete time approach to poisson gaussian bond option pricing in the heath jarrow morton model abstract term structure models employing poisson gaussian processes may be used to accommodate the observed skewness and kurtosis of interest rates this paper extends the discrete time pure gaussian version of the heath jarrow morton model to the pricing of american type bond options when the underlying term structure of interest rates follows a poisson gaussian process the poisson gaussian process is specified using a hexanomial tree six nodes emanating from each node and the tree is shown to be recombining the scheme is parsimonious and convergent this model extends the class of hjm models by i introducing a more generalized volatility specification than has been used so far and ii including jumps yet retaining lattice recombination thus making the model useful for practical applications

the implied jump risk of libor rates abstract this paper examines implied parameters from options on libor futures jump diffusion models are found to offer superior in sample and out of sample performance when compared to their pure diffusion counterpart the need to incorporate stochastic jump magnitudes into libor dynamics is also documented in addition empirical evidence reveals that the jump component in libor rates is important for pricing their derivatives furthermore variation in jump risk often coincides with federal open market committee fomc decisions and a small subset of macroeconomic announcements

valuation of american futures options theory and empirical tests this paper reviews the theory of futures option pricing and tests the valuation principles on transaction prices from the s p 500 equity futures option market the american futures option valuation equations are shown to generate mispricing errors which are systematically related to the degree the option is in the money and to the option s time to expiration the models are also shown to generate abnormal risk adjusted rates of return after transaction costs the joint hypothesis that the american futures option pricing models are correctly specified and that the s p 500 futures option market is efficient is refuted at least for the sample period january 28 1983 through december 30 1983 futures option contracts now trade on every major futures exchange and on a wide variety of underlying futures contracts the chicago mercantile exchange the chicago board of trade the new york futures exchange and the commodity exchange now collectively have more than twenty options written on futures contracts where the underlying spot commodities are financial assets such as stock portfolios bonds notes and eurodollars foreign currencies such as west german marks swiss francs and british pounds precious metals such as gold and silver livestock commodities such as cattle and hogs and agricultural commodities such as corn and soybeans moreover new contract applications are before the commodity futures trading commission and should be actively trading in the near future with the markets for these new contingent claims becoming increasingly active it is appropriate that the fundamentals of futures option valuation be reviewed and tested black 5 provides a framework for the analysis of commodity futures options although his work is explicitly directed at pricing european options on forward contracts it applies to european futures contracts as well if the riskless rate of interest is constant during the futures option life 1 the options currently

counterparty risk and the pricing of defaultable securities motivated by recent financial crises in east asia and the united states where the downfall of a small number of firms had an economy wide impact this paper generalizes existing reduced form models to include default intensities dependent on the default of a counterparty in this model firms have correlated defaults due not only to an exposure to common risk factors but also to firm specific risks that are termed counterparty risks numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps it has been well documented in moody s reports on historical default rates of corporate bond issuers that the number of defaults the number of credit rating downgrades and credit spreads are all strongly correlated with the business cycle this has motivated reduced form models such as duffie and singleton 1999 and lando 1994 1998 which assume that the intensity of default is a stochastic process that derives its randomness from a set of state variables such as the short term interest rate this approach has the convenient features that conditioning on the state variables defaults become independent events and default correlation arises due to the common inf luence of these state variables on the other hand a default intensity that depends linearly on a set of smoothly varying macroeconomic variables is unlikely to account for the clustering of defaults around an economic recession this is evident from a casual inspection of the exhibits in the latest moody s report see keenan 2000 within the usual affine framework one can model the state variables as jump diffusions see duffie pan and single

numerical evaluation of multivariate contingent claims we develop a numerical approximation method for valuing multivariate contingent claims the approach is based on an n dimensional extension of the lattice binomial method closed form solutions for the jump probabilities and the jump amplitudes are obtained the accuracy of the method is illustrated in the case of european options when there are three underlying assets article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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 performance of alternative interest rate risk measures and immunization strategies under a heath jarrow morton framework using a monte carlo simulation this study addresses the question of how traditional risk measures and immunization strategies perform when the term structure evolves in a heath jarrow morton 1992 manner the results suggest that for immunization purposes im munization strategies and portfolio formation strategies are more important than interest rate risk measures the performance of immunization strategies depends more on the transaction costs and the holding period than on the risk measures moreover the immu nization performance of bullet and barbell portfolios is not very sensitive to interest rate risk measures

vix option pricing and cboe vix term structure a new methodology for volatility derivatives valuation abstract this study integrates cboe vix term structure and vix futures to simplify vix option pricing in multifactor models exponential and hump volatility functions with one to three factor models of the vix evolution are used to examine their pricing for vix options across strikes and maturities the results show that using exponential volatility functions presents an effective choice as pricing models for vix calls whereas hump volatility functions provide efficient out of sample valuation for most vix puts in particular with deep in the money and deep out of the money pricing errors for calls can be further reduced with a two factor model

implied volatility functions in arbitrage free term structure models abstract we test six term structure models in the heath jarrow and morton 1992 class using eurodollar futures and options data from 1987 1992 we study the time series of implied interest rate volatilities from these models using one day lagged implied volatilities our one and two parameter models simultaneously price an average of 18 5 options each day with an average absolute error of one and a half to two basis points although the models fit well we document systematic strike price and time to maturity biases for all models we also implement simple trading strategies to test whether the models identify genuine biases

valuation of american call options on dividend paying stocks empirical tests abstract this paper examines the pricing performance of the valuation equation for american call options on stocks with known dividends and compares it with two suggested approximation methods the approximation obtained by substituting the stock price net of the present value of the escrowed dividends into the black scholes model is shown to induce spurious correlation between prediction error and 1 the standard deviation of stock return 2 the degree to which the option is in the money or out of the money 3 the probability of early exercise 4 the time to expiration of the option and 5 the dividend yield of the stock a new method of examining option market efficiency is developed and tested

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