interest rate caps smile too but can the libor market models capture the smile using 3 years of interest rate caps price data we provide a comprehensive documentation of volatility smiles in the caps market to capture the volatility smiles we develop a multifactor term structure model with stochastic volatility and jumps that yields a closed form formula for cap prices we show that although a three factor stochastic volatility model can price at the money caps well significant negative jumps in interest rates are needed to capture the smile the volatility smile contains information

50th anniversary article option pricing valuation models and applications this paper surveys the literature on option pricing from its origins to the present an extensive review of valuation methods for european and american style claims is provided applications to complex securities and numerical methods are surveyed emphasis is placed on recent trends and developments in methodology and modeling

a pricing model for secondary market yield based floating rate notes subject to default risk abstract the purpose of this article is to price secondary market yield based floating rate notes smy frns subject to default risk smy frns are derivatives on the default free term structure of interest rates on the term structures for default risky credit classes and on the structure of a determined pool of bonds the main problem in smy frn pricing as compared to the pricing of standard interest rate or credit derivatives is market incompleteness which makes traditional no arbitrage pricing by replication fail in general smy frns are subject to two types of default risk first the smy frn issuer may go bankrupt direct default risk second the possibility of the bankruptcy of the issuers in the underlying pool has an influence on the smy frn coupons indirect default risk this article is the first one which provides a no arbitrage pricing model for smy frns with direct and indirect default risks it is also the first article applying incomplete market pricing methodology to smy frns

a joint framework for consistently pricing interest rates and interest rate derivatives dynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options most existing option pricing practices take the yield curve as given thus having little to say about the fair valuation of the underlying interest rates this paper proposes an m n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options the first m factors capture the yield curve variation whereas the latter n factors capture the interest rate options movements that cannot be effectively identified from the yield curve we propose a sequential estimation procedure that identifies the m yield curve factors from the libor and swap rates in the first step and the n options factors from interest rate caps in the second step the three yield curve factors explain over 99 of the variation in the yield curve but account for less than 50 of the implied volatility variation for the caps incorporating three additional options factors improves the explained variation in implied volatilities to over 99

the valuation of floating rate instruments abstract a framework for valuing floating rate notes is developed to examine the effects of 1 lags in the coupon formula 2 special contractual features and 3 default risk evidence from a sample of floaters indicates they sold at significant discounts while lags in the coupon formulas and other contractual features make these notes more variable they do not account for the magnitude of the discounts we conclude that the fixed default premium in the coupon formula of a typical note is inadequate to compensate for time varying default premiums demanded by investors who treat other corporate short term paper as close substitutes

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 equilibrium model of bond pricing and a test of market efficiency in two previous and related papers 3 4 the authors have reported the results of estimating a particular equilibrium model of bond pricing using quarterly data on canadian government bonds for the period 1964 to 1979 this paper reports the results of applying a similar model to the pricing of u s government bonds for the period 1958 1979 using data from the crsp government bond file the paper also extends the previous empirical analysis by evaluating the ability of the pricing model to detect underpriced and overpriced bonds the data reveal a strong relation between price prediction errors and subsequent bond returns

a new analysis of the determinants of the real dollar sterling exchange rate 1871 1994 the high persistence of both ppp deviations and the proxy variables for the equilibrium real rate might create a problem of spurious coefficient significance within recently applied nonlinear models to illustrate we consider the real dollar sterling exchange rate over the period 1871 1994 a nonlinear estar process with a time varying equilibrium seems to parsimoniously fit the data appropriate significance levels are obtained using the wild bootstrap method to adequately capture the conditional heteroskedasticity in the data our results provide further evidence for the nonlinear model and the implied speed of adjustment is found to be substantially faster than previously reported in the literature

the default risk of swaps we characterize the exchange of financial claims from risky swaps these transfers are among three groups shareholders debtholders and the swap counterparty from this analysis we derive equilibrium swap rates and relate them to debt market spreads we then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders in a simplified case we obtain closed form solutions for the value of the default risk in the swap for interest rate swaps we obtain numerical solutions for the equilibrium swap rate including default risk we compare these with equilibrium debt market default risk spreads swaps have been one of the most explosive and important innovations in international capital markets in the last 10 years in its simplest form a swap consists of an agreement hetween two entities called counterparties to exchange in the future two streams of cash flows in a currency swap these streams of cash flows consist of a stream of interest and principal payments in one cvtrrency exchanged for a stream of interest and principal payments of the same maturity in another currency in an interest rate swap they consist of streams of interest payments of one type fixed or floating exchanged for streams of interest payments of the other type in the same currency the two types of swap are shown in appendix 1 the economic importance of swap transactions is the fact that they can he comhined with deht issues to change the nature of the liahility for the borrower the sum of a hond issue and a currency swap gives a net liability stream which is equivalent to transforming the bond liability into a different currency a floating rate note combined with an interest rate swap results in a liability equivalent to fixed rate debt two issues have dominated the academic literature on swaps the first concerns the reasons for their use arbitrage of imperfections in capital markets was the original cause of their appearance price and henderson 1984 turnbull 1987 shows that lowering borrowing costs by a synthetic transaction involving a swap is not possible in a complete integrated capital market subsequent authors wall and pringle 1988 arak estrella groodman and silver 1988 smith smithson and wakeman 1987 observe

a tractable interest rate model with explicit monetary policy rates abstract this paper proposes a novel interest rate model that presents simple analytical pricing formulas for interest rate based derivatives including swaps futures swaptions caps and floors exploring the regime switching feature of markov chains the proposed model focuses on discrete changes in the central bank policy rates the main driver of short term rate fluctuations an empirical analysis shows that the proposed model generally outperforms other standard short term rate models in fitting cross sections of options prices moreover the explicit nature of policy rates to some extent enables the model to infer risk neutral probabilities of the central bank rate decisions

default risk in a market model abstract this paper presents a theoretical model of default risk in the context of the market model approach to interest rate dynamics we propose a model for finite interval interest rates such as libor which explicitly takes into account the possibility of default through the influence of a point process with deterministic intensity we relate the defaultable interest rate to the non defaultable interest rate and to the credit risk characteristics default intensity and recovery rate we find that the spread between defaultable and non defaultable rate depends on the non defaultable rate even when the default intensity is deterministic prices of a cap on the defaultable rate and of a credit spread option are derived we consider swaps with unilateral and bilateral default risk and derive the fair fixed swap rate in both cases under the condition that both counterparties are of the same risk class we show that for a monotonously increasing term structure the swap rate for a defaultable swap will lie below the swap rate for a swap without default risk

a defaultable hjm modelling of the libor rate for pricing basis swaps after the credit crunch abstract a great deal of recent literature discusses the major anomalies that have appeared in the interest rate market following the credit crunch in august 2007 there were major consequences with regard to the development of spreads between quantities that had remained the same until then in particular we consider the spread that opened up between the libor rate and the ois rate and the consequent empirical evidence that fra rates can no longer be replicated using libor spot rates due to the presence of a basis spread between floating legs of different tenors we develop a credit risk model for pricing basis swaps in a multi curve setup the libor rate is considered here as a risky rate subject to the credit risk of a generic counterparty whose credit quality is refreshed at each fixing date a defaultable hjm methodology is used to model the term structure of the credit spread defined through the implied default intensity of the contributing banks of the libor corresponding to a chosen tenor a forward credit spread volatility function depending on the entire credit spread term structure is assumed in this context we implement the model and obtain the price of basis swaps using a numerical scheme based on the euler maruyama stochastic integral approximation and the monte carlo method

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

a flexible matrix libor model with smiles abstract we present a flexible approach for the valuation of interest rate derivatives based on affine processes we extend the methodology proposed in keller ressel et al in press by changing the choice of the state space we provide semi closed form solutions for the pricing of caps and floors we then show that it is possible to price swaptions in this multifactor setting with a good degree of analytical tractability this is done via the edgeworth expansion approach developed in collin dufresne and goldstein 2002 a numerical exercise illustrates the flexibility of wishart libor model in describing the movements of the implied volatility surface

ppp strikes back aggregation and the real exchange rate we show the importance of a dynamic aggregation bias in accounting for the ppp puzzle we prove that the aggregate real exchange rate is persistent because its components have heterogeneous dynamics established time series and panel methods fail to control for this using eurostat data we find that when heterogeneity is taken into account the estimated persistence of real exchange rates falls dramatically its half life for instance may fall to as low as eleven months significantly below the consensus view of three to five years

optimal combination of energy crops under different policy scenarios the case of northern greece energy crops production is considered as environmentally benign and socially acceptable offering ecological benefits over fossil fuels through their contribution to the reduction of greenhouse gases and acidifying emissions energy crops are subjected to persistent policy support by the eu despite their limited or even marginally negative impact on the greenhouse effect the present study endeavors to optimize the agricultural income generated by energy crops in a remote and disadvantageous region with the assistance of linear programming the optimization concerns the income created from soybean sunflower proxy for energy crop and corn different policy scenarios imposed restrictions on the value of the subsidies as a proxy for eu policy tools the value of inputs costs of capital and labor and different irrigation conditions the results indicate that the area and the imports per energy crop remain unchanged independently of the policy scenario enacted furthermore corn cultivation contributes the most to ifncome maximization whereas the implemented cap policy plays an incremental role in uptaking an energy crop a key implication is that alternative forms of motivation should be provided to the farmers beyond the financial ones in order the extensive use of energy crops to be achieved

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

income volatility of energy crops the case of rapeseed abstract the adoption of energy crops may generate significant benefits from reduced foreign energy dependence improved rural economies and achieved environmental goals nevertheless important issues arise as these crops are strongly competed by other presumably more standard uses of farmland and their choice will be restrictive unless profit becomes a powerful motive for farmers the abolishment of specific policies supporting first generation biofuels gives rise to the question whether the tactic of bioenergy land use change is just to be abandoned by european farmers the present paper endeavours to evaluate the reduction in income volatility in the case of the rapeseed energy crop a cultivation extensively used in biofuels in the european union employing the concept of entropy the results provide a vague picture regarding the limitations in rapeseed income volatility among the european member states consequently the issue of income uncertainties as a determinant of bioenergy cropland demand has been left pending the innovation of the study lies in the use of entropy concept and the kapetanios and shin unit root test in the case of income volatility for energy crops in the european context the estimation of the random components with the assistance of auto regressive integrated mean average models may provide a tool for confining income uncertainties with the assistance of other policy schemes including insurances within the common agricultural policy

a dynamic model for the forward curve this article develops and estimates a dynamic arbitrage free model of the current forward curve as the sum of i an unconditional component ii a maturity specific component and iii a date specific component the model combines features of the preferred habitat model the expectations hypothesis et and affine yield curve models it permits a class of low parameter multiple state variable dynamic models for the forward curve we show how to construct alternative parametric examples of the three components from a sum of exponential functions verify that the resulting forward curves satisfy the heath jarrow morton hjm conditions and derive the risk neutral dynamics for the purpose of pricing interest rate derivatives we select a model from alternative affine examples that are fitted to the fama bliss treasury data over an initial training period and use it to generate out of sample forecasts for forward rates and yields for forecast horizons of 6 months or longer the forecasts of this model significantly outperform those from common benchmark models jel c53 e43 e47 the structure of forward rates for fixed maturity loans to begin at various dates in the future can be inferred from the prices of treasury securities or directly observed from the extremely active eurodollar futures market the constellation of these rates or of the related yields plays a central role intheallocationofcapital therandombehaviorofthis yieldcurve or the relationship between the yields and the term to maturity is a subject of considerable theoretical and empirical study

tests for unit root versus threshold specification with an application to the purchasing power parity relationship we consider modeling the real exchange rate by a stationary three regime self exciting threshold autoregressive setar model with possibly a unit root in the middle regime this representation is consistent with purchasing power parity in the presence of trading costs our main contribution is to provide statistical tools for testing unit root versus a setar first we show that a setar with a unit root in the middle regime is stationary and mixing under reasonable assumptions second we derive analytically the asymptotic distribution of our unit root test under the null using monthly real exchange rate data our test rejects the null of unit root against a threshold process for five european series

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

nonparametric estimation of state price densities implicit in interest rate cap prices based on a multivariate extension of the constrained locally polynomial estimator of ait sahalia and duarte 2003 we provide one of the first nonparametric estimates of probability densities of libor rates under forward martingale measures and state price densities spds implicit in interest rate cap prices the forward densities and spds depend significantly on the slope and volatility of libor rates and mortgage markets activities have strong impacts on the shape of the forward densities the spds exhibit a pronounced u shape as a function of future libor rates suggesting that the state prices are high at both extremely low and high interest rates which tend to be associated with recessions and periods of high inflation respectively our results provide nonparametric evidence of unspanned stochastic volatility and suggest that the unspanned factors could be partly driven by activities in the mortgage markets the author 2009 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

farm level constraints on the domestic supply of perennial energy crops in the uk abstract there are a number of estimates of the land area that could potentially be dedicated to perennial energy crops such as short rotation coppice src willow and miscanthus in the uk but little is known about how farmers will respond to the opportunities presented by these relatively novel crops perennial energy crops face competition from other arguably more flexible uses of farmland and if not seen as attractive propositions to individual farmers they will not be grown farmers decisions are therefore a key constraint on potential supply this paper reviews the policy background and considers whether policy is based on any consideration of likely supply response before presenting outcomes of focus groups composed of farmers who already grow or are considering growing perennial energy crops there appear to be a number of barriers to adoption in addition to concerns over the security of contracts the current high wheat price increases the opportunity cost of committing land to perennial energy crops there are also worries about the impact of willow roots on field drains and the cost of returning the land to other uses this paper outlines a number of issues of importance to policy makers and suggests future research needs

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

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

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

time dependent variance and the pricing of bond options in this paper we develop a model for valuing debt options that takes into account the changing characteristics of the underlying bond by assuming that the standard deviation of return is proportional to the bond s duration the resulting model uses the bond price as the single state variable and thus preserves much of the simplicity and robustness of the black scholes approach the paper provides comparisons between option prices computed using this model and those using the black scholes and brennan and schwartz models the last decade has seen a dramatic increase in the volatility of bond markets leading to a growing interest in financial instruments that can be used to hedge this risk thus in the u s canada and the u k there has been a proliferation of new interest rate dependent securities such as bond futures options on bonds options on bond futures swap agreements and bonds with option features such as callability putability retractability and so forth with the development of these markets the problems of valuation and the derivation of the hedging strategies have become subjects of increasing importance to both practitioners and academics several valuation methods have been suggested in the literature but so far no consensus has emerged as to the best solution to these problems the simplest approach to the valuation of debt options and probably the most widely used in practice is the black scholes model 3 this method originally developed for the valuation of stock options assumes that the variance of the rate of return on the underlying security is constant while this assumption is plausible for common stocks it is clearly unreasonable for bonds with a finite maturity the distinctive feature of the problem of debt option valuation is that the characteristics of the underlying asset change over time because the price is constrained to converge to the face value of the bond at maturity a second drawback of the black scholes approach is that it assumes a constant short term interest rate an assumption that is clearly inconsistent with stochastic returns on bonds in spite of these problems the black scholes model has been frequently used in practice to value debt options because of its overwhelming simplicity in comparison with other available methods

the pricing of default free interest rate cap floor and collar agreements the paper focuses on the valuation of caps floors and collars in a contingent claim framework under continuous time these instruments are interpreted as options on traded zero coupon bonds the bond prices themselves are used as the underlying stochastic variables this has the advantage that we end up with closed form solutions which are easy to compute special attention is devoted to the choice of the stochastic process appropriate for the price dynamics of the underlying zero coupon bonds the increased volatility of interest rates and the introduction of numerous variable rate instruments have led to a more intensive use of highly sophisticated risk hedging tools among them interest rate caps floors and collars have recently gained a growing popularity an interest rate cap is an agreement between the provider of the cap and a borrower to limit the borrower s floating interest rate to a specific level for a given period of time to be more precise the borrower selects a reference rate to hedge e g libor a period of time to hedge e g 5 years and the level of protection desired e g a ceiling of 200 basis points above the current level of the libor if the market rate exceeds the ceiling rate the cap provider will make payments to the buyer sufficient to bring his rate back to the ceiling when the market rate is below the ceiling no payment is made

interest rate term structure modelling abstract this article surveys approaches to modelling the term structure of interest rates over the last few decades several frameworks have been developed which are actively used in banks for the pricing and risk management of interest rate related products there seems to be a need for an introductory overview of modelling approaches aimed at the yet unfamiliar reader with a quantitative background

primal dual simulation algorithm for pricing multidimensional american options this paper describes a practical algorithm based on monte carlo simulation for the pricing of multidimensional american i e continuously exercisable and bermudan i e discretely exercisable

large data sets nonlinearity and the speed of adjustment to real exchange rate shocks a well known puzzle in international finance concerns the very slow speeds of adjustment of real exchange rates observed in response to shocks in this article we explore whether allowing for a wide range of influences on the real exchange rate in a nonlinear framework can help resolve this puzzle using recently proposed econometric methods for summarizing very large macroeconomic data sets into a small number of observable factors we find that there is a long run relationship between these factors and real exchange rates when put into a nonlinear framework we find that allowing for the effects of macroeconomic factors dramatically increases the measured speed of adjustment of the real exchange rate

inflation indexed swaps and swaptions this article considers the pricing and hedging of inflation indexed swaps and the pricing of inflation indexed swaptions and options on inflation indexed bonds to price the inflation indexed swaps we suggest an extended hjm model the model allows both the forward rates and the consumer price index to be driven not only by a standard multidimensional wiener process but also by a general marked point process our model is an extension of the hjm approach proposed by jarrow and yildirim jarrow r yildirim y 2003 pricing treasury inflation protected securities and related derivatives using an hjm model journal of financial and quantitative analysis 38 409 430 and later also used by mercurio mercurio f 2005 pricing inflation indexed derivatives quantitative finance 5 3 289 302 to price inflation indexed swaps furthermore we price options on so called tips bonds assuming the model is purely wiener driven we then introduce an inflation swap market model to price inflation indexed swaptions all prices derived have explicit closed form solutions furthermore we formally prove the validity of the so called foreign currency analogy

on the feasibility of arbitrage based option pricing when stochastic bond price processes are involved abstract there are many options which are based on interest rate sensitive assets for example debt options and currency options are best priced when a stochastic bond price process is included however not all stochastic bond price processes are feasible for use in pricing options by standard arbitrage techniques this work draws on the results of harrison and kreps j econ theory 20 1979 381 408 and relates them to pricing in the presence of stochastic bond price processes examples of feasible and infeasible bond price processes are given

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

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

developing a sustainability framework for the assessment of bioenergy systems the potential for biomass to contribute to energy supply in a low carbon economy is well recognised however for the sector to contribute fully to sustainable development in the uk specific exploitation routes must meet the three sets of criteria usually recognised as representing the tests for sustainability economic viability in the market and fiscal framework within which the supply chain operates environmental performance including but not limited to low carbon dioxide emissions over the complete fuel cycle and social acceptability with the benefits of using biomass recognised as outweighing any negative social impacts this paper describes an approach to developing a methodology to establish a sustainability framework for the assessment of bioenergy systems to provide practical advice for policy makers planners and the bioenergy industry and thus to support policy development and bioenergy deployment at different scales the approach uses multi criteria decision analysis mcda and decision conferencing to explore how such a process is able to integrate and reconcile the interests and concerns of diverse stakeholder groups

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

closed form solutions for term structure derivatives with log normal interest rates we derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero coupon bonds the crucial assumption is that simple interest rates over a fixed finite period that matches the contract which we want to price are log normally distributed moreover this assumption is shown to be consistent with the heath jarrow morton model for a specific choice of volatility closed form solutions for interest rate derivatives in particular caps floors and bond options have been obtained by a number of authors for markovian term structure models with normally distributed interest rates or alternatively log normally distributed bond prices see for example jamshidian 1989 1991a heath jarrow and morton 1992 brace and musiela 1994 geman el karoui and rochet 1995 these models support black scholes type formulas most frequently used by practitioners for pricing bond options and swaptions unfortunately these models imply negative interest rates with positive probabilities and hence they are not arbitrage free in an economy with opportunities for riskless and costless storage of money briys crouhy and schobel 1991 apply the gaussian framework to derive closed form solutions for caps floors and european zero coupon bond options to exclude the influence of negative forward rates on the pricing of zero coupon bond options they introduce an additional boundary condition as shown by rady and sandmann 1994 these pricing formulas are only supported by a term structure model with an absorbing boundary for the forward rate at zero where the absorbing probability is not negligible which for a term structure model is a quite problematic assumption

general equilibrium real and nominal interest rates we derive the general equilibrium short term real and nominal interest rates in a monetary economy affected by technological and monetary shocks and where the price level dynamics is endogenous assuming fairly general processes for technology and money supply we show that an inherent feature of our equilibrium is that any real variable dynamics in particular that of the short term real interest rate is driven by both monetary and real factors this money non neutrality is generic as it does not stem from any friction such as price stickiness or from a particular utility function non neutrality obtains because the ex ante cost of real money holdings is random due to inflation uncertainty we then analyze in depth a specialized version of this economy in which the state variables follow square root processes and the representative investor has a log separable utility function the short term nominal rate dynamics we obtain encompasses most of the dynamics present in the literature from vasicek and cir to recent quadratic and more generally non linear interest rate models moreover our results pave the way to several new nominal term structures

the willingness of farmers to engage with bioenergy and woody biomass production a regional case study from cumbria abstract in this paper we explore the willingness of cumbrian farmers to switch land use from food production to biomass production in a landscape where food production is both heavily subsidised and the area is a centre for tourism this is against a policy background of a switch of subsidies from food production to environmental benefits increased concerns about emissions from farming and an increased demand for renewable energy we identified an awareness of new markets for renewable energy alongside increasing volatility of other crops against a background of increasing demand for food from this our conclusions are that the main short term opportunities for increasing biomass production in this region are through intensifying management of existing woodlands in the medium term as the financial case for biomass crops becomes more certain we can envisage a tipping point which would favour a switch from marginal agricultural land to biomass

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

macroeconomic forecasting using diffusion indexes this article studies forecasting a macroeconomic time series variable using a large number of predictors the predictors are summarized using a small number of indexes constructed by principal component analysis an approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecasts the method is used to construct 6 12 and 24 monthahead forecasts for eight monthly u s macroeconomic time series using 215 predictors in simulated real time from 1970 through 1998 during this sample period these new forecasts outperformed univariate autoregressions small vector autoregressions and leading indicator models