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

stochastic modeling of financial electricity contracts abstract we discuss the modeling of electricity contracts traded in many deregulated power markets these forward futures type contracts deliver either physically or financially electricity over a specified time period and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price we propose to use the heath jarrow morton approach to model swap prices since the notion of a spot price is not easily defined in these markets for general stochastic dynamical models we connect the spot price the instantaneous delivery forward price and the swap price and analyze two different ways to apply the heath jarrow morton approach to swap pricing either one specifies a dynamics for the non existing instantaneous delivery forwards and derives the implied swap dynamics or one models directly on the swaps the former is shown to lead to quite complicated stochastic models for the swap price even when the forward dynamics is simple the latter has some theoretical problems due to a no arbitrage condition that has to be satisfied for swaps with overlapping delivery periods to overcome this problem a practical modeling approach is analyzed the market is supposed only to consist of non overlapping swaps and these are modelled directly a thorough empirical study is performed using data collected from nord pool our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes however this is an area of further research

risk neutral parameter shifts and derivatives pricing in discrete time we obtain a large class of discrete time risk neutral valuation relationships or preference free derivatives pricing models by imposing a simple restriction on the state price density process the risk neutral stock return and forward rate dynamics are obtained by changing only a location parameter which can be determined independent of the preference and true location parameters the gaussian models of rubinstein 1976 brennan 1979 and c mera 2003 and the gamma model of heston 1993 are all special cases the model provides simple relationships between expected returns and state price density parameters analogous to the diffusion case

the minimum variance hedge ratio under stochastic interest rates in an environment where interest rates are stochastic we examine the case of a pure hedger endowed with a fixed position in a long term bond in contrast to conventional wisdom according to which the difference between hedging through forward contracts and futures is immaterial it turns out that the minimum variance hedge ratio using forwards comprises two terms instead of one only when using futures the magnitude of the difference between the two hedge ratios may be important under some plausible assumptions this result is due to the presence of additional interest rate risk that bears on the profit and loss statement associated with the forward position this sheds some additional light on the respective features of forward and futures contracts written on interest rate sensitive securities

nonlinear mean reversion in the short term interest rate using a new bayesian method for the analysis of diffusion processes this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative the assumption of stationarity which is common in the literature represents a nontrivial prior belief about the shape of the drift function this belief and the use of flat priors contribute strongly to the finding of nonlinear mean reversion implementation of an approximate jeffreys prior results in virtually no evidence for mean reversion in interest rates unless stationarity is assumed finally the article documents that nonlinear drift is primarily a feature of daily rather than monthly data and that these data contain a transitory element that is not reflected in the volatility of longermaturity yields the drift of the short term interest rate is an important determinant of a wide variety of asset prices both inside and outside the boundaries of what is often called fixed income while volatilities may be estimated relatively accurately using high frequency observations of the short rate the short rate s extreme persistence makes identifying the true shape of the drift function a particularly elusive goal if our goal is merely to fit prices then the difficulty in estimating a drift function can be avoided by backing out implied drifts using a no arbitrage approach such as hull and white 1990 or heath jarrow and morton 1992 these methods bypass the true distribution entirely focusing on solving for the risk neutral drift function that is consistent with the cross section of bond prices if our goal however is to learn from prices and to be able to assess theories such as the expectations hypothesis that link short and long rates then estimating the drift function under the true measure is unavoidable in several recent articles a variety of sophisticated econometric techniques have been brought to bear on the problem in particular

the second fundamental theorem of asset pricing a new approach this article presents a new definition of market completeness that is independent of the notions of no arbitrage and equivalent martingale measures our definition has many advantages all shown herein first it preserves the second fundamental theorem of asset pricing even in complex economies second under our definition the market can be complete yet arbitrage opportunities exist this is important in practice and stands in contrast to the traditional definitions third under the assumption of no arbitrage and when used in the standard models our definition is equivalent to the traditional one

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

generalising interest rate duration with directional derivatives direction x and applications conventional or fisher weil duration is an ordinary derivative that measures the response of portfolio value to marginal parallel shifts in the term structure while other proposed measures are generally specific to particular interest rate processes in this paper we show that portfolio responses to arbitrary shifts in the term structure may be handled by the use of frechet or directional derivatives presenting a simple algorithm for the directional derivative of a fixed interest portfolio viewed as a set of cash flows for a given portfolio one can locate the most sensitive areas along the term structure by computing a function or profile direction x that gives the term structure movement to which the portfolio is most exposed immunisation techniques can be based on choosing ancillary assets that ensure that the portfolio directional derivative is zero or as close to zero as possible this generalises approaches based on factor models of the term structure the analysis is applied to both continuous and discrete time

valuing risky fixed rate debt an extension this paper develops a corporate bond valuation model that takes into account both early default and interest rate risk it corrects a defect of recent contributions where pricing equations do not assure that the payment to bondholders upon bankruptcy is no greater than firm value the bankruptcy triggering mechanism is directly related to the payoff received by bondholders when early bankruptcy is forced upon the firm more specifically the default barrier is defined simply as a fixed quantity discounted at the riskless rate up to the maturity date of the risky corporate bond as soon as this threshold is crossed bondholders receive an exogenously specified fraction ofthe remaining assets deviations from the absolute priority rule also are captured because it accounts for gaussian interest rate uncertainty default risk and deviations from the absolute priority rule this model is capable of producing quite diverse shapes for the term structure of yield spreads

a hicksian multiplier accelerator model with floor determined by capital stock this article reconsiders the hicksian multiplier accelerator model with the floor related to the depreciation on actual capital stock through the introduction of the capital variable a growth trend is created endogenously by the model itself along with growth rate oscillations around it the ceiling can be dispensed with altogether as everything is growing in such a model a variable transformation is introduced to focus relative dynamics of the income growth rate and the actual capital output ratio

pricing claims under garch level dependent interest rate processes this article considers the pricing of interest rate sensitive claims when the underlying interest rate is driven by a two state variable garch process analytical solutions are established for the case when the innovations in the short rate are normal and or chi squared random variables and the volatility of rates take on a special garch form garch models that nest level dependent interest rate models including the cox ingersoll and ross model are also considered algorithms are provided that permit the efficient pricing of american style interest rate claims under a rather broad array of garch level dependent processes

implementing a stochastic model for oil futures prices this paper develops a parsimonious three factor model of the term structure of oil futures prices that can be easily estimated from available futures price data in addition it proposes a new simple spreadsheet implementation procedure the procedure is flexible may be used with market prices of any oil contingent claim with closed form pricing solution and easily deals with missing data problems the approach is implemented using daily prices of all futures contracts traded at the new york mercantile exchange between 1991 and 2001 in sample and out of sample tests indicate that the model fits the data extremely well though the paper concentrates on oil the approach can be used for any other commodity with well developed futures markets

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

solar energy applications and development in nigeria drivers and barriers abstract in this study current perspectives of solar energy utilization as a renewable energy option in nigeria are examined and discussed from the standpoint of sustainable development the country being a world crude oil and natural gas producer is over dependent on these energy sources for electricity generation and other energy applications this has currently put the country at a risk of impending energy crises in view of the fast diminishing fossil reserves inadequate refining capacity to meet domestic consumption and serious cases of energy insecurity in restive regions where exploitations exist in spite of the vast fossil based energy reserves a meager electricity production capacity that is put at 4517 6 mw as at december 2012 is generated to support the economy of a teeming population of approximately 170 million people nigeria is naturally endowed with abundant deposit of renewable energy resources of which solar energy from the sun being the world s most abundant and permanent energy source has for decades been enjoying very high level utilization by rural dwellers for agricultural processings in the country it is vastly deposited with an estimated 17 459 215 2 million mj day of solar energy falling on the country s 923 768 km2 land area approximate range of 12 6 mj m2 day in the coastal region to about 25 2 mj m2 day in the far north the different applications to which solar resources have been put and the extent of utilization including details of existing projects in the country were thoroughly investigated and discussed the possible motivations for extensive development of solar energy conversion systems in nigeria are also discussed and some of the barriers and challenges are presented steps and policy measures to overcome the barriers and facilitates the utilization of this resource are suggested

the price setting behavior of banks an analysis of open end leverage certificates on the german market abstract this paper presents the first analysis of open end leverage certificates on the german market the major innovations of these certificates are twofold first issuers announce a price setting formula according to which they are willing to buy and sell the certificates over time second the product s lifetime is potentially endless our main findings are that the price setting formula is i designed to strongly favor the issuer and ii is consistent with the main outcome of the life cycle hypothesis for structured financial products stoimenov p a wilkens s 2005 are structured products fairly priced an analysis of the german market for equity linked instruments journal of banking and finance 29 2971 2993 iii this holds for different product features and also in the presence of issuers credit risk and jump risk in the underlying

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

the cost and duration of cash balance pension plans controversy about the fairness of early transitions from traditional defined benefit plans to cash balance plans may have overshadowed the subtleties of funding a cash balance pension liability because crediting rates of cash balance liabilities float with market rates the same techniques used to value and hedge floating rate bonds provide the present value cost and effective duration of a cash balance liability the present value cost of funding a liability varies dramatically across the menu of irs sanctioned crediting alternatives for example given the yield curve from november 15 1999 the present value per 1 00 of cash balance of funding a liability paying off 30 years from now varies between 0 90 and 1 48 the effective duration of a cash balance liability also varies dramatically according to various crediting rates the effective duration is typically positive but much shorter than the expected time until retirement or other payment and depending on the choice of crediting rate can vary

a reexamination of the uncovered interest rate parity hypothesis abstract it is now widely known that the uncovered interest rate parity uip hypothesis which states that forward exchange rates are unbiased predictors of future spot exchange rates is generally rejected by empirical evidence we show in this paper by means of a cox et al 1985 model extended to a two country economy that a careful examination of the no arbitrage principle leads to a different formulation for this hypothesis roughly speaking this new formulation states that the expected future spot exchange rate is equal to the forward exchange rate multiplied by a term premium whose closed form expression can be derived moreover this multiplicative term premium reduces to 1 i e the standard uip hypothesis holds if and only if conditional variances are deterministic in short we show that rejection of the standard uip hypothesis is not surprising as long as arch effects have been evidenced in exchange rate data as a by product we provide a parametric and tractable specification for the so called risk premium i e the component of the expected exchange rate in excess of the forward exchange rate

the hicksian trade cycle with floor and ceiling dependent on capital stock this article reconsiders the hicksian multiplier accelerator model with floor and ceiling the new thrust is that these constraints are tied to the actual stock of capital the floor to the depreciation on this stock the ceiling to capital as a limiting production factor according to the fixed proportions technology that also underlies the principle of acceleration for capital formation just the hicksian investment theory is used the result is one unified model creating economic growth and growth rate cycles

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

hedging in the possible presence of unspanned stochastic volatility evidence from swaption markets this paper examines whether higher order multifactor models with state variables linked solely to underlying libor swap rates are by themselves capable of explaining and hedging interest rate derivatives or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary our research shows that swaptions and even swaption straddles can be well hedged with libor bonds alone we examine the potential benefits of looking outside the libor market for factors that might impact swaption prices without impacting swap rates and find them to be minor indicating that the swaption market is well integrated with the libor swap market

an interest rate risk management model for commercial banks abstract this paper develops a goal programming model to assist a commercial bank in managing its exposure to interest rate risk the bank s objective is to immunize its equity position against innovations in interest rates while maximizing its market value to accomplish this task a duration gap framework is developed that does not require interest rate forecasts as decision variables the model includes assets liabilities and off balance sheet derivative securities the focus is on a protective put strategy that uses options on interest rate futures but to provide contrast a short interest rate futures position is examined as well application of the model to an illustrative environment indicates that for larger interest rate changes the option strategy provides better protection against interest rate risk than the short futures position

pricing and hedging in incomplete markets abstract we present a new approach for positioning pricing and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable by assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure we derive a counterpart to the first fundamental theorem of asset pricing we also derive a counterpart to the second fundamental theorem which leads to unique derivative security pricing and hedging even though markets are incomplete for products that are not spanned by the liquid assets of the economy we show how our methodology provides more realistic bid ask spreads

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

cournot duopoly when the competitors operate multiple production plants this article considers a cournot duopoly under an isoelastic demand function and cost functions with built in capacity limits the special feature is that each firm is assumed to operate multiple plants which can be run alone or in combination each firm has two plants with different capacity limits so each has three cost options the third being to run both plants dividing the load according to the principle of equal marginal costs as a consequence the marginal cost functions come in three disjoint pieces so the reaction functions derived on basis of global profit maximization may also consist of disjoint pieces this is reflected in a particular bifurcation structure due to border collision bifurcations and to particular basin boundaries related to the discontinuities it is shown that stable cycles may coexist and the non existence of unstable cycles constitutes a new property we also compare the coexistent short periodic solutions in terms of the resulting real profits

spreading currency forwards why and how abstract in this paper we have adopted a continuous time framework in which a hedger has a currency risk sensitive non traded cash position the hedger has the opportunity to hedge against risk by using two currency forward contracts that differ only in their maturities the hedger is able to reach a perfect hedge of his non traded position by using only two currency forward contracts with different maturities even though four sources of uncertainty drive the international economy this perfect hedge is reached by spreading forward contracts where the hedger is short in the nearby contract and long in the deferred contract this strategy is easy to implement since no parameter has to be estimated empirically when the hedger is a price taker finally the analysis has been extended to currency futures contracts we show in explicit terms how the marking to market of futures positions affects the spreading strategy

arbitrage cointegration and testing the unbiasedness hypothesis in financial markets we use a no arbitrage cost of carry asset pricing model to show that the existence of coin tegration between spot and forward futures prices depends on the time series properties of the cost of carry we argue that the conditions for cointegration are more likely to hold in currency markets than in commodity markets explaining many of the empirical results in the literature we also use this model to demonstrate why the forward rate forecast error the basis and the forward premium are serially correlated and to develop econometric tests ofthe unbiasedness hypothesis sometimes called the simple efficiency hypothesis in various financial markets the unbiasedness hypothesis is so prevalent in the finance liter ature that many tests for it have been developed we examine four of the common tests and and use our cointegration results to demonstrate why each of these tests should reject the null hypothesis of unbiasedness we find strong support for our hypothesis in the existing empirical literature

a new measure of cross sectional risk and its empirical implications for portfolio risk management abstract litterman et al litterman r scheinkman j weiss l 1991 volatility and the yield curve journal of fixed income 1 june 49 53 and engle and ng engle r f ng v k 1993 time varying volatility and the dynamic behavior of the term structure journal of money credit and banking 25 3 336 349 provide empirical evidence of a relation between yield curve shape and volatility this study offers theoretical support for that finding in the general context of cross sectional time series we introduce a new risk measure quantifying the link between cross sectional shape and market risk a simple econometric procedure allows us to represent the risk experienced by cross sections over a time period in terms of independent factors reproducing possible cross sectional deformations we compare our risk measure to the traditional cross yield covariance according to their relative performance empirical investigation in the us interest rate market shows that 1 cross shape risk factors outperform cross yield risk factors i e yield curve level slope and convexity in explaining the market risk of yield curve dynamics 2 hedging multiple liabilities against cross shape risk delivers superior trading strategies compared to those stemming from cross yield risk management

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

a path dependent approach to security valuation with application to interest rate contingent claims abstract the last two decades have witnessed a tremendous growth in the volume of assets and liabilities whose cash flows depend in a variety of ways on the path of interest rates some of these including floating rate notes and swap agreements contractually base cash flows on current and past interest rates and contain caps floors and other more complex features others including mortgages many corporate bonds and time deposits are fixed rate instruments that contain embedded options such as those to prepay call or withdrawal the irregular exercise of these options causes cash flows to vary as time proceeds and interest rates rise or fall this paper develops a state contingent claims technique for valuing such securities it is derived from the option based model of breeden and litzenberger 1978 using the transition matrix approach of banz and miller 1978 particular attention is paid to valuing so called path dependent securities whose contemporaneous cash flows depend on the historical path of interest rates as well as their current level a detailed example is provided in which an adjustable rate mortgage is valued under a variety of economic and security specific assumptions

a two factor stochastic programming model of danish mortgage backed securities abstract danish mortgage loans have several features that make them interesting short term revolving adjustable rate mortgages are available as well as fixed rate 10 20 or 30 year annuities that contain embedded options call and delivery options the decisions faced by a mortgagor are therefore non trivial both in terms of deciding on an initial mortgage and in terms of managing rebalancing it optimally we propose a two factor arbitrage free interest rate model calibrated to observable security prices and implement on top of it a multi stage stochastic optimization program with the purpose of optimally composing and managing a typical mortgage loan we model accurately both fixed and proportional transaction costs as well as tax effects risk attitudes are addressed through utility functions and through worst case min max optimization the model is solved in up to 9 stages having 19 683 scenarios numerical results which were obtained using standard soft and hardware indicate that the primary determinant in choosing between adjustable rate and fixed rate loans is the short long interest rate differential i e term structure steepness but volatility also matters refinancing activity is influenced by volatility and of course transaction costs

an integrated pricing model for defaultable loans and bonds abstract in recent years credit risk has played a key role in risk management issues practitioners academics and regulators have been fully involved in the process of developing studying and analysing credit risk models in order to find the elements which characterize a sound risk management system in this paper we present an integrated model based on a reduced pricing approach for market and credit risk its main features are those of being mark to market and that the spread term structure by rating class is contingent on the seniority of debt within an arbitrage free framework we introduce issues such as the integration of market and credit risk the use of stochastic recovery rates and recovery by seniority moreover we will characterize default risk by estimating migration risk through a mortality rate actuarial based approach the resultant probabilities will be the base for determining multi period risk neutral transition probability that allow pricing of risky debt in the trading and banking book

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

pricing derivatives on financial securities subject to credit risk this article provides a new methodology for pricing and hedging derivative securities involving credit risk two types of credit risks are considered the first is where the asset underlying the derivative security may default the second is where the writer of the derivative security may default we apply the foreign currency analogy of jarrow and turnbull 1991 to decompose the dollar payoff from a risky security into a certain payoff and a spot exchange rate arbitrage free valuation techniques are then employed this methodology can be applied to corporate debt and over the counter derivatives such as swaps and caps the purpose of this article is to provide a new theory for pricing and hedging derivative securities involving credit risk two sources of credit risk are identified and analyzed the first is where the asset underlying the derivative security may default paying off less than promised this is the case for example with imbedded options on corporate debt the second is the credit risk introduced by the writer of the derivative security who may also default examples include over the counter writers of options on eurodollar futures swaps and swaptions for pricing derivative securities involving credit risk there are currently two approaches the first views these derivatives as contingent claims not on the financial securities themselves but as compound options on the assets underlying the financial securities this is the case for example with the pricing of imbedded options on corporate debt see merton 1974 1977 black and cox 1976 ho and singer 1982 chance 1990 and kim ramaswamy and sundaresan 1993 or the pricing of vulnerable options see johnson and stulz 1987 in practice however this valuation methodology is difficult to use first the assets underlying the financial security are often not tradeable and therefore their values are not observable this makes application of the theory and estimation of the relevant parameters problematic second as in the case of corporate debt all of the other liabilities of the firm senior to the corporate debt must first and simultaneously be valued this generates significant computational difficulties as a result this approach has not

risk management of non maturing liabilities abstract risk management of non maturing liabilities is a relatively unstudied issue of significant practical importance non maturing liabilities include most of the traditional deposit accounts like demand deposits savings accounts and short time deposits and form the basis of the funding of depository institutions therefore the asset and liability management of depository institutions depends crucially on an accurate understanding of the liquidity risk and interest rate risk profile of these deposits in this paper we propose a stochastic three factor model as general quantitative framework for liquidity risk and interest rate risk management for non maturing liabilities it consists of three building blocks market rates deposit rates and deposit volumes we give a detailed model specification and present algorithms for simulation and calibration our approach to liquidity risk management is based on the term structure of liquidity a concept which forecasts for a specified period and probability what amount of cash is available for investment for interest rate risk management we compute the value the risk profile and the replicating bond portfolio of non maturing liabilities using arbitrage free pricing under a variance minimizing measure the proposed methodology is demonstrated by means of a case study the risk management of savings accounts

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

governing the transition to renewable energy a review of impacts and policy issues in the small hydropower boom abstract the transition to renewable energy technologies raises new and important governance questions with small hydropower shp expanding as part of renewable energy and climate mitigation strategies this review assesses its impacts and identifies escalating policy issues to provide a comprehensive literature review of small hydropower we evaluated over 3600 articles and policy documents this review identified four major concerns 1 confusion in small hydropower definitions is convoluting scholarship and policy making 2 there is a lack of knowledge and acknowledgement of small hydropower s social environmental and cumulative impacts 3 small hydropower s promotion as a climate mitigation strategy can negatively affect local communities posing contradictions for climate change policy and 4 institutional analysis is needed to facilitate renewable energy integration with existing environmental laws to ensure sustainable energy development for readers interested in small hydropower we clarify areas of confusion in definition and explain the corresponding impacts for distinct system designs for a broader readership we situate small hydropower implementation within international trends of renewable energy development the contradictory impacts of climate change policy emerging dynamics in energy finance and reliance on market mechanisms our paper provides a timely contribution to scholarship on small hydropower and the transition to renewable energy

modeling the term structure of interest rates a new approach abstract the term structure of interest rates is modeled as a random field with conditional volatility random field models allow consistency with the current shape of the term structure without the need for recalibration however most such models are gaussian with no conditional volatility state dependent volatility is introduced while a key property of gaussian random field models is retained each forward rate is part of a low dimensional diffusion process simplifying estimation and derivatives pricing the modeling approach also implies that in general the set of zero coupon bonds does not complete the market and term structure derivatives cannot always be priced by arbitrage

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

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

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

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

bond pricing and the term structure of interest rates a discrete time approximation this paper studies the binomial approximation to the continuous trading term structure model of heath jarrow and morton 1987 the discrete time approximation makes the original methodology accessible to a wider audience and provides a computational proce dure necessary for calculating the contingent claim values derived in the continuous time paper this paper also extends and generalizes ho and lee s 1986 model to include multiple random shocks to the forward rate process and to include an analysis of continu ous time limits the generalization provides insights into the limitations of the existing empirical implementation of ho and lee s model

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

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

pricing of long dated commodity derivatives do stochastic interest rates matter abstract does modelling stochastic interest rates beyond stochastic volatility improve pricing performance on long dated commodity derivatives to answer this question we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables we examine the empirical pricing performance of these models on pricing long dated crude oil derivatives estimating the model parameters from historical crude oil futures prices and option prices we find that stochastic interest rate models improve pricing performance on long dated crude oil derivatives when the interest rate volatility is relatively high furthermore increasing the model dimensionality does not tend to improve the pricing performance on long dated crude oil option prices but it matters for long dated futures prices we also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long dated crude oil option prices

towards understanding the benefits and challenges of smart micro grid for electricity supply system in nigeria the poor state of electricity supply system in nigeria is threatening the welfare and security of life and properties of millions of individuals with adverse economic consequences for the country the inadequacy of the national grid especially the inability of the electricity generation capacity to match increasing demand in the country has led to increasing agitation for increased penetration of renewable energy sources ress into the electricity supply mix while great attention has been focused on the potential of ress for electricity generation in the country little or no attention has been given to the application of smart micro grid sm g technologies to the ageing nigeria grid infrastructures and electrification of the rural areas the aim of this paper is to bring into focus the benefits and challenges of enabling sm g in the electricity supply system in nigeria sm g will bring benefits to the electricity stakeholders in form of improvements in reliability efficiency economics environment security and safety the paper gives an overview and reviews the current state of the electricity supply system in the country it discusses the sm g concepts and associated technologies and highlights how they can help address the electricity problems in the country the challenges of applying these concepts in nigeria context are also discussed enabling sm g in the country will not only lead to improvement in the quality efficiency and reliability of the electricity grid but also promote the provision of electricity supply to the remote rural areas using ress

on deposit volumes and the valuation of non maturing liabilities abstract in this paper we propose a framework for the modelling of non maturing liabilities the latter referring to deposits without a specific maturity or deposits whose actual time horizon significantly differs from their contractual maturity the set of non maturing liabilities include most of the traditional deposit accounts like demand deposits and savings accounts and form the basis of the funding for depository institutions our framework consists of three pieces models for market rates deposit rates and deposit volumes for the market rate an extended one factor vasicek model is used but the framework developed is general and any other and potentially more sophisticated and accurate model for the market rate can be applied deposit rates are modelled using policy functions which are allowed to depend on the current market rate and the volume deposited concerning deposit volumes we develop a framework in which models for deposit volumes can be derived in theoretically sound way this is done in two steps in the first step we propose reasonable rules or strategies based on which we attempt to capture the behaviour of the individual customer in the second step we then define notions of homogeneity in customer behaviour and use these to derive models for the behaviour of the average customer and for the volumes deposited by the average customer finally the pieces of the framework are integrated in a valuation formula we here use the approach of jarrow and van deventer 1998 the arbitrage free valuation and hedging of demand deposits and credit card loans journal of banking and finance 22 249 272 and a value is assigned to a portfolio of demand deposits this valuation formula also forms the basis for the risk management of the interest rate risk embedded in the demand deposits

small hydropower shp development in nigeria an assessment this paper evaluates small hydropower shp development and examines the current situation in nigeria with respect to the established policies and energy power sector reform epsr act 2005 hydropower sector witnessed about 360 growth between 1971 and 2005 and yet only about 5 of the vast small hydropower shp potential is tapped by the few plants built between 1923 and 1964 operating and maintenance costs are in favor of shp development in the country being the lowest when compared with the situation in european countries the nigerian government has taken steps to diversify energy sources in order to promote renewable energy development by encouraging private investments in the energy sector through reforms but this may not be adequate as there remain barriers against shp development in the country it is concluded that government must incorporate subsidies feed in tariffs and framework for price purchase agreements ppa into the policies in order to further promote renewable energy and attract both indigenous and foreign investments for quick adoption and rapid expansion of shp technologies

regular and chaotic growth in a hicksian floor ceiling model in some previous papers the present authors reassembled the hicksian trade cycle model in a new way the floor was tied to depreciation on capital itself the cumulative sum of past net investments for which the principle of acceleration provided an explanation hence no alien elements were needed to include capital and so close the system the resulting model created a growth trend along with growth rate cycles which could be periodic or quasiperiodic in the current paper the ceiling using capital stock as a capacity limit for production is added it then turns out that pure growth no longer exists and chaos and multistability become possible which they were not in the previous model a variety of bifurcation scenarios is explored and a full understanding of the working of the four piece originally three dimensional piecewise smooth map is attained using a reduction to a one dimensional return map

the arbitrage free valuation and hedging of demand deposits and credit card loans abstract using a market segmentation argument this paper uses the interest rate derivative s arbitrage free methodology to value both demand deposit liabilities and credit card loan balances in markets where deposits loan rates may be determined under imperfect competition in this context these financial instruments are shown to be equivalent to a particular interest rate swap where the principal depends on the past history of market rates solutions are obtained which are independent of any particular model for the evolution of the term structure of interest rates

determination of the adequate capital for default protection under the one factor gaussian term structure model abstract in practice credit risk is measured by one of the two different methodologies one measures the prices and sensitivities of the credit linked instruments another measures the required collateral or capital needed to cover a potential default loss this paper introduces a pricing methodology which also determines the required capital conventionally the value at risk method is used to determine collateral requirements artzner et al demonstrated that the resulting adequate capital measures may fail to capture the credit diversification effect which is critical in credit risk management cf artzner p delbaen f eber j m heath d 1997 definition of coherent measures of risk paper presented at the symposium on risk management european finance association vienna august 27 30 in order to overcome this problem this paper introduces a new approach which combines closed form solutions and the hull white trinomial tree this combined approach is computationally faster than a naively implemented monte carlo based var methodology the pricing model is based on the rating based gaussian term structure model developed by nakazato this approach is applicable to a wide variety of credit derivatives and their portfolios in a coherent fashion in this paper however attention is concentrated on determining the collateral requirement for the counter party risk when there is the risk of credit rating change on an issue and also risk of default on that issue or on any protection already written on the issue

pricing interest rate derivatives a general approach the relationship between affine stochastic processes and bond pricing equations in exponential term structure models has been well established we connect this result to the pricing of interest rate derivatives if the term structure model is exponential affine then there is a linkage between the bond pricing solution and the prices of many widely traded interest rate derivative securities our results apply to m factor processes with n diffusions and l jump processes the pricing solutions require at most a single numerical integral making the model easy to implement we discuss many options that yield solutions using the methods of the article

default parameter estimation using market prices this article presents a new methodology for estimating recovery rates and the pseudo default probabilities implicit in both debt and equity prices in this methodology recovery rates and default probabilities are correlated and depend on the state of the macroeconomy this approach makes two contributions first the methodology explicitly incorporates equity prices in the estimation procedure this inclusion allows the separate identification of recovery rates and default probabilities and the use of an expanded and relevant data set equity prices may contain a bubble component which is essential in light of recent experience with internet stocks second the methodology explicitly incorporates a liquidity premium in the estimation procedure which is also essential in light of the large observed variability in the yield spread between risky debt and u s treasury securities and the illiquidities present in risky debt markets

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