nonparametric and semiparametric estimation an analysis of multiproduct returns to scale the nonparametric and semiparametric regression models based on kernel density estimation are reviewed and they are applied to the analysis of returns to scale in dairy farms using a multioutput cost function semiparametric tests of constant returns to scale and homogeneity of production are developed and their implementation show that both of these hypotheses are rejected kernel estimation of the local degree of multiproduct returns to scale confirms that the sample s dairy farms are characterized by a considerable degree of scale economies

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

ironing out the kinks in executive compensation linking incentive pay to average stock prices abstract traditional stock option grant is the most common form of incentive pay in executive compensation applying a principal agent analysis we find this common practice suboptimal and firms are better off linking incentive pay to average stock prices among other benefits averaging reduces volatility by about 42 making the incentive pay more attractive to risk averse executives holding the cost of the option grant to the firm constant asian stock options are more cost effective than traditional stock options and provide stronger incentives to increase stock price more importantly the improvement is achieved with little impact on the option grant s risk incentives after adjusting for option cost finally averaging also improves the value and incentive effects of indexed stock options

ambiguity aversion in buyer seller relationships a contingent claims and social network explanation negotiations between buyers and sellers or suppliers of goods and services have become increasingly important due to the growing trend towards international purchasing outsourcing and global supply networks together with the high uncertainty associated with them this paper examines the effect of ambiguity aversion on price negotiations using multiple priors based real options with non extreme outcomes we study price negotiation between a buyer and seller in a dual contingent claims setting call option holding buyer vs put option holding seller to derive optimal agreement conditions under ambiguity with and without social network effects we find that while higher ambiguity aversion raises the threshold for commitment for the seller it has equivocal effects on the buyer s negotiation prospects in the absence of network control conversely when network position and relative bargaining power are accounted for we find the buyer s implicit price or negotiation threshold decreases or increases unequivocally with increasing aversion to ambiguity extending extant real options research on price negotiation to the case of ambiguity this set of results provides new insights into the role of ambiguity aversion and network structures in buyer seller relationships including how they influence the range of negotiation agreement between buyers and sellers the results also help assist managers in formulating robust buying selling strategies for bargaining under uncertainty by knowing their network positions and gathering background information or inferring the other party s ambiguity tolerance beforehand buyers and sellers can anticipate where the negotiation is heading in terms of price negotiation range and mutual agreement possibilities

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

prudence with respect to ambiguity under expected utility prudence is equivalent to a positive third derivative of utility and plays a crucial role in precautionary saving behaviour eeckhoudt and schlesinger 2006 proposed behavioural definitions of prudence and of higher order risk preferences the present paper proposes a similar definition for prudence with respect to ambiguity i e situations in which objective probabilities are not available implications for several ambiguity models are derived ambiguity prudence is implied by hansen and sargent s 2001 multiplier preferences empirically correlates with financial behaviour and plays a key role in prevention behaviour this article is protected by copyright all rights reserved

nonparametric conditional pricing of higher order multivariate contingent claims abstract this paper describes and applies a nonparametric model for pricing multivariate contingent claims multivariate contingent claims are contracts whose payoffs depend on the future prices of more than one underlying variable the pricing however of these kinds of contracts represents a challenge all known models are adaptations of earlier ones that have been introduced to price plain vanilla calls and puts they are imposing strong assumptions on the distributional properties of the underlying variables in contrast this study adopts a methodology that relaxes such restrictions following barone adesi g bourgoin f giannopoulos k 1998 don t look back risk 11 august 100 104 barone adesi g engle r mancini l 2004 garch options in incomplete markets mimeo university of applied sciences of southern switzerland long x 2004 semiparametric multivariate garch model mimeo university of california riverside multivariate pathways for a set of underlying variables are constructed before the option payoffs are computed this enables the covariances in addition to the means and variances to be modelled in a dynamic and nonparametric manner the model is particular suitable for options whose payoffs depend on variables that are characterised by high nonlinearities and extremes and on higher order multivariate options whose underlying variables are more unlikely to conform to a common theoretical distribution

flexible and risk sharing supply contracts under price uncertainty we study supply contracts for deterministic demand but in an environment of uncertain prices we develop valuation methodologies for different types of supply contracts a time inflexible contract requires the firm to specify not only how many units it will purchase but also the timing of the purchase a time flexible contract allows the firm to specify the purchase amount over a given period of time without specifying the exact time of purchase other than time flexibility the suppliers may offer quantity flexibility to the firm as well i e purchase quantities could be within a prespecified quantity window finally risk sharing features can be incorporated in the contract in terms of the purchase price that the firm eventually pays to a supplier within a prespecified price window the firm pays the realized price but outside of it the firm shares in an agreed way added costs or benefits given the structure of a supply contract we study the firm s decision when to purchase and how many units in each purchase such that the expected net present value of the purchase cost plus inventory holding cost is minimized we discuss optimal purchasing strategies for both time flexible and time inflexible contracts with risk sharing features other interesting results include the analysis of two supplier sourcing environments and the exploitation of quantity flexibility in such contracts our discussion illustrates how time flexibility quantity flexibility supplier selection and risk sharing when carefully exercised can effectively reduce the sourcing cost in environments of price uncertainty

non additive beliefs and strategic equilibria abstract this paper studies n player games where players beliefs about their opponents behaviour are modelled as non additive probabilities the concept of an equilibrium under uncertainty which is introduced in this paper extends the equilibrium notion of dow and werlang 1994 j econom theory 64 305 324 to n player games in strategic form existence of such an equilibrium is demonstrated under usual conditions for low degrees of ambiguity equilibria under uncertainty approximate nash equilibria at the other extreme with a low degree of confidence maximin equilibria appear finally robustness against a lack of confidence may be viewed as a refinement for nash equilibria journal of economic literature classification numbers c72 d81

public goods game with ambiguous threshold abstract various collective action problems can be described as a discrete public goods game with a threshold in this game players may be reluctant to contribute to the provision of public goods when the threshold value is uncertain we derive equilibria when players face ambiguity i e knightian uncertainty on the threshold value by using choquet expected utility furthermore we show that in a class of neo additive capacities an increase in ambiguity decreases the equilibrium maximal number of contributors irrespective of players ambiguity attitudes this contrasts to what mcbride 2006 shows when the probability distribution is known

on nonparametric supply response analysis in this paper we explore the usefulness of nonparametric methods in the investigation of production behavior and the estimation of price elasticities of output supply and input demand functions the approach can handle the situation where some data points are not consistent with production theory the method is illustrated by estimating supply demand elasticities of outputs and inputs in u s agriculture

pricing options under generalized garch and stochastic volatility processes in this paper we develop an efficient lattice algorithm to price european and american options under discrete time garch processes we show that this algorithm is easily extended to price options under generalized garch processes with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases we establish one unifying algorithm that can price options under almost all existing garch specifications as well as under a large family of bivariate diffusions in which volatility follows its own perhaps correlated process through an equilibrium argument duan 1995 shows that options can be priced when the dynamics for the price of the underlying instrument follows a general autoregressive conditionally heteroskedastic garch process the theory of pricing under such processes is now well understood however the design of efficient numerical procedures for pricing them is lacking most applications resort to large sample simulation methods with a variety of variance reduction techniques the complexity of pricing arises from the massive path dependence inherent in garch models this path dependence causes typical lattice based procedures to grow exponentially in the number of time increments the lack of efficient numerical schemes hinders empirical tests among the wide array of competing garch models most tests of garch models limit themselves to the use of high frequency data on spot assets with little attention placed on the information content of options 1

valuing modularity as a real option we provide a general valuation approach for capital budgeting decisions involving the modularization in the design of a system within the framework developed by baldwin and clark baldwin c y k b clark 2000 design rules the power of modularity mit press cambridge ma we implement a valuation approach using a numerical procedure based on the least squares monte carlo method proposed by longstaff and schwartz longstaff f a e s schwartz 2001 valuing american options by simulation a simple least squares approach rev financial stud 14 1 113 147 the approach is accurate general and flexible

disappointment in decision making under uncertainty decision analysis requires that two equally desirable consequences should have the same utility and vice versa most analyses of financial decision making presume that two consequences with the same dollar outcome will be equally preferred however winning the top prize of 10 000 in a lottery may leave one much happier than receiving 10 000 as the lowest prize in a lottery this paper explores the implications of disappointment a psychological reaction caused by comparing the actual outcome of a lottery to one s prior expectations for decision making under uncertainty explicit recognition that decision makers may be paying a premium to avoid potential disappointment provides an interpretation for some known behavioral paradoxes and suggests that decision makers may be sensitive to the manner in which a lottery is resolved the concept of disappointment is integrated into utility theory in a prescriptive model

an economic model for evaluating mining and manufacturing ventures with output yield uncertainty this paper develops an operational risk management model for evaluating production efforts in manufacturing and mining industries where the resource to be exploited is nonhomogenous using acontingent claims methodology now commonly encountered in financial applications we formulate a production control model in an environment characterized bymarket andprocess uncertainty in our analysis market risk is depicted by the output price while process uncertainty is captured by the random variability inherent in the output s yield in this light adjustments to the rate of production are viewed as a sequence of nested real options affording operating flexibility we account for an optimal sequence of production adjustments over a preestablished production horizon by taking the production rate as an adapted positive real valued process accordingly techniques of stochastic control theory and contingent claims analysis cca are employed to ensure value maximizing production policies are rendered in a manner consistent with an equilibrium price structure

jump diffusion option valuation in discrete time we develop a simple discrete time model to value options when the underlying process follows a jump diffusion process multivariate jumps are superimposed on the binomial model of cox ross and rubinstein 1979 to obtain a model with a limiting jump diffusion process this model incorporates the early exercise feature of american options as well as arbitrary jump distributions it yields an efficient computational procedure that can be implemented in practice as an application of the model we illustrate some characteristics of the early exercise boundary of american options with certain types of jump distributions jump diffusion processes are popular in option valuation models these processes were incorporated by merton 1976 into the theory of option valuation and constitute an important alternative to the lognormal diffusion process assumed in the black and scholes 1973 model in this paper we develop a tractable discrete time model for valuing options with these processes many authors have suggested that incorporating jumps in option valuation models may explain some of the large empirical biases exhibited by the black scholes model 1 however in many cases closed form solutions for valuing options are not available for example this is true when there is a positive probability of early exercise when the jump distribution is neither lognormal nor discrete or when the option is based on the term structure of interest rates see ahn and thompson 1988 and jarrow and madan 1991 in these important cases the model developed in this paper can be used to value options another aim of this paper is to provide a model which relies on only simple mathematics to price options with jump diffusion processes it is hoped that the key economic relationships underlying jump diffusion models are transparent in this model we provide enough details to make the procedure readily accessible

climate change catastrophes and insuring decisions a study in the presence of ambiguity abstract this paper attempts to study how individuals respond to the availability of an insurance that would safeguard their interests if a climate change catastrophe occurred if such an insurance is available to them do individuals insure themselves sufficiently further the study investigates if information regarding the past occurrence of the catastrophic event leads to an increase in insurance subscriptions and or the emergence of a lemons market finally policy implications are investigated can an indirect intervention in the form of a nudge ensure a better outcome

ambiguity optimism and pessimism in adverse selection models we investigate the effect of ambiguity and ambiguity attitude on the shape and properties of the optimal contract in an adverse selection model with a continuum of types using the parametric model of ambiguity and ambiguity aversion called the neo additive model chateauneuf eichberger and grant 2007 we show that it necessarily features efficiency and a jump at the top and pooling at the bottom of the distribution conditional on the degree of ambiguity the pooling section may or may not be supplemented by a separating section as a result ambiguity adversely affects the principal s ability to solve the adverse selection problem and therefore the least efficient types benefit from ambiguity with respect to risk conversely ambiguity is detrimental to the most efficient types this is confirmed in the comparative statics section

ambiguity and uncertainty in ellsberg and shackle this paper argues that the similarities between ellsberg s and shackle s frameworks for discussing the limits of the probabilistic approach to decision theory are more important than usually admitted the paper discusses the grounds on which the ambiguity surrounding the decision maker in ellsberg s urn experiments can be deemed analogous to the uncertainty faced by shackle s entrepreneur taking crucial decisions the two authors insights are assessed and special attention is paid to the criteria for decision under uncertainty they put forward the paper establishes a link between ellsberg s and shackle s perspectives and the non additive probability approach of gilboa and schmeidler an approach that offers an alternative to standard probability calculus which can be of use to analyse both ambiguity and uncertainty the comparison between ellsberg and shackle draws on an interpretation of keynes s treatise on probability emphasising keynes s rejection of both well defined probability functions and maximisation as a guide to human conduct it is shown that keynes s viewpoint implies a reconsideration of the boundaries of probability theory that is in the same vein of ellsberg s and shackle s concern in the years of the consolidation of savage s new probabilistic mainstream copyright the author 2009 published by oxford university press on behalf of the cambridge political economy society all rights reserved oxford university press

pricing american style securities using simulation abstract we develop a simulation algorithm for estimating the prices of american style securities i e securities with opportunities for early exercise our algorithm provides both point estimates and error bounds for the true security price it generates two estimates one biased high and one biased low both asymptotically unbiased and converging to the true price combining the two estimators yields a confidence interval for the true price the proposed algorithm is especially attractive compared with lattice and finite difference methods when there are multiple state variables and a small number of exercise opportunities preliminary computational evidence is given

optimists pessimists and the precautionary principle the precautionary principle has emerged as a leading guide to public decision making about environmental risks under irreversibility and uncertainty in this paper we adopt a two period model with irreversibility and agents differentiated by their degree of optimism to characterize the conditions under which the precautionary principle applies we show in particular that it is more often applied if the decision maker has an intermediate optimism index if scientific research is more effective at reducing uncertainty and if the same decision maker makes the decisions for both periods moreover we show that socially optimal decisions lead to apply the precautionary principle more often than an elected decision maker does

options on the minimum or the maximum of two risky assets analysis and applications this paper provides analytical formulas for european put and call options on the minimum or the maximum of two risky assets the properties of these formulas are discussed in detail options on the minimum or the maximum of two risky assets are useful to price a wide variety of contingent claims of interest to financial economists applications discussed in this paper include the valuation of foreign currency debt option bonds compensation plans risk sharing contracts secured debt and growth opportunities involving mutually exclusive investments

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

pricing multivariate contingent claims using estimated risk neutral density functions abstract many asset price series exhibit time varying volatility jumps and other features inconsistent with assumptions about the underlying price process made by standard multivariate contingent claims mvcc pricing models this article develops an interpolative technique for pricing mvccs flexible nls pricing that involves the estimation of a flexible multivariate risk neutral density function implied by existing asset prices as an application the flexible nls pricing technique is used to value several bivariate contingent claims dependent on foreign exchange rates in 1993 and 1994 the bivariate flexible risk neutral density function more accurately prices existing options than the bivariate log normal density implied by a multivariate geometric brownian motion in addition the bivariate contingent claims analyzed have substantially different prices using the two density functions suggesting flexible nls pricing may improve accuracy over standard methods

monte carlo valuation of american options through computation of the optimal exercise frontier this paper introduces a monte carlo simulation method for pricing multidimensional american options based on the computation of the optimal exercise frontier we consider bermudan options that can be exercised at a finite number of times and compute the optimal exercise frontier recursively we show that for every date of possible exercise any single point of the optimal exercise frontier is a fixed point of a simple algorithm once the frontier is computed we use plain vanilla monte carlo simulation to price the option and obtain a low biased estimator we illustrate the method with applications to several types of options

short term variations and long term dynamics in commodity prices in this article we develop a two factor model of commodity prices that allows meanreversion in short term prices and uncertainty in the equilibrium level to which prices revert although these two factors are not directly observable they may be estimated from spot and futures prices intuitively movements in prices for long maturity futures contracts provide information about the equilibrium price level and differences between the prices for the short and long term contracts provide information about short term variations in prices we show that although this model does not explicitly consider changes in convenience yields over time this short term long term model is equivalent to the stochastic convenience yield model developed in gibson and schwartz 1990 we estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil linked assets to demonstrate its use and some of its advantages over the gibson schwartz model

simple binomial processes as diffusion approximations in financial models a binomial approximation to a diffusion is defined as computationally simple if the number of nodes grows at most linearly in the number of time intervals it is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models the convergence of the sequence of bond and european option prices from these processes to the corresponding values in the diffusion limit is also demonstrated numerical examples from the constant elasticity of variance stock price and the cox ingersoll and ross 1985 discount bond price are provided article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

generalised soft binomial american real option pricing model fuzzy stochastic approach abstract the stochastic discrete binomial models and continuous models are usually applied in option valuation valuation of the real american options is solved usually by the numerical procedures therefore binomial model is suitable approach for appraising the options of american type however there is not in several situations especially in real option methodology application at to disposal input data of required quality two aspects of input data uncertainty should be distinguished risk stochastic and vagueness fuzzy traditionally input data are in a form of real crisp numbers or crisp stochastic distribution function therefore hybrid models combination of risk and vagueness could be useful approach in option valuation generalised hybrid fuzzy stochastic binomial american real option model under fuzzy numbers t numbers and decomposition principle is proposed and described input data up index down index growth rate initial underlying asset price exercise price and risk free rate are in a form of fuzzy numbers and result possibility expected option value is also determined vaguely as a fuzzy set illustrative example of equity valuation as an american real call option is presented

convergence from discrete to continuous time contingent claims prices this article generalizes the cox ross and rubinstein 1979 binomial option pricing model and establishes a convergence from discrete time multivariate multinomial models to continuous time multidimensional diffusion models for contigent claims prices the key to the approach is to approximate the n dimensional diffusion price process by a sequence of n variate n 1 nomial processes it is shown that contingent claims prices and dynamic replicating portfolio strategies derived from the discrete time models converge to their corresponding continuous time limits article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

valuation of product mix flexibility using real options abstract flexibility in manufacturing operations is becoming increasingly more important to industrial firms due to e g increasing market demand volatility internationalisation of markets and competition and shorter product life cycles defining measuring and evaluating manufacturing flexibility have not been straightforward neither in theory nor in practice the use of real options has shown to be an accessible approach for the valuation of certain types of flexibility when using real options for capital budgeting purposes it is possible to take flexibility options into account in the valuation process in this paper we use real options to evaluate one specific type of manufacturing flexibility i e product mix flexibility we provide both theoretical and practical perspectives based on a real case the main interest of the company under study is to evaluate product mix flexibility with respect to capacity set ups level of automation and multi functionality of resources the case involves multiple products and demand uncertainty wherefore product demands are used as the underlying asset in the real options models thus the contribution of this paper concerns the combination of real case multiple products capacity constraints and set up costs the results of the analysis show that i the value of flexibility decreases when demand volatility increases ii flexible resources add substantial value as compared to dedicated resources and iii the flexibility value of marginal capacity decreases with increasing levels of capacity

nonparametric estimation of crop yield distributions implications for rating group risk crop insurance contracts we use nonparametric density estimation procedures to evaluate county level crop yield distributions implications for rating area yield crop insurance contracts are discussed the procedures developed are used to measure yield risk and calculate insurance premium rates for wheat and barley in the 1995 96 group risk program

the public accounting industry production function abstract a translog function is specified to represent the relation between revenue and human resource inputs in public accounting firms estimation of the model using a balanced panel of annual data for 64 large cpa firms for the period 1995 1999 indicates that increasing returns to scale prevail in the public accounting industry justifying recent merger and acquisition activities among accounting firms average marginal revenue product of partners increased monotonically from 1995 to 1998 decreased slightly in 1999 and was about nine times that of other professionals during 1995 1999 the public accounting industry exhibited continuing improvement in productivity over the 5 years

ambiguity social opinion and the use of common property resources in this paper we argue that ambiguity combined with social opinion formation can be used as the foundation of a game theoretic equilibrium concept that transcends the standard nash equilibrium concept applied to a model of the tragedy of the commons our approach sheds light on the international environmental crisis and the relevant ongoing international negotiations we conclude that social opinion formation in most cases has a significant impact on equilibrium common property resource usage

risk uncertainty and option exercise many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty motivated by experimental evidence such as the ellsberg paradox we follow knight 1921 and distinguish risk from uncertainty to capture this distinction we adopt the multiple priors utility model we show that the impact of ambiguity on the option exercise decision depends on the relative degrees of ambiguity about continuation payoffs and termination payoffs consequently ambiguity may accelerate or delay option exercise we apply our results to investment and exit problems and show that the myopic npv rule can be optimal for an agent having an extremely high degree of ambiguity aversion

abandonment of natural gas production and investment in carbon storage abstract long term mitigation scenarios rely heavily on carbon capture and storage ccs for achieving ambitious climate change targets the amount of co 2 storage in these scenarios depends on the co 2 price and exogenously determined availability and costs of storage capacity we analyze investment in ccs in more detail by taking the opportunity costs of co 2 storage into account assuming that co 2 injection and resource extraction are mutually exclusive using real option valuation we study the impact of i correlation between gas and co 2 prices ii volatility of co 2 prices and iii regulatory deadlines on the value of the option to invest in ccs we find that the value of the option to exchange gas production for co 2 injection is decreasing in the correlation of gas and co 2 prices but increasing in the volatility of co 2 prices and in shorter regulatory deadlines for removal of gas production facilities this implies that next to consistent and high pricing of co 2 extending the deadline for removal of gas production facilities could increase the incentive to invest in co 2 storage in mature gas fields we argue that considering these dynamics in mitigation scenarios could lead to more realistic projections of ccs application

the quality delivery option in treasury bond futures contracts this paper uses three methods to estimate quality option values for cbot treasury bond futures contracts it presents evidence regarding 1 payoffs from exercising this option at delivery 2 estimates from a t bond futures pricing model that incorporates this option and 3 estimates obtained from an exchange option pricing formula the results indicate that this option is worth considerably less than reported by kane and marcus 1986a for example payoffs obtained by switching from the bond cheapest to deliver three months prior to delivery to the one cheapest at time of delivery average less than 0 30 percentage points of par

moderate stake variations for risk and uncertainty gains and losses methodological implications for comparative studies risk attitudes are known to be sensitive to large stake variations however little is known on the sensitivity to moderate variations in stakes this is important for studies that want to compare risk attitudes between countries or over time i find that variations of 20 affect only utility while larger variations may affect also probability weighting surprisingly the effect on weighting functions is larger for losses than for gains it is also more pronounced for risk than for uncertainty

asset pricing in a lucas fruit tree economy with the best and worst in mind this paper studies a lucas 1978 fruit tree economy under the assumption that the agents are choquet expected utility ceu rather than standard expected utility decision makers more speci cally the agents non additive beliefs about the economy s dividend payment process are modelled as neo additive capacities so that the agents decision behavior emphasizes the best respectively worst possible economic scenarios in contrast to existing models of lucas type economies with ambiguity averse agents epstein and wang 1994 which ensure dynamic consistency through heavy restrictions on admissible ambiguity attitudes my ap

precautionary principle as a rule of choice with optimism on windfall gains and pessimism on catastrophic losses abstract the paper investigates a decision making process involving both risk and ambiguity differently from existing papers basili m chateauneuf a fontini f 2005 choices under ambiguity with familiar and unfamiliar outcomes theory and decision 58 195 207 chichilnisky g 2000 axiomatic approach to choice under uncertainty with catastrophic risks resources and energy economics 22 221 231 chichilnisky g 2002 in el shaarawi a h piegorsch w w eds catastropic risks encyclopedia of environmetrics vol 1 john wiley sons ltd chichester uk pp 274 279 we assume that in a choquet expected utility framework the decision maker is pessimistic with respect to unfamiliar catastrophic losses optimistic with respect to unfamiliar windfall gains and ambiguity neutral with respect to the familiar world a representation of the decision maker s choice is obtained that mimics the restricted bayes hurwicz criterion in this way a characterization of the precautionary principle is introduced for decision making processes under ambiguity with catastrophic losses and or windfall gains

a bias aggregation theorem abstract in a market where some traders are rational maximize expected utility and others are systematically biased deviate from expected utility due to some bias parameter do equilibrium prices necessarily depend on focusing on the case where there is an aggregate and systematic bias in the population we show that market prices can still be unbiased hence we establish that systematically biased agents do not necessarily imply biased market prices

a note on the pricing of commodity linked bonds the owner of a commodity linked bond can exchange the bond s face value for the maturity value of a commodity in an interesting application of optionpricing theory schwartz 7 provides a general framework for valuing commodity linked bonds this very general valuation framework allows for commodity price risk default risk and interest rate risk along with interest payments and dividends a partial differential equation and its associated boundary condition are derived but not solved schwartz states that the solution to the general problem is difficult even by numerical methods in order to find closed form solutions schwartz considers commodity price risk in conjunction with default risk or interest rate risk but not both this note presents a closed form solution for the value of a commodity linked bond when all three types of risk are present

option pricing in a multi asset complete market economy this paper extends the seminal cox ross rubinstein 1979 crr hereafter binomial model to multiple assets it differs from previous models in that it is derived under the complete market environment specified by duffie and huang 1985 and he 1990 the complete market assumption requires the number of states to grow linearly with the number of assets however the number of correlations grows at a faster rate causing the crr model to be indirectly extendable we solve such a problem by recognizing that the fast growing correlation number is matched by the number of the angles of the edges of a hypercube spanned by the risky assets as a result we derive a solution that allows the number of equations to equal the number of risky assets and the riskless bond the resulting tree structure hence provides the same intuition of pricing and hedging contingent claims as that provided by the crr model finally the proposed model is not only as easy to implement as the one dimensional crr model but also it is more memory efficient than the existing multi factor lattice models

the rich domain of uncertainty source functions and their experimental implementation we often deal with uncertain events for which no probabilities are known several normative models have been proposed descriptive studies have usually been qualitative or they estimated ambiguity aversion through one single number this paper introduces the source method a tractable method for quantitatively analyzing uncertainty empirically the theoretical key is the distinction between different sources of uncertainty within which subjective choice based probabilities can still be defined source functions convert those subjective probabilities into willingness to bet we apply our method in an experiment where we do not commit to particular ambiguity attitudes but let the data speak

clustered pricing in the corporate loan market theory and empirical evidence abstract existing theories explaining security price clustering as well as clustering in the retail deposit and mortgage markets are incompatible with the clustering in the corporate loan market we develop a new theoretical model that the attitude of the lender toward the uncertainty about the quality of the borrower leads to the clustering of spreads our empirical results support our theoretical model and we find that clustering increases with the degree of uncertainty between the lender and the borrower in contrast clustering is less likely when the uncertainty about the quality of the borrower has been reduced through repeated access and through prior interactions of the lender and the borrower

dynamic r d investment policies this paper examines dynamic r d investment policies and the valuation of r d programs in a contingent claims framework we incorporate the following characteristics of r d programs into our model learning by doing collateral learning between different projects in the program interaction between project cash flows periodic reevaluations of the program different intensities of investment capital rationing constraints and competition we show that a firm may invest in multiple projects even if only one can be implemented after development is complete furthermore the firm may significantly alter its funding policy over time for example it may simultaneously develop multiple projects for a period of time then focus on a lead project and potentially resume funding of a backup project if the lead project fails to deliver on its early promise we show how a firm can forecast expected r d spending through time for an optimally executed r d program while project volatility plays an important role in determining r d program value we find that for high volatility projects the optimal investment policy is not very sensitive to changes in or misestimation of volatility in considering whether to accelerate development of a project a firm should balance the adverse effects of increased costs and the loss of investment flexibility against the positive effects of rapid uncertainty resolution and accelerated cash flows in the presence of a budget constraint that prevents the firm from simultaneously accelerating projects and developing projects in parallel we find that if one project significantly dominates another early in the development stage the option to accelerate the lead project is likely to be more valuable than the option to exchange projects thus the backup project would be shelved in order to commit extra resources to development of the lead project finally competition from other firms leads to more parallel investment in the early development stages of projects less parallel investment in the latter stages of development and lower overall investment

a more robust definition of subjective probability the goal of choice theoretic derivations of subjective probability is to separate a decisionmaker s underlying beliefs subjective probabilities of events from their preferences attitudes toward risk classical derivations have all relied upon some form of the marschak samuelson independence axiom or the savage sure thing principle which imply that preferences over lotteries conform to the expected utility hypothesis this paper presents a choice theoretic derivation of subjective probability in a savage type setting of purely subjective uncertainty which neither assumes nor implies that the decisionmaker s preferences over lotteries necessarily conform to the expected utility hypothesis copyright 1992 by the econometric society

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

numerical valuation of high dimensional multivariate european securities we consider the problem of pricing a contingent claim whose payoff depends on several sources of uncertainty using classical assumptions from the arbitrage pricing theory the theoretical price can be computed as the discounted expected value of future cash flows under the modified risk neutral information process although analytical solutions have been developed elsewhere for a few particular option pricing problems computing the arbitrage prices of securities under several sources of uncertainty is still an open problem in many instances in this paper we present efficient numerical techniques based upon monte carlo simulation for pricing european contingent claims depending on an arbitrary number of risk sources we introduce in particular the method of quadratic resampling qr a new powerful error reduction technique for monte carlo simulation quadratic resampling can be efficiently combined with classical variance reduction methods such as importance sampling our numerical experiments show th

the spark spread and clean spark spread option based valuation of a power plant with multiple turbines abstract this paper offers a novel study of two key factors that affect the valuation of a natural gas fired power plant having multiple turbines carbon allowance prices and the ability to switch among turbines amid stricter environmental rules on co2 emissions a power plant operator needs to be able to judge how the purchase of carbon allowances affects the plant s expected value and whether the plant s value rises from switching among turbines this paper presents a model analysis of a spark spread and clean spark spread option based valuation of a power plant with multiple gas turbines using a bivariate and a tri variate lattice respectively results demonstrate that the purchase of co2 allowances lowers the plant s expected value conversely when operations of turbines are switched in response to price movements the plant s value increases this outcome has implications for plant management decisions when to switch among turbines and how the purchase of co2 allowances affects the plant s value

valuing an investment project using no arbitrage and the alpha maxmin criteria from knightian uncertainty to risk we consider a two period irreversible investment decision problem in which the firm can either invest in period 0 or in period 1 the firm is assumed to be able to specify a set of three scenarios or more but not a probability measure assuming the option to wait is valued with the no arbitrage principle when the firm makes use of the criteria maxmin we show the firm ends up with a known probability measure that assigns a positive probability to three or four scenarios only

a lattice approach for pricing of multivariate contingent claims abstract the lattice approach developed by boyle evnine and gibbs beg is hitherto one of the most appealing when it comes to pricing multivariate contingent claims the beg approach has however some problems two of the major ones being that the method can lead to negative jump probabilities and has a slow rate of convergence in this paper a lattice approach the nek approach is developed which avoids both of the aforementioned problems of the beg approach it is shown that the nek approach has a very fast rate of convergence the results are accurate enough for most needs with as few as ten time steps and the results are astonishingly accurate with twenty time steps moreover the nek approach is simple and easy to understand and also easy to implement the latter property follows from the fact that all jump probabilities are equal and that the formulas for the jump sizes are extremely simple

options on the maximum or the minimum of several assets using an intuitive approach that also provides new intuition concerning the black and scholes equation this paper extends the results of johnson and stulz to the pricing of options on the minimum or the maximum of several risky assets

numerical valuation of high dimensional multivariate american securities we consider the problem of pricing an american contingent claim whose payoff depends on several sources of uncertainty several efficient numerical lattice based techniques exist for pricing american securities depending on one or few up to three risk sources however these methods cannot be used for high dimensional problems since their memory requirement is exponential in the number of risk sources we present an efficient numerical technique that combines monte carlo simulation with a particular partitioning method of the underlying assets space which we call stratified state aggregation ssa using this technique we can compute accurate approximations of prices of american securities with an arbitrary number of underlying assets our numerical experiments show that the method is practical for pricing american claims depending on up to 400 risk sources

choice under uncertainty with the best and worst in mind neo additive capacities the concept of a non extreme outcome additive capacity neo additive capacity is introduced neo additive capacities model optimistic and pessimistic attitudes towards uncertainty as observed in many experimental studies moreover neo additive capacities can be applied easily in economic problems as we demonstrate by examples this paper provides an axiomatisation of choquet expected utility with neo capacities in a framework of purely subjective uncertainty

do students behave like real taxpayers in the lab evidence from a real effort tax compliance experiment we report on data from a real effort tax compliance experiment using three subject pools students who do not pay income tax company employees whose income is reported by their employer and self employed taxpayers who are responsible for filing and payment while compliance behavior is unaffected by changes in the level of or information about the audit probability higher fines increase compliance we find subject pool differences self assessed taxpayers are the most compliant while students are the least compliant through a simple framing manipulation we show that such differences are driven by norms of compliance from outside the lab

optimism and pessimism in games this paper considers the impact of ambiguity in strategic situations it extends the earlier literature by allowing for optimistic responses to ambiguity ambiguity is modelled by ceu preferences we propose a new solution concept for players who may express ambiguitypreference then we study comparative statics of changes in ambiguity attitude in games with strategic complements this gives a precise statement of the impact of ambiguity on economic behaviour

decision theory under ambiguity we review recent advances in the field of decision making under uncertainty or ambiguity we start with a presentation of the general approach to a decision problem under uncertainty as well as the standard bayesian treatment and issues with this treatment we present more general approaches choquet expected utility maximin expected utility smooth ambiguity and so forth that have been developed in the literature under the name of models of ambiguity sensitive preferences we draw a distinction between fully subjective models and models incorporating explicitly some information we review definitions and characterizations of ambiguity aversion in these models we mention the challenges posed by some of the models presented we end with a review of part of the experimental literature and applications of these models to economic settings

derivative pricing with wishart multivariate stochastic volatility this paper deals with the pricing of derivatives written on several underlying assets or factors satisfying a multivariate model with wishart stochastic volatility matrix this multivariate stochastic volatility model leads to a closed form solution for the conditional laplace transform and quasi explicit solutions for derivative prices written on more than one asset or underlying factor two examples are presented i a multiasset extension of the stochastic volatility model introduced by heston 1993 and ii a model for credit risk analysis that extends the model of merton 1974 to a framework with stochastic firm liability stochastic volatility and several firms a bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional laplace transform of the stock returns

comparing three ways to update choquet beliefs abstract we analyze three rules for updating neo additive capacities only for generalized bayesian updating is relative optimism the same for both updated and unconditional capacities for updates of the other two either the updated capacity is fully optimistic or fully pessimistic

a definition of uncertainty aversion a definition of uncertainty or ambiguity aversion is proposed it is argued that the definition is well suited to modelling within the savage as opposed to anscombe and aumann domain of acts the defined property of uncertainty aversion has intuitive empirical content behaves well in specific models of preference multiple priors and choquet expected utility and is tractable tractability is established through use of a novel notion of differentiability for utility functions called eventwise differentiability

destructive effects of constructive ambiguity in risky times unclear bailout policy underinvestment and calls for greater responsibility by bankers are some of the observations from the recent financial crisis the paper explains underinvestment as an inefficient equilibrium under ambiguous bailout policy agents suffer from a lack of information about the insolvency resolution methods the beliefs of bankers regarding whether an insolvent bank is liquidated may differ from those of depositors even if bankers and depositors possess absolutely symmetric information about the economy this disrupts the flow of funds through the banking channel if the investment climate is characterized by high aggregate risk the paper suggests policy implications aimed at a reduction of the anxiety of agents and at aligning their beliefs to restore efficiency

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

gains and structural effects of exploiting scale economies in norwegian dairy production abstract in this paper we present calculations of the economic gains in terms of reduced costs by exploiting scale economies in dairy production in norway and the effect this would have had on the number of farms we also explore whether or not optimal scale and unexploited scale economies change over time due to scale augmenting technical change the analysis is based on homothetic cost functions estimated by means of data for individual dairy farms for the period 1972 1996 for 1972 we find that by full exploitation of scale economies the costs could have been reduced by almost 40 while the number of farms would have been reduced by more than 85 the number of small farms has been substantially reduced in the period considered this fact combined with small scale augmenting technical change implies that the gains and structural effects of exploiting scale economies have decreased over time in 1996 costs could have been reduced by close to 30 by full exploitation of scale economies while the number of farms would have been reduced by slightly more than 70 thus both gains and structural effects are substantially less than in 1972 nevertheless the calculated gains for 1996 make almost 5 billion nok this corresponds almost exactly to the total public support to the dairy farms in 1996 the unexploited scale economies are largely due to the agricultural policy thus a substantial share of the same can be considered as part of the price the norwegian society has to pay for this policy in addition there are likely to be large hidden costs of this policy due in particular to the quota system and other direct production regulations they imply that technical innovations and other efficiency improving investments requiring increased production to be profitable are not carried out this is the more likely explanation for the extremely poor efficiency development in norwegian dairy production in the period studied

ambiguity made precise a comparative foundation the theory of subjective expected utility has been recently extended to allow ambiguity to matter for choice we propose a notion of absolute ambiguity aversion by building on a notion of comparative ambiguity aversion we characterize it for a preference model which encompasses some of the most popular models in the literature we next build on these ideas to provide a definition of unambiguous act and event and show the characterization of the latter as an illustration we consider the classical ellsberg 3 color urn problem and find that the notions developed in the paper provide intuitive answers journal of economic literature classification number d81

a lattice framework for option pricing with two state variables a procedure is developed for the valuation of options when there are two underlying state variables the approach involves an extension of the lattice binomial approach developed by cox ross and rubinstein to value options on a single asset details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables this procedure can be used to price any contingent claim whose payoff is a piece wise linear function of two underlying state variables provided these two variables have a bivariate lognormal distribution the accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for european options one advantage of the lattice approach is that it handles the early exercise feature of american options in addition it should be possible to use this approach to value a number of financial instruments that have been created in recent years

an algorithm for computing values of options on the maximum or minimum of several assets an approximate method is developed for computing the values of european options on the maximum or the minimum of several assets the method is very fast and is accurate for parameter ranges that are often of the most interest the approach casts the problem in terms of order statistics and can be used to handle situations where the initial asset prices the asset variances and the covariances are all unequal numerical values are given to illustrate the accuracy of the method

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

valuing operational flexibility under exchange rate risk in this paper we develop a stochastic dynamic programming formulation for the valuation of global manufacturing strategy options with switching costs overall we adopt a hierarchical approach first exchange rates are modeled as stochastic diffusion processes that exhibit intercountry correlation second the firm s global manufacturing strategy determines options for alternative product designs as well as supply chain network designs product options introduce international supply flexibility supply chain network options determine the firm s manufacturing flexibility through production capacity and supply chain network linkages third switching costs determine the cost of operational hedging i e the costs associated with reducing downside risks overall the firm maximizes its expected discounted global after tax value through the exercise of product and supply chain network options and or through exploitation of operational flexibility contingent on exchange rate realizations in this environment the firm must trade off fixed operating costs switching costs and the economic benefits derived from exploiting differentials in factor costs and corporate tax rates a multinomial approximation of correlated exchange rate processes is proposed that leads to a consistent and tractable lattice model for this compound option valuation problem we then demonstrate how the global manufacturing strategy planning model framework can be utilized to analyze financial and operational hedging strategies

discrete time valuation of american options with stochastic interest rates we develop an arbitrage free discrete time model to price american style claims for which domestic term structure risk foreign term structure risk and currency risk are important this model combines a discrete version of the heath jarrow and morton 1992 term structure model with the binomial model of cox ross and rubinstein 1979 it converges weakly to the continuous time models in amin and jarrow 1991 1992 the general model is path dependent and can be implemented with arbitrary volatility functions to value claims with maturity up to five years the model is illustrated with applications to long dated american currency warrants and a cross rate swap from the quanto class article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies