real option valuation of power transmission investments by stochastic simulation abstract network expansions in power markets usually lead to investment decisions subject to substantial irreversibility and uncertainty hence investors need valuing the flexibility to change decisions as uncertainty unfolds progressively real option analysis is an advanced valuation technique that enables planners to take advantage of market opportunities while preventing or mitigating losses if future conditions evolve unfavorably in the past many approaches for valuing real options have been developed however applying these methods to value transmission projects is often inappropriate as revenue cash flows are path dependent and affected by a myriad of uncertain variables in this work a valuation technique based on stochastic simulation and recursive dynamic programming called least square monte carlo is applied to properly value the deferral option in a transmission investment the effect of option s maturity the initial outlay and the capital cost upon the value of the postponement option is investigated finally sensitivity analysis determines optimal decision regions to execute postpone or reject the investment projects

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

macro economic stability and policy rules in a two sector model of an open economy purchasing power parity exchange rate rules are often used in open economies to stabilize the demand for exports and domestic output r dornbusch 1982 shows tha t such rules may increase the variability of output via the supply si de by destabilizing the price of imported intermediate goods here a two sector wage spillover model is employed to demonstrate that this result is more likely because although exchange rate indexation woul d decrease the variability of output in the traded goods sector it m ay increase the variability of output in the nontraded goods sector a nd in the aggregate via the wage linkage between sectors

the forecasting approach to efficiency in the wool market this paper develops and presents estimates of a simultaneous equations model of the australian wool market the world s largest producer and exporter of fine wool the model contains functional relationships for unhedged inventories consumption of raw wool and the activities of both hedgers and speculators in wool futures expectations are represented by the adaptive hypothesis this model extends the work of leuthold and hartmann 1979 and leuthold and garcia 1988 by including expectations in the spot futures model and that of goss and giles 1986 by including composite equations for hedger speculators extending the expectations hypothesis to the consumption equation and by using the model to test the efficient markets hypothesis wald tests and likelihood ratio tests for unit roots in wool cash prices are conducted and in no case can the hypothesis of a single unit root be rejected estimation is by three stage least squares with correction for first order serial correlation the model provide

a unified approach to bermudan and barrier options under stochastic volatility models with jumps abstract many financial assets such as currencies commodities and equity stocks exhibit both jumps and stochastic volatility which are especially prominent in the market after the financial crisis some strategic decision making problems also involve american style options in this paper we develop a novel fast and accurate method for pricing american and barrier options in regime switching jump diffusion models by blending regime switching models and markov chain approximation techniques in the fourier domain we provide a unified approach to price bermudan american options and barrier options under general stochastic volatility models with jumps the models considered include heston hull white stein stein scott the 3 2 model and the recently proposed 4 2 model and the hypergeometric model with general jump amplitude distributions in the return process applications include the valuation of discretely monitored contracts as well as continuously monitored contracts common in the foreign exchange markets numerical results are provided to demonstrate the accuracy and efficiency of the proposed method

evaluating natural resource investments notwithstanding impressive advances in the theory of finance over the past 2 decades practical procedures for capital budgeting have evolved only slowly the standard technique which has remained unchanged in essentials since it was originally proposed see dean 1951 bierman and smidt 1960 derives from a simple adaptation of the fisher 1907 model of valuation under certainty under this technique expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk and the resulting present value is compared with the cost of the project this standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory but see brennan 1973 bogue and roll 1974 turnbull 1977 constantinides 1978 the inadequacy of this approach to capital budgeting is widely acknowledged although not widely discussed its obvious deficiency is its the evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices it is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing and abandoning them the approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern

generalized analytical upper bounds for american option prices this paper generalizes and tightens chen and yeh s 2002 analytical upper bounds for american options under stochastic interest rates stochastic volatility and jumps where american option prices are difficult to compute with accuracy we first generalize theorem 1 of chen and yeh 2002 and apply it to derive a tighter upper bound for american calls when the interest rate is greater than the dividend yield our upper bounds are not only tight but also converge to accurate american call option prices when the dividend yield or strike price is small or when volatility is large we then propose a general theorem that can be applied to derive upper bounds for american options whose payoffs depend on several risky assets as a demonstration we utilize our general theorem to derive upper bounds for american exchange options and american maximum options on two risky assets

pricing american options under stochastic volatility and stochastic interest rates we introduce a new analytical approach to price american options using an explicit and intuitive proxy for the exercise rule we derive tractable pricing formulas using a short maturity asymptotic expansion depending on model parameters this method can accurately price options with time to maturity up to several years the main advantage of our approach over existing methods lies in its straightforward extension to models with stochastic volatility and stochastic interest rates we exploit this advantage by providing an analysis of the impact of volatility mean reversion volatility of volatility and correlations on the american put price

evaluating income streams a decision analysis approach most important decision problems virtually all capital investiments and planning situations involve risky cash flows with uncertainties that are resolved over time in most of these problems the decision maker has access to financial markets and may borrow and lend to smooth consumption over time yet because of the difficulty of incorporating these borrowing and lending decisions into the evaluation models these opportunities are rarely explicitly modeled in decision and risk analyses of these investments in this paper we study the errors induced by failing to account for these borrowing and lending decisions and we develop extensions to the standard decision and risk analysis procedures that given certain market and preference assumptions take these borrowing and lending opportunities into account without overburdening the evaluation models

the american put option valued analytically an analytic solution to the american put problem is derived herein the hedge ratio and other derivatives of the solution are presented the formula derived implies an exact duplicating portfolio for the american put consisting of discount bonds and stock sold short the formula is extended to consider put options on stocks paying cash dividends a polynomial expression is developed for evaluating these formulae values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated tabulated and compared with values derived by numerical integration and binomial approximation as with european options evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods finally applications of this american put solution are discussed

exchange rate rules and macroeconomic stability this paper discusses exchange rate rules in their role as macroeconomic instruments we abstract throughout from the trend part of exchange rate behaviour a crawling peg necessitated by differences in trend inflation and emphasise instead the implications of exchange rate rules in providing flexibility of real wages or in affecting the stability of output or prices

risk aversion and adaptive management insights from a multi armed bandit model of invasive species risk this article explores adaptive management am for decision making under environmental uncertainty in the context of targeting invasive species inspections of agricultural imports i find that risk aversion increases the relative value of am and can increase the rate of exploratory action while calls for am in natural resource management are common many analyses have identified modest gains from this approach i analytically and numerically examine the distribution of outcomes from am under risk neutrality and risk aversion the inspection decision is framed as a multi armed bandit problem and solved using the lagrangian decomposition method results show that even when expected gains are modest asymmetry in the distribution of outcomes has important implications notably am can serve to buffer against large losses even if the most likely outcome is a small loss

pricing american style derivatives with european call options we present a new approach to pricing american style derivatives that is applicable to any markovian setting i e not limited to geometric brownian motion for which european call option prices are readily available by approximating the value function with an appropriately chosen interpolation function the pricing of an american style derivative with arbitrary payoff function is converted to the pricing of a portfolio of european call options leading to analytical expressions for those cases where analytical european call prices are available e g the merton jump diffusion process furthermore in many settings the approach yields upper and lower analytical bounds that provably converge to the true option price we provide computational results to illustrate the convergence and accuracy of the resulting estimators

insights on the effect of land use choice the perpetual option on the best of two underlying assets abstract we consider the effect of land use choice on speculative land value and on development timing as reflected in the optimal hurdle ratio which triggers immediate development we find that land use choice i e multiple use zoning may add over 40 to land value under typical economic circumstances the conditions for optimal development of the land become markedly more difficult to achieve higher hurdle ratio required when the two land uses have similar values indeed a rational indecision result obtains in theory development will never occur when the two land use choices have equal value

a dynamic programming procedure for pricing american style asian options pricing european style asian options based on the arithmetic average under the black and scholes model involves estimating an integral a mathematical expectation for which no easily computable analytical solution is available pricing their american style counterparts which provide early exercise opportunities poses the additional difficulty of solving a dynamic optimization problem to determine the optimal exercise strategy a procedure for pricing american style asian options of the bermudan flavor based on dynamic programming combined with finite element piecewise polynomial approximation of the value function is developed here a convergence proof is provided numerical experiments illustrate the consistency and efficiency of the procedure theoretical properties of the value function and of the optimal exercise strategy are also established

monte carlo methods for security pricing the monte carlo approach has proved to be a valuable and flexible computational tool in modern finance this paper discusses some of the recent applications of the monte carlo method to security pricing problems with emphasis on improvements in efficiency we first review some variance reduction methods that have proved useful in finance then we describe the use of deterministic low discrepancy sequences also known as quasi monte carlo methods for the valuation of complex derivative securities we summarize some recent applications of the monte carlo method to the estimation of partial derivatives or risk sensitivities and to the valuation of american options we conclude by mentioning other applications

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

introduction to the stability of rational expectations equilibrium abstract this paper surveys the literature which examines the stability of the expectations that agents are assumed to have in a rational expectations equilibrium ree this issue is more complex than the usual statistical estimation problem because the relationship between observable variables and payoff relevant variables is endogenous one approach taken in the literature yields convergence to a ree but requires agents to have extensive knowledge about the structure and dynamics of the model that prevails while they learn a second approach does not assume that agents have correctly specified likelihood functions and finds that ree may not be stable

valuing flexibility as a complex option this paper develops an approach for valuing flexible production systems using contingent claims pricing demand curves for our model s underlying assets output products may be downward sloping in contrast with the standard option pricing assumption also our marginal production exercise costs may be increasing in addition we allow for multiple products and a production capacity constraint these elements of the model result in complex exercise decisions for the contingent claims which comprise the production system s value we illustrate our approach by valuing a flexible system that produces two products which have profit margin functions with stochastic parameters

valuation of adjustable rate mortgages with automatic stretching maturity abstract in hong kong 35 of residential mortgage loans are adjustable rate mortgages with variable tenor vrt that is with a change in interest rates the loan adjusts its maturity and principal payment such that the monthly installment remains the same in other words instead of bearing a volatility on monthly payments as in a fixed tenor variable payment vrp mortgage vrt mortgagors bear interest rate risk by bearing a tenor risk in this paper we analyze the valuation of this type of mortgages and the results are compared with the conventional vrp mortgages we find vrt loans are less expensive from a borrower s perspective than vrp loans but the difference between the loans becomes less significant if a tenor cap is added to the vrt loan

marketing information a competitive analysis selling information that is later used in decision making constitutes an increasingly important business in modern economies jensen jensen fred o 1991 information services congram friedman eds the ama handbook of marketing for the service industries chapter 22 ama com new york 423 443 information is sold under a large variety of forms industry reports consulting services database access and or professional opinions given by medical engineering accounting financial and legal professionals among others this paper is the first attempt in marketing to study competition in the rapidly emerging information sector specifically we are interested in answering the following questions 1 is competition fundamentally different when competing firms sell information rather than traditional goods and services and if yes why 2 what are the implications of such differences for decision makers marketers and regulators 3 can we explain some of the observed marketing strategies in the information industry as such the audience of the paper includes academics as well as professionals who are interested in understanding what is specific about competition in information markets familiarity with the practical implications of such differences and understanding of the mechanisms that drive them is essential for those who are faced with the problem of marketing information to answer the above research questions we build a simple game theoretic model that consists of two firms selling information to a population of consumers who are heterogeneous in their willingness to pay for the quality of information the most important features of the model are the following information products sold by the two firms are modeled as random draws from two normal distributions having equal mean the variances of these distributions and their correlatedness constitute the product attribute space which is assumed to be common knowledge consumers are interested in assessing the mean of the distributions and to do so they can buy the sample from any of the firms or they can buy both samples and combine them to obtain a more accurate estimate quality of information is linked to the accuracy of consumers estimate of the mean which in turn is influenced by the accuracy of each sample as well as by their correlatedness consumers utility depends on the quality of information they purchased on their inherent utility for quality taste and on the total price they paid to acquire information knowing consumer preferences firms simultaneously price their information products the main finding of the paper is that information markets face unique competitive structures in particular the qualitative nature of competition changes depending on basic product characteristics while traditional products and services compete either as substitutes or as complements in the relevant product attribute space information may be one or the other depending on its position within the same product attribute space said differently the nature of competition changes qualitatively with a continuous change in basic product attribute levels the intuition behind this finding is the following when purchasing information consumers facing important decisions may find it beneficial to purchase from several information sellers this is more likely to happen when the reliability of information is low and the sources of information are independent under such conditions information products tend to be complements and as a result competition between sellers is relatively mild in the opposite case when information is reliable and or sellers sources are highly correlated consumers are satisfied after consulting a single source in this case information products are substitutes and sellers tend to undercut one another s prices to induce consumers to choose their brand understanding this discontinuity in competitive structures has important implications for decision makers as very different strategies are optimal under different product characteristics under substitution traditional strategies to avoid competition e g differentiation are recommended when the competing products reliability is generally low they are complements firms are better off accommodating competition in fact we find that a firm may benefit from inviting a competitor finally our findings are also important for regulators of information markets as the literature on complementarity suggests price fixing agreements between firms offering complementary products may benefit firms as well as consumers

multinomial approximating models for options with k state variables contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive this article extends the literature on multinomial approximating models specifically new multinomial models are presented that include as special cases existing models the more general models are shown to be computationally more efficient

fast delta computations in the swap rate market model abstract we develop an efficient algorithm to implement the adjoint method that computes sensitivities of an interest rate derivative to different underlying rates in the co terminal swap rate market model the order of computation per step of the new method is shown to be proportional to the number of rates times the number of factors which is the same as the order in the libor market model

an object oriented framework for valuing shout options on high performance computer architectures abstract a shout option is a financial contract which allows the holder to change the payoff during the lifetime of the contract complex versions of these options are embedded in financial products which offer various types of maturity guarantees such as segregated funds marketed by canadian insurance companies the value of these options can be determined by solving a collection of coupled partial differential equations in this work we develop an object oriented framework for valuing these contracts which is capable of exploiting modern high performance computer architectures we use this framework to study practical aspects of valuing and hedging these contracts

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

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

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

risk aversion information acquisition and technology adoption we use a dynamic programming model to study the impacts of risk aversion on information acquisition in technology adoption decisions in this model the benefit of the technology is uncertain and in each period the decision maker dm may adopt the technology reject the technology or pay to acquire a signal about the benefit of the technology the dynamic programming state variables are the dm s wealth and a probability distribution that describes the dm s beliefs about the benefit of the technology these distributions are updated over time using bayes rule if the signal generating process satisfies the monotone likelihood ratio property and the dm is risk neutral the value functions and policies satisfy natural monotonicity properties a likelihood ratio improvement in the distribution on benefits leads to an increase in the value function and moves the dm away from rejection and toward adoption with risk aversion the value functions now representing expected utilities will be monotonic but

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

practical policy iteration generic methods for obtaining rapid and tight bounds for bermudan exotic derivatives using monte carlo simulation abstract we introduce a set of improvements which allow the calculation of very tight lower bounds for bermudan derivatives using monte carlo simulation these tight lower bounds can be computed quickly and with minimal hand crafting our focus is on accelerating policy iteration to the point where it can be used in similar computation times to the basic least squares approach but in doing so introduce a number of improvements which can be applied to both the least squares approach and the calculation of upper bounds using the andersen broadie method the enhancements to the least squares method improve both accuracy and efficiency results are provided for the displaced diffusion libor market model demonstrating that our practical policy iteration algorithm can be used to obtain tight lower bounds for cancellable cms steepener snowball and vanilla swaps in similar times to the basic least squares method

real option value and random jumps application of a simulation model this article studies how sensitive real option valuations are to incorrect assumptions about the stochastic process followed by the state variables we design a valuation model which combines monte carlo simulation and dynamic programming and provides an appropriate framework to evaluate the effect of estimation errors on both the value of real options and their critical frontier although the model is flexible enough to value american type options contingent on a wide range of stochastic processes we focus on the analysis of the effect of stochastic jumps we apply our model to the valuation of an investment in the car parts industry documented in previous literature our results clearly show that underestimating this type of jumps might lead to substantial misjudgements in a firm s decision making processes for instance it may lead to profitable projects being rejected when jump diffusion is low or negative expanded net present value projects being accepted

pricing and exercising american options an asymptotic expansion approach abstract this paper proposes and implements a novel asymptotic expansion approach for pricing discretely monitored american options and approximating their optimal early exercise boundaries under a generic class of multivariate derivative pricing models incorporating both stochastic volatility and levy driven jumps in asset return the price and the critical value can be expanded up to any arbitrary order around those under a simple constant volatility jump diffusion model the expansion terms are then efficiently implemented by exactly solving some backward inductions via closed form fourier transforms where a substantial extension of the hilbert transform method of feng and linetsky 2008a 2009 plays an important role the efficiency of our method is illustrated through some representative examples as applications we analyze the impacts of various model parameters on the optimal early exercise boundary compare the optimal early exercise boundaries under different models and propose a derivative proxy based method for practically exercising american options under models with stochastic volatility and jumps

extending quadrature methods to value multi asset and complex path dependent options abstract the exposition of the quadrature quad method andricopoulos widdicks duck and newton 2003 universal option valuation using quadrature methods journal of financial economics 67 447 471 see also corrigendum journal of financial economics 73 603 2004 is significantly extended to cover notably more complex and difficult problems in option valuations involving one or more underlyings trials comparing several techniques in the literature adapted from standard lattice grid and monte carlo methods to tackle particular types of problem show that quad offers far greater flexibility superior convergence and hence increased accuracy and considerably reduced computational times the speed advantage of quad means that even under the curse of dimensionality it is not necessary to resort to monte carlo methods certainly for options involving up to five underlying assets given the universality and flexibility of the method it should be the method of choice for pricing options involving multiple underlying assets in the presence of many features such as early exercise or path dependency

a moving boundary approach to american option pricing this paper describes a method to solve the free boundary problem that arises in the pricing of american options most numerical methods for american option pricing exploit the representation of the option price as the expected pay off under the risk neutral measure and calculate the price for a given time to expiration and stock price they do not solve the related free boundary problem explicitly the advantage of solving the free boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly our approach which we term the moving boundary approach is based on using a boundary guess and the value associated with the guess to construct an improved boundary it is also shown that on iteration the sequence of boundaries converge monotonically to the optimal exercise boundary examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented finally we compare runtimes and speeds with other methods that solve the free boundary problem and compute the optimal boundaries explicitly like the front fixing method penalty method method based on the integral representations and the method by brennan and schwartz 1977 the valuation of american put options journal of finance 32 2 449 462

government institutional effects on the value of seasonal climate forecasts the impact of government institutions on the value of improved climate forecasts is examined results suggest that crop insurance and earned income tax credit have little effect on the expected change in after tax cash flows federal tax law has only a modest influence as expected the disaster program decreases the value of improved climate forecasts with no price changes the farm program lowers the value of the forecasts because of the acreage reduction provisions with at least some price decreases the farm program increases the value of climate forecasts here the price supports override the acreage reduction provisions

information and preference reversals in lotteries several approaches have been proposed for evaluating information in expected utility theory among the most popular approaches are the expected utility increase the selling price and the buying price while the expected utility increase and the selling price always agree in ranking information alternatives hazen and sounderpandian 11 have demonstrated that the buying price may not always agree with the other two that is in some cases where the expected utility increase would value information a more highly than information b the buying price may reverse these preferences in this paper we discuss the conditions under which all these approaches agree in a generic decision environment where the decision maker may choose to acquire arbitrary information bundles

convergence and biases of monte carlo estimates of american option prices using a parametric exercise rule abstract this paper presents an algorithm for pricing american options using monte carlo simulation the method is based on using a parametric representation of the early exercise decision it is shown that as long as this parametric representation subsumes all relevant stopping times error bounds can be constructed using two different estimates one which is biased low and one which is biased high both are consistent and asymptotically unbiased estimators of the true option value results for high dimensional american options confirm the viability of the numerical procedure the convergence results of the paper shed light into the biases present in other algorithms proposed in the literature

pricing foreign currency options under stochastic interest rates abstract in this paper we build a general framework to price contingent claims on foreign currencies using the heath et al 1987 model of the term structure closed form solutions are obtained for european options on currencies and currency futures assuming that the volatility functions determining the term structure are deterministic as such this paper provides an example of a bond price process for both the domestic and foreign economies consistent with grabbe s 1983 formulation of the same problem

optimal strategies for selecting project portfolios using uncertain value estimates abstract practically all organizations seek to create value by selecting and executing portfolios of actions that consume resources typically the resulting value is uncertain and thus organizations must take decisions based on ex ante estimates about what this future value will be in this paper we show that the bayesian modeling of uncertainties in this selection problem serves to i increase the expected future value of the selected portfolio ii raise the expected number of selected actions that belong to the optimal portfolio ex post and iii eliminate the expected gap between the realized ex post portfolio value and the estimated ex ante portfolio value we also propose a new project performance measure defined as the probability that a given action belongs to the optimal portfolio finally we provide analytic results to determine which actions should be re evaluated to obtain more accurate value estimates before portfolio selection in particular we show that the optimal targeting of such re evaluations can yield a much higher portfolio value in return for the total resources that are spent on the execution of actions and the acquisition of value estimates

the determinants of information value synthesizing some general results this paper identifies the determinants of information value and synthesizes some general results concerning their effects while some attributes of an information system exhibit a consistent directional effect on information value attributes of the decision setting and decision maker do not

rejection of unbiasedness is not rejection of market efficiency reply to gilbert 1986 rejection of unbiasedness is not rejection of market efficiency reply to gilbert applied economics vol 18 no 11 pp 1167 1178

evaluating natural resource projects with embedded options and limited reserves this study proposes a dynamic option simulation dos approach to evaluate natural resource investment projects that contain several embedded options and limited reserves to construct a practical pricing model dos combines simulation and dynamic programming techniques that can value natural resource investments with multi variable early exercise various embedded options and finite reserve properties a copper mine project offers a demonstration the mine holder may temporarily close reopen and abandon the mine at specific times before the expiration date the mine holder may also accelerate mining speed to be optimal referred to as the acceleration option numerical analyses of the copper price and interest rate effects on the copper mine value suggest that dos can efficiently assess complex multiple variable american style real options problems

valuing forecast characteristics in a dynamic agricultural production system a dynamic programming model of east central illinois corn production is utilized to determine the value of seasonal climate forecasts results indicate that the value of climate forecasts is sensitive to economic conditions as well as forecast characteristics a trade off between forecast accuracy and lead time exists a less accurate forecast received earlier in the production process may be more valuable than a more accurate forecast received later additional characteristics evaluated include forecast periods of greatest importance prior knowledge assumptions and interactions between forecasting adjacent periods

valuing risky projects option pricing theory and decision analysis in the academic literature and professional practice there are a number of alternative and apparently competing methods for valuing risky projects in this paper we compare and contrast three different approaches risk adjusted discount rate analysis option pricing analysis and decision analysis focusing on the last two we show that in contrast to some of the claims made in the real options literature when both option pricing and decision analysis methods are correctly applied they must give consistent results we also explore ways in which option pricing and decision analysis methods can be profitably integrated in particular we show how option pricing techniques can be used to simplify decision analysis when some risks can be hedged by trading and conversely how decision analysis techniques can be used to extend option pricing techniques to problems with incomplete securities markets

optimal exercise policies and simulation based valuation for american asian options american asian options are average price options that allow early exercise in this paper we derive structural properties for the optimal exercise policy which are then used to develop an efficient numerical algorithm for pricing such options in particular we show that the optimal policy is a threshold policy the option should be exercised as soon as the average asset price reaches a characterized threshold which can be written as a function of the asset price at that time by exploiting this and other structural properties we are able to parameterize the exercise boundary and derive gradient estimators for the option payoff with respect to the parameters of the model these estimators are then incorporated into a simulation based algorithm to price american asian options computational experiments carried out indicate that the algorithm is very competitive with other recently proposed numerical algorithms

american options under stochastic volatility the problem of pricing an american option written on an underlying asset with constant price volatility has been studied extensively in literature real world data however demonstrate that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on european options we consider the problem of pricing american options under stochastic volatility which has had relatively much less attention from literature first we develop a transformation procedure to compute the optimal exercise policy and option price and provide theoretical guarantees for convergence second using this computational tool we explore a variety of questions that seek insights into the dependence of option prices exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility the speed and accuracy of the procedure are compared against existing methods as well

optimal oil production and the world supply of oil abstract we study the optimal oil extraction strategy and the value of an oil field using a multiple real option approach the numerical method is flexible enough to solve a model with several state variables to discuss the effect of risk aversion and to take into account uncertainty in the size of reserves optimal extraction in the baseline model is found to be volatile if the oil producer is risk averse production is more stable but spare capacity is much higher than what is typically observed we show that decisions are very sensitive to expectations on the equilibrium oil price using a mean reverting model of the oil price where the equilibrium price is also a random variable oil production was cut during the 2008 2009 crisis and we find that the cut in production was larger for opec members for countries facing a lower discount rate and for countries whose governments finances are less dependent on oil revenues however the net present value of a country s oil reserves would be increased significantly by 100 in the most extreme case if production was cut completely when prices fall below the country s threshold price if several producers were to adopt such strategies world oil prices would be higher but more stable

information technology and organization design locating decisions and information we study the impact of information technology it on the profitability of individual organization designs and on the relative profitability of different organization designs we develop models where organization design is defined by the location of investment decision authority we consider global and local investment when there is an information asymmetry between a central authority and decentralized nodes decentralized nodes make better local investment decisions because of their local knowledge we define three separate organization designs a hierarchy where all investments are made by a central authority a market where all investments are made by the decentralized nodes and a mixed mode where global investments are made by a central authority and local investments are made by decentralized nodes because of complementarities between global and local investment we show that there is under investment relative to first best in all three organization designs we also find that it can be used to mitigate that underinvestment either by bringing information to the decision maker or by redesigning the monitoring and incentive structure we demonstrate that it does not necessarily favor decentralized organization designs and we show how the costs of coordination may resultin the mixed mode being dominated by one or both of the alternative organization designs thus collocation of investment decision rights and information that results in decisions that require coordination might not be optimal when the costs of not synchronizing global and local investment are high

one factor interest rate models and the valuation of interest rate derivative securities this paper compares different approaches to developing arbitrage free models of the term structure it presents a numerical procedure that can be used to construct a wide range of one factor models of the short rate that are both markov and consistent with the initial term structure of interest rates

efficiency of experimental security markets with insider information an application of rational expectations models the study reports on the ability of competing models of market information integration and dissemination to explain the behavior of simple laboratory markets for a one priced security returns to the security depended upon a randomly drawn state of nature some agents insiders whose identity was unknown to other agents knew the state before the markets opened with replication of market conditions the predictions of a fully revealing rational expectations model are relatively accurate prices adjusted immediately to near rational expectations prices profits of insiders were virtually indistinguishable from non insiders and efficiency levels converged to near 100 percent

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

payoff dependence of comparative statics results on information structure abstract this paper investigates in a general decision problem how a first period choice is influenced by varying amounts of information with cara utility functions the effect of a better information structure is established by conditions on the outcome function

interrelafionships between spot and futures markets some implications of rational expectations the view that futures contract prices for storable agricultural commodities are rationally held expectations of subsequent cash prices has been widely accepted since holbrook working first explained commodity market intertemporal price behavior in these terms in 1958 subsequent analyses by brennan weymar tomek and gray and others adopted and extended working s interpretation yet despite its acceptance implications of the rational expectations view have been all but ignored in econometric modeling efforts directed at explaining and predicting intertemporal price relations the purpose of this paper is a to propose an econometric modeling approach that recognizes the role of rational expectation formation in joint determination of commodity cash and futures prices and b to explore the implications of such an approach for the following issues i the direction and magnitude of changes in cash and futures prices occurring in response to changes in economic information and the direction of causality between cash and futures prices and ii the function of futures markets as agencies for forecasting price and the probable forecasting performance of futures contract prices some issues addressed here have implications for all futures traded commodities the arguments presented however relate most clearly to storable continuously inventoried commodities the nature of storage behavior and thus the relation between cash and futures prices for some commodities livestock in particular has not yet been resolved satisfactorily but these issues are not addressed here working s theory of anticipatory prices 1958 asserts that decisions on cash and futures prices take into account all available and relevant information concerning historical relationships as well as current and expected supply demand conditions according to this theory the current period futures price for a contract maturing in time t t is the current market expectation of the subsequent cash market price in t t with only slight modification this interpretation can be considered equivalent to the more current rational expectations or equally redundant efficient market hypothesis formally stated the rational expectations hypothesis muth s extended version asserts that expectations of individual market participants the subjective probability distribution of price outcomes tend to be distributed for the same information set about the predictions of the theory the objective probability distribution of price outcomes in another interpretation it is simply asserted that economic agents use the appropriate economic model in forming their expectations of future prices if valid this latter interpretation has clear implications for the construction of econometric models of futures traded commodities to explore these implications we posit a model which assumes rational expectation formation

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

information acquisition and the adoption of new technology the profitability of a new technology is rarely known with certainty at its announcement date consequently prior to making an adoption decision it behooves the firm considering the adoption of this innovation to reduce the level of uncertainty associated with its profitability the firm accomplishes this by sequentially gathering information updating its prior estimate of profitability in a bayesian manner quantifying the uncertainty regarding the innovation permits application of dynamic programming techniques criteria are derived which tell the firm when to stop collecting information and make the adoption decision it will be shown that it is optimal for the firm to continue to collect information until its estimate of profitability crosses one of two thresholds upon crossing the upper threshold the firm adopts the technology whereas the firm rejects the technology if the lower threshold is crossed the model predicts that even the manager who behaves optimally will occasionally adopt unprofitable technologies and reject profitable ones

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

information acquisition as an american option abstract many information acquisition activities can be postponed within a predefined time frame in uncertain situations the option to postpone the information acquisition to a later more favorable time may create value we discuss the value that comes from holding an option to acquire information in a time period and suggest a simulation based numerical approach to calculate the associated value we discuss that the value of information in a time period may be very different from the value of information in a single point in time this value is closely linked to the uncertainty of the decision outcomes over the time period

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

intertemporal allocation in the corn and soybean markets with rational expectations this paper addresses the intertemporal allocation of supplies and the simultaneous determination of spot and futures prices in the u s corn and soybeans markets these markets were selected for study because of their importance in the u s grain trade and in u s futures markets on the chicago board of trade in 1981 these two grains accounted for 81 26 of all trading in grain futures simultaneous equations models of commodity futures markets have received some attention in the literature stein 1961 1964 developed a two equation simultaneous model comprising functional relationships for discretionary hedging and speculation in commodity markets more recently dewbre estimated a two equation model of spot and futures price determination in commodity markets with rational expectations our study however constitutes the first application of a simultaneous equations model to a comparative study of u s commodity markets with separate functional relationships for long and short hedgers long and short speculators in futures and consumers and holders of unhedged inventories this model is based on peston and yamey although that model did not account explicitly for the activities of long hedgers and short speculators the next section discusses the specification of the equations and the third section outlines the data and estimation method employed the results and validation of the model are discussed in the fourth section the conclusions are stated in the last section while cash and futures prices are endogenous variables in this model the variances of these prices are not treated as endogenous moreover the model is estimated separately for the corn and soybeans markets rather than as a joint model for corn and soybeans products both these matters may be worthwhile extensions of the approach employed here although they go beyond what is attempted in this paper

the efficient estimation of econometric models with rational expectations the efficient estimation of econometric models with rational expectations by the substitution method usually entails the use of a non linear simultaneous equations estimator and hence is not very attractive computationally it is shown that for a wide class of problems efficient estimates can also be obtained with standard estimation methods if instead an errors in variables approach is used for many other problems although not providing fully efficient estimates because rationality is not imposed the errors in variables method will still have a strong appeal because otherwise it uses all of the structural information in the model unlike the substitution method when an incomplete information set is used it guarantees consistent estimates and it is easy to compute

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

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

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

time to build option value and investment decisions abstract investment decisions and outlays are often made sequentially for example the rate at which construction proceeds is usually flexible and can be adjusted with the arrival of new information traditional discounted cash flow methods which treat the pattern of investment as fixed ignore this flexibility and understate the value of the project this paper uses contingent claims analysis to derive optimal decision rules and to value such investments we determine the effects of time to build opportunity cost and uncertainty on the investment decision for reasonable parameter values we show how a simple npv rule can lead to gross errors