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

relaxations of approximate linear programs for the real option management of commodity storage the real option management of commodity conversion assets gives rise to intractable markov decision processes mdps in part because of the use of high dimensional models of commodity forward curve evolution as commonly done in practice focusing on commodity storage we identify a deficiency of approximate linear programming alp which we address by developing a novel approach to derive relaxations of approximate linear programs we apply our approach to obtain a class of tractable alp relaxations also subsuming an existing method we provide theoretical support for the use of these alp relaxations rather than their associated approximate linear programs applied to existing natural gas storage instances our alp relaxations significantly outperform their corresponding approximate linear programs our best alp relaxation is both near optimal and competitive with albeit slower than state of the art methods for computing heuristic policies and lower bounds on the value of commodity storage but is m

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

effective sub simulation free upper bounds for the monte carlo pricing of callable derivatives and various improvements to existing methodologies abstract we present a new non nested approach for computing additive upper bounds for callable derivatives using monte carlo simulation it relies on the regression of greeks computed using adjoint methods we also show that it is possible to early terminate paths once points of optimal exercise have been reached a natural control variate for the multiplicative upper bound is introduced which renders it competitive to the additive one in addition a new bi iterative family of upper bounds is introduced which takes a stopping time an upper bound and a martingale as inputs

exchange rates inflation and the sterilization problem germany 1975 1981 when the goals of internal and external macroeconomic equilibrium are in conflict sterilized intervention in the foreign exchange market may provide an independent policy instrument through which the central bank can resolve its dilemma in the short run this paper is concerned with the west german bundesbank s use of sterilization during the recent years of exchange rate flexibility the paper asks whether the bundesbank pursued sterilization during the years 1995 1981 and whether sterilized foreign exchange intervention exerts a significant influence on the exchange rate in the german case estimation of a stylized bundesbank reaction function suggests an affirmative answer to the first of these questions to assess the efficacy of sterilized intervention a structural portfolio balance model of german asset markets and prices is estimated dynamic perfect foresight simulations of the empirical model are used to ascertain whether imperfect substitutability between foreign and domestic bonds is sufficient to allow the bundesbank to attain independent internal and external goals over the short run of about a month the model s verdict is that the bundesbank has little if any power to influence the exchange rate over that time span without altering current or expected future money market conditions this abstract was borrowed from another version of this item

tests of the foreign exchange risk premium using the expected second moments implied by option pricing abstract this paper utilizes the second moment expectations implied by currency option pricing to demonstrate that these expectations are systematically related to expected return differentials across assets denominated in different currencies because the measured deviations from uncovered interest rate parity are tied to variables which theory links to the risk premium the results provide substantial evidence that a risk premium does indeed exist as opposed to the alternative of a violation of rational expectations however like previous attempts the data do not support an explicit mean variance formulation of the risk premium

cournot duopoly with two production periods and cost differentials abstract saloner 1987 analyzes a cournot model with two production periods before the market clears if costs do not vary across periods any point on the outer envelope of the reaction functions between the firms stackelberg outputs is attainable with a subgame perfect nash equilibrium spne saloner s analysis is generalized by allowing for cost differences across periods the continuum of equilibria vanishes for any cost differential if costs fall slightly over time there are multiple leader follower equilibria otherwise the model generates a unique spne where both firms produce their single period cournot outputs in the period when production is cheaper

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

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

on the endogeneity of cournot nash and stackelberg equilibria games of accumulation abstract we characterize equilibria of games with two properties i agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur but ii they can only add to their initial amounts the equilibrium set consists of just the cournot nash outcome one or both stackelberg outcomes or a continuum of points including the cournot nash outcome and one or both stackelberg outcomes a simple theorem that uses agents standard one period reaction functions and the one period cournot nash and stackelberg equilibria delineates the equilibrium set applications include contribution oligopoly and rent seeking games

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

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

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

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

the analytic valuation of american options no analytic solutions exists for the valuation of american options written on futures contracts and foreign currencies for which early exercise may be optimal this article formulates the american option valuation problem in economically and mathematically meaningful ways this enables us to derive valuation formulas for american options the properties associated with the optimal exercise boundary are examined and a numerical technique to implement the valuation formulas is presented article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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 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

money bonds and foreign exchange in the theory of finance capital markets provide securities which allow the ownership of productive assets to be allocated among investors according to their willingness to bear risk in exchange for return and independently of their tastes for the productive services provided by the assets this paper uses the theory of finance to study the role of money as a productive asset and the transformation of money into a portfolio asset true to its purpose the capital market provides securities nominal bonds that allow an allocation of the current services of the money supply according to its current productivity and without regard for its future purchasing power risk and an allocation of the future purchasing power risk of the money supply according to the willingness of investors to bear this risk in exchange for return and without regard for investor needs for the future transactions services of money in open

mercantilism as strategic trade policy the anglo dutch rivalry for the east india trade this paper interprets seventeenth century mercantilism in light of recent theories of strategic trade policy long distance international commerce during the mercantilist period was undertaken chiefly by state chartered monopoly trading companies and was therefore conducted under conditions of imperfect competition the economic structure of the anglo dutch rivalry for the east india trade provides an excellent illustration of an environment in which the profit sharting motive for strategic trade policies exists dutch supremacy in the early east india trade was facilitated by a managerial incentive scheme in the monopoly charter that enabled it to achieve a stackelberg leadership position against the english using data from the east india trade around 1620 in a cournot duopoly model i find that the managerial incentives yielded greater dutch profits than would have been obtained from a standard profit maximizing objective and that the scope for other strategic trade policies was clearly present

sales maximization and specific human capital profit maximizing owners of firms may find it optimal to provide managers with incentives to maximize sales in addition to profits this influences the outcome of the bargaining game between workers and managers over workers wages and helps to solve the problem of underinvestment by workers in specific human capital iinvestigate optimal managerial contracts from this point of view and show that the optimal contract is a function of sales in addition to profits

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

on the effects of barriers to international investment a simple model is presented in which it is costly for domestic investors to hold foreign assets the implications of the model for the composition of optimal portfolios at home and abroad are derived it is shown that all foreign assets with a beta larger than some beta plot on either one of two security market lines some foreign assets with a beta smaller than are not held by domestic investors even if their expected return is increased slightly while it is obviously not true that asset markets are completely segmented between countries there is evidence of barriers to international investment although reality seems to lie in that grey area between complete segmentation and no segmentation at all most international asset pricing models are concerned with the extreme case of no barriers to international investment no effort seems to have been made to study the effect on portfolio choice of such barriers which make it costly to hold foreign securities as opposed to domestic securities but which do not in general render international diversification so onerous that investors avoid foreign securities completely casual empiricism suggests that models without barriers to international investment should be suspect those models cannot explain why it appears that in every country investors on average hold more domestic securities than would be required if they held the world market portfolio 2 this paper constructs a model of international asset pricing in which there is a cost associated with holding either long or short risky foreign securities for the sake of simplicity in most of the paper we assume that while domestic investors face barriers to international investment foreign investors face no such barriers it turns out that nothing significant is lost with such an assumption the main conclusions of this paper for the case in which foreign investors face no barriers to international investment are 1 in the presence of barriers to international investment some risky foreign

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

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

strategic managerial incentives in a two period cournot duopoly abstract this paper examines the nature of optimal managerial incentives in the context of a duopoly marked by competition between the firm s managers in a dynamic production environment if the marginal cost of production falls moderately over time or remains unchanged there exists an equilibrium where one owner requires her manager to maximize profit whereas the rival owner requires her manager to maximize sales revenue the profit maximizing manager turns his firm into a stackelberg leader while the sales revenue maximizing manager turns his firm into a stackelberg follower further the profit maximizing manager may generate a larger firm profit relative to the sales revenue maximizing manager

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

an inverse finite element method for pricing american options abstract the pricing of american options has been widely acknowledged as a much more intriguing problem in financial engineering in this paper a convergency proved ife inverse finite element approach is introduced to the field of financial engineering to price american options for the first time without involving any linearization process at all the current approach deals with the nonlinearity of the pricing problem through an inverse approach numerical results show that the ife approach is quite accurate and efficient and can be easily extended to multi asset or stochastic volatility pricing problems the key contribution of this paper to the literature is that we have managed to provide a comprehensive convergence analysis for the ife approach including not only an error estimate of the adopted discrete scheme but also the convergence of the adopted iterative scheme which ensures that our numerical solution does indeed converge to the exact one of the original nonlinear system

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

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

a stochastic control approach to manage operational risk in power systems in this paper the novel method operational risk managing optimal power flow ormopf for minimizing the expected cost of power system operation is proposed in contrast to previous research in the area the proposed method does not use a security criterion instead the expected cost of operation includes expected costs of system failures this will lead to more flexible operating limits giving a more adequate balance between risk and economic benefit of transmission the method assumes a set of observable system variables such as transfers through specific transmission corridors system frequency or distance to a bifurcation surface then impulse control is applied to find an optimal strategy for activation of tertiary reserves based on the values of the observables

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

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

international asset pricing with time varying risk premia abstract recent empirical evidence that forward exchange rates are biased predictors of future spot rates can also be interpreted as evidence against the hypothesis of a constant risk premium consequently reconciliation of this evidence with efficient international capital markets requires the existence of time varying risk premia this paper modifies kouri s 1977 asset pricing model to allow time varying exected returns on assets eliminates the assumption of a risk free real asset and derives the characteristics of the risk premia in the forward market as well as the equilibrium yield relationships among the equities and riskless nominal bonds of all countries

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

tests of rational expectations and no risk premium in forward exchange markets abstract this paper tests the simple efficiency hypothesis i e that traders have rational expectations and charge no risk premium in the forward exchange market it uses a statistical procedure which is consistent under a large class of heteroscedasticity and a set of data which takes into account the institutional features of the forward exchange market the results show that this procedure leads to stronger rejections of the simple efficiency hypothesis than do procedures using the standard assumption of homoscedasticity

a financial model of foreign exchange exposure the paper describes a model of foreign exchange exposure this is defined as the sensitivity of a specific investment s value in reference currency to changes in exchange rate forecasts this sensitivity may result because some share of the investment cash flows are denominated in foreign currency alternatively a share of cash flows denominated in reference currency which are affected by future exchange rates can also generate sensitivity

capital market imperfections and countercyclical markups theory and evidence during recessions output prices seem to rise relative to wages and raw material prices one explanation is that imperfectly competitive firms compete less aggressively during recessions that is markups of price over marginal cost are countercyclical the authors present a model of countercyclical markups based on capital market imperfections during recessions liquidity constrained firms boost short run profits by raising prices to cut their investments in market share the authors provide evidence from the supermarket industry in support of this theory during regional and macroeconomic recessions more financially constrained supermarket chains raise their prices relative to less financially constrained chains copyright 1996 by american economic association

stackelberg equilibria in managerial delegation games abstract managerial compensation packages do not only influence managers behavior but also have an impact on competing firms in a managerial delegation game investigating the latter aspect it is shown that the inherent prisoner s dilemma situation can be resolved without changing the normally studied setup or timing in the first stage owners choose an incentive function for their managers in the second stage they choose the weights assigned to that function besides profits and in the third stage managers play a cournot game solving this continuous optimization problem with the implicit function theorem shows that choosing an incentive from the set of multiplicative incentives i e any generalized affine transformation of the product of both firms quantities which includes e g relative profit ensures that the stackelberg outcome is among the set of equilibrium outcomes furthermore it is the unique outcome if the rival owner opts for one of the well known incentives like sales revenue or market share the general approach used allows demonstrating that with no other linear incentive a stackelberg outcome results and that incentives like profit to cost ratio should be avoided selecting a multiplicative incentive is a dominant strategy of the game

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

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

the strategic choice of managerial incentives do firms with separate owners and managers maximize profits we address this question for an oligopoly where managers compete in quantities or prices as in the cournot or bertrand models and owners choose their managers incentives we find that there is a strategic aspect in the problem of selecting incentives and that profit maximizing behavior does not result in particular in the oligopoly we study the behavior of firms competing in quantity price more closely resembles perfectly competitive collusive behavior than cournot bertrand behavior

dynamic portfolio optimization with transaction costs heuristics and dual bounds we consider the problem of dynamic portfolio optimization in a discrete time finite horizon setting our general model considers risk aversion portfolio constraints e g no short positions return predictability and transaction costs this problem is naturally formulated as a stochastic dynamic program unfortunately with nonzero transaction costs the dimension of the state space is at least as large as the number of assets and the problem is very difficult to solve with more than one or two assets in this paper we consider several easy to compute heuristic trading strategies that are based on optimizing simpler models we complement these heuristics with upper bounds on the performance with an optimal trading strategy these bounds are based on the dual approach developed in brown et al brown d b j e smith p sun 2009 information relaxations and duality in stochastic dynamic programs oper res 58 4 785 801 in this context these bounds are given by considering an investor who has access to perfect information about future returns but is penalized for using this advance information these heuristic strategies and bounds can be evaluated using monte carlo simulation we evaluate these heuristics and bounds in numerical experiments with a risk free asset and 3 or 10 risky assets in many cases the performance of the heuristic strategy is very close to the upper bound indicating that the heuristic strategies are very nearly optimal this paper was accepted by dimitris bertsimas optimization

the valuation of american barrier options using the decomposition technique in this paper we propose an alternative approach for pricing and hedging american barrier options speci cally we obtain an analytic representation for the value and hedge parameters of barrier options using the decomposition technique of separating the european option value from the early exercise premium this allows us to identify some new put call symmetry relations and the homogeneity in price parameters of the optimal exercise boundary these properties can be utilized to increase the computational e ciency of our method in pricing and hedging american options our implementation of the obtained solution indicates that the proposed approach is both e cient and accurate in computing option values and option hedge parameters our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and e ciency in particular the method is free of the di culty that existing

american option sensitivities estimation via a generalized infinitesimal perturbation analysis approach in this paper we develop efficient monte carlo methods for estimating american option sensitivities the problem can be reformulated as how to perform sensitivity analysis for a stochastic optimization problem with model uncertainty we introduce a generalized infinitesimal perturbation analysis ipa approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter the ipa estimators are unbiased if the optimal decisions are explicitly known to quantify the estimation bias caused by intractable exercising policies in the case of pricing american options we also provide an approximation guarantee that relates the sensitivity under the optimal exercise policy to that computed under a suboptimal policy the price sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high dimensional environments and various process settings we can easily embed them into many of the most popular pricing algorithm

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

the forward exchange rate and macroeconomics abstract this paper discusses the conditions under which a risk premium is incorporated in the forward exchange rate a new condition for the existence of a risk premium is proposed we show that earlier models of the risk premium which emphasize either the role of net foreign investment or of the relative supplies of outside assets are not suited for assessing the effects of changes in macroeconomic policy

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

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

stackelberg equilibrium in oligopoly an explanation based on managerial incentives abstract this paper shows that in a model of managerial delegation in a duopoly if an owner s decision to hire a manager is modeled explicitly then the subgame perfect equilibrium may coincide with the stackelberg solution interestingly this can happen even when the cost of hiring a manager is the same for the owner of each firm

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

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

foreign exchange market efficiency tests implications of recent empirical findings abstract the recent empirical literature on the efficiency of the foreign exchange market has been characterized by strikingly contradictory conclusions drawn from similar empirical evidence these contradictions result because 1 different maintained hypotheses are held and 2 different criteria e g micro versus macroeconomic are used to judge the evidence in this survey we organize the empirical literature under several headings the presence of risk premiums empirical regularities in regression tests profitable trading rules and advanced econometric techniques in integrating this material we consider the implications of the current evidence for investors forecasters policy makers and theorists

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

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

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

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

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