from food availability to nutritional capabilities advancing food security analysis abstract this paper has a threefold objective first it provides a comprehensive review of different approaches to analysing food security second it highlights the added value provided by the capability approach and the human development paradigm third it proposes a methodology to assess food security through this approach our proposal entails three basic steps 1 analysis of food entitlements 2 analysis of nutritional capabilities and 3 analysis of the capability to be food secure in this way we can move beyond income entitlement or livelihood related frameworks and identify the root causes of food insecurity food insecurity can be the result of a lack of education health or other basic capabilities that constitute people s wellbeing this therefore allows situating the study within the broader area of wellbeing and development

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

rethinking the global food crisis the role of trade shocks although fundamental factors were clearly responsible for shifting the world to a higher food price equilibrium in the years leading up the 2008 food crisis there is little doubt that when food prices peaked in june of 2008 they soared well above the new equilibrium price numerous arguments have been proposed to explain overshooting including financial speculation depreciation of the united states us dollar low interest rates and reductions in grain stocks however observations that international rice prices surged in response to export restrictions by india and vietnam suggested that trade related factors could be an important basis for overshooting especially given the very tangible link between export volumes and export prices in this paper we revisit the trade story by closely examining monthly data from thailand the largest exporter of rice and the united states the largest exporter of wheat and maize and the third largest exporter of soybeans in all cases except soybeans we find that large surges in export volumes preceded the price surges the presence of these large demand surges together with back of the envelope estimates of their price impacts suggests that trade events played a much larger and more pervasive role than previously thought

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

a quick algorithm for pricing european average options an algorithm is described that prices european average options the algorithm is tested against monte carlo estimates and is shown to be accurate the speed of the algorithm is comparable to the black scholes algorithm a closed form solution is derived for european geometric average options

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

pricing european average rate currency options abstract this paper develops a simple methodology that yields closed form analytical approximations for valuing european option claims involving the arithmetic average of future foreign exchange rates the main advantage of the approach is that it avoids the need to adopt time consuming numerical procedures the precision of the resulting formula and the distributional assumption that underlies it is examined by way of monte carlo simulations jel f31

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

how important is improving food availability for reducing child malnutrition in developing countries abstract do increases in the food supply per person in a country i e national food availability contribute substantially to reductions in malnutrition among its children this paper sets out to answer this controversial question using panel data from 63 developing countries over 1970 1996 this paper gives evidence in support of a statistically significant and strong positive impact of national food availability on child nutrition finding that increased food supplies have resulted in significant reductions in malnutrition since the 1970s despite population increases over the period however per capita food supplies have a declining marginal impact their effect is quite strong for countries with very low food availability e g most countries in sub saharan africa and south asia but weak or non existent for those with high levels e g most countries in the near east and north africa further non food factors such as women s education and status and the quality of health environments are also important determinants of children s nutritional status depending on the state of food availability in any particular geographic area and relative costs these factors may merit greater priority in policies to reduce malnutrition

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

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

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

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

repeated games with differential time preferences when players have identical time preferences the set of feasible repeated game payoffs coincides with the convex hull of the underlying stage game payoffs moreover all feasible and individually rational payoffs can be sustained by equilibria if the players are sufficiently patient neither of these facts generalizes to the case of different time preferences first players can mutually benefit from trading payoffs across time hence the set of feasible repeated game payoffs is typically larger than the convex hull of the underlying stage game payoffs second it is not usually the case that every trade plan that guarantees individually rational payoffs can be sustained by an equilibrium no matter how patient the players are this paper provides a simple characterization of the sets of nash and of subgame perfect equilibrium payoffs in two player repeated games

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

trade subsidies export bans and price stabilization lessons of bangladesh india rice trade in the 2000s abstract during the world food price crisis of 2007 08 rice importing countries suffered through a sharp increase in international rice prices and disruptions in supply as several rice exporters restricted trade to mitigate their domestic price increases perhaps no country was more affected by these disruptions than bangladesh our analysis shows that prior to the 2007 crisis when bangladesh imported an average of nearly 1 million tons of rice per year from india domestic wholesale prices of rice in bangladesh were co integrated with import parity prices of subsidized below poverty line bpl rice when in mid 2007 india sharply curtailed exports rice prices surged in bangladesh model simulations show that a relatively small increase in private consumer stocks equivalent to about 2 weeks of normal consumption could account for the large surge in domestic prices in bangladesh and that an additional 300 000 tons in addition to approximately 700 000 tons of net rice distribution that actually occurred would have been sufficient to stabilize prices in the november 2007 april 2008 period the bangladesh analysis thus shows that in spite of the uncertainty in international markets careful planning timely interventions and openness to trade can substantially reduce requirements for public stockholding

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

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

the macro dimensions of food security economic growth equitable distribution and food price stability abstract rather than asking how to cope with hunger and famine the question might be how to escape their threat altogether important in this regard is recognizing that agriculture and the rural economy are greatly influenced by policies and outcomes in the rest of the economy strategies include economic growth with unchanging income distribution and growth with redistribution the latter encourages balanced growth to create non farm employment opportunities while investing in rural infrastructure

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

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

trade liberalization and food security in nepal among south asian countries nepal liberalized most extensively during the 1980s and 1990s on both domestic and external fronts in south asia nepal has the lowest per capita income highest dependence of population on agriculture and second highest poverty rate at the same time nepal has the lowest average tariffs in south asia and has taken several steps to downsize its public food distribution system and remove a host of agricultural subsidies the outcomes from these policy reforms in nepal are mixed aggregate indicators of food sufficiency and security per capita food availability extent of malnourishment show improvement in nepal since liberalization relative to other south asian countries nepal is doing better on some indicators like extent of undernourished population while on other indicators like stunting of children nepal is actually doing the worst more importantly the gains from liberalization across regions in nepal have been uneven the reason for such an uneven outcome is lack of complementary policies from the government that would lead to spatial integration of markets e g the creation of physical and marketing infrastructure liberalization has in effect reinforced the ex ante hierarchy across regions in nepal the paper then reviews the role and reform of the nepal food corporation nfc within this broader context

fair trade or trade fair international food trade and cross border macronutrient flows abstract this study examines global food trade from a nutritional perspective paying particular attention to its implications for food security in low income countries by describing food trade in terms of the quantities of three essential macronutrients carbohydrates lipids and proteins embedded in food the analysis goes beyond a simple description of trade values quantities or caloric content as is common in the literature furthermore the study provides estimates of the implicit price of each macronutrient their evolution over time and their implications in terms of north south food trade the data show that over the 1996 2014 period the volume of macronutrients exchanged on international markets has more than doubled with carbohydrates accounting for over 60 of trade flows but proteins and lipids growing at a faster pace proteins were found to be the most expensive macronutrient followed by lipids and carbohydrates in general macronutrients embedded in animal and processed products are more expensive than those in vegetal and unprocessed food the results also suggest that the participation in international food trade has positive effects on low income countries aggregate food availability and food access two pillars of food security indeed low income countries register a net inflow of all macronutrients and take advantage of nutritional arbitrages available on international food markets due to macronutrients price differentials

food self sufficiency making sense of it and when it makes sense food self sufficiency gained increased attention in a number of countries in the wake of the 2007 08 international food crisis as countries sought to buffer themselves from volatility on world food markets food self sufficiency is often presented in policy circles as the direct opposite of international trade in food and is widely critiqued by economists as a misguided approach to food security that places political priorities ahead of economic efficiency this paper takes a closer look at the concept of food self sufficiency and makes the case that policy choice on this issue is far from a straightforward binary choice between the extremes of relying solely on homegrown food and a fully open trade policy for foodstuffs it shows that in practice food self sufficiency is defined and measured in a number of different ways and argues that a broader understanding of the concept opens up space for considering food self sufficiency policy in relative terms rather than as an either or policy choice conceptualizing food self sufficiency along a continuum may help to move the debate in a more productive direction allowing for greater consideration of instances when the pursuit of policies to increase domestic food production may make sense both politically and economically

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

how important is economic growth for reducing undernourishment in developing countries abstract there is intense debate in the literature about how important economic growth is for solving the problem of undernourishment this paper focuses on the rate of change in the prevalence of undernourishment and looks at whether higher economic growth speeds up reductions in undernutrition in developing countries the analysis uses panel data analysis on data spanning 22 years 1991 2012 and covering 27 developing countries results reveal that faster annual economic growth leads to larger annual improvements in undernourishment rates both annual and long term economic growth are relevant sustained economic growth has a greater positive impact on undernutrition than short term economic growth in addition to economic growth investments in health education and access to drinking water are also enabling factors for reducing undernourishment in conclusion increased income growth can hasten the effects of food policies aimed at reducing undernourishment but not to the extent that sustained growth and better access to health education and drinking water can

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

collusion and heterogeneity of firms we examine the impact of heterogeneous discounting on collusion in dynamic bertrand competition we show exactly when collusion can be sustained and how collusion would be organized efficiently with heterogeneous discounting first we show that collusion is possible if and only if the average discount factor exceeds a certain threshold with or without capacity constraints next we identify a dynamic pattern of market share that characterizes efficient collusion and obtain the unique long run prediction despite the presence of multiple equilibria in the long run the most patient firm and the most impatient firm tend to dominate the market

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

a bargaining model with incomplete information about time preferences etude d un jeu de negociation strategique sequentiel avec information incomplete caracterisation d une classe d equilibres sequentiels appeles equilibres sequentiels de negociation et demonstration de l unicite de cet equilibre

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

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

multilateral agricultural trade liberalisation the contrasting fortunes of developing countries in the doha round an applied general equilibrium model is used to assess the impact of multilateral trade liberalisation in agriculture with particular emphasis on developing countries we use original data and the model includes some specific features such as a dual labour market applied tariffs including those under preferential regimes and regional agreements are taken into account at the detailed product level together with the corresponding bound tariffs on which countries negotiate the various types of farm support are detailed and several groups of developing countries are distinguished simulations give a contrasted picture of the benefits developing countries would draw from the doha development round the results suggest that previous studies have neglected preferential agreements and the binding overhang in tariffs as well as domestic support and have treated developing countries with a high level of aggregation and been excessively optimistic about the actual benefits of multilateral trade liberalisation regions like sub saharan africa are more likely to suffer from the erosion of existing preferences the main gainers of the doha round are likely to be developed countries and cairns group members

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

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

the unintended consequence of an export ban evidence from benin s shrimp sector summary the inability of benin to comply with eu standards led to a ban on its shrimp exports we show that the ban had a negative impact on the income of fishmongers and fishermen in the short run but also several years after it was lifted the impact persisted because exports to the eu did not revive and the local shrimp demand could not fully compensate for the loss of the eu market a small number of local actors coped with the ban by moving out of the sector but the large majority were locked in the local fishery sector

collusion among asymmetric firms the case of different discount factors abstract this study investigates collusive behavior among asymmetric firms for this purpose we develop a selection criterion for deriving a unique collusive outcome and apply it to the case when firms have different discount factors our analysis reveals that for collusion to be self enforcing it is unnecessary that all firms have sufficiently high discount factors but rather only that firms on average have a sufficiently long run view the optimal collusive outcome entails a strict ordering of output quotas in which firms with relatively low discount factors receive a disproportionate share of market demand as found in the case of a common discount factor a fall in a firm s discount factor reduces the likelihood of successful collusion this effect reduces firm profits on the other hand in the event that firms can collude a lowering of a firm s discount factor increases its output quota so that its profits rise

connected we stand a network perspective on trade and global food security we analyze the link between virtual water trade that is the flow of water embodied in the international trade of agricultural goods and vulnerability to external shocks from the vantage point of network analysis while a large body of work has shown that virtual water trade can enhance water saving on a global scale being especially beneficial to arid countries there are increasing concerns that openness makes countries more dependent on foreign food suppliers and in this way more prone to external shocks our evidence reveals that the increased globalization witnessed in the last three decades is not associated with the increased frequency of adverse shocks in food production furthermore building on recent advances in network analysis that connect the stability of a complex system to its topological features we find that the world is more interconnected but not necessarily less stable

path dependent options extending the monte carlo simulation approach monte carlo simulation has been used to value options since boyle s seminal paper monte carlo simulation however has not been used to its fullest extent for option valuation because of the belief that the method is not feasible for american style options this paper demonstrates how to incorporate optimal early exercise in the monte carlo method of valuing options by linking forward moving simulation and the backward moving recursion of dynamic programming through an iterative search process to demonstrate the potential of this method we use it to value american style options on the average price or asian options the computational experience reveals a flexible valuation technique with potential for application to a range of securities and financial decision problems

general properties of option prices when the underlying price process is a one dimensional diffusion as well as in certain restricted stochastic volatility settings a contingent claim s delta is bounded by the infimum and supremum of its delta at maturity further if the claim s payoff is convex concave the claim s price is a convex concave function of the underlying asset s value however when volatility is less specialized or when the underlying process is discontinuous or non markovian a call s price can be a decreasing concave function of the underlying price over some range increasing with the passage of time and decreasing in the level of interest rates much of the financial options literature derives precise option prices when the underlying asset price process is completely specified since it is empirically difficult to ascertain what the true underlying process is another part of that literature is concerned with deriving general properties of option prices when the underlying price process is not fully specified but instead is assumed to belong to some general class of stochastic processes merton 1973 cox and ross 1976 jagannathan 1984 in particular in the absence of arbitrage opportunities and assuming that the risk neutralized stock price follows a proportional stochastic process a risk neutral return distribution independent of price merton 1973 and jagannathan 1984 show that a call option s price is an increasing convex function of the stock price cox and ross 1976

trade matters in the fight against poverty narratives perceptions and lack of evidence in the case of fish trade in africa two opposing views exist in the literature on the potential role that international fish trade plays in economic development while some claim that fish trade has a pro poor effect others denounce the negative effect of fish export on local populations food security and doubt its contributions to the macro economy in this paper we explore this debate in sub saharan africa our analysis did not find any evidence of direct negative impact of fish trade on food security neither did it find evidence that international fish trade generates positive pro poor outcomes this paper discusses the possible reasons for this apparent lack of development impact and highlights the unsupported assumptions underlying the current discourse about international fish trade we suggest that given lack of evidence for the development benefits of fish trade between africa and developed countries fisheries policy could consider support for regional africa to africa trade that meets the growing african demand for lower value fish means of overcoming barriers to intra african trade in fish are discussed

trade liberalization and national food security rice trade between bangladesh and india abstract following a poor harvest in late 1997 and a massive flood in 1998 private sector traders in bangladesh imported several million metric tons of rice from india this paper presents evidence that this trade made possible by separate trade liberalizations in india and bangladesh in the early 1990s augmented domestic supplies and stabilized prices in bangladesh at import parity levels letters of credit data indicating the participation of hundreds of importers and a close correlation of price movements across the two countries suggest that the trade was competitive a risk of co incident crop shortfalls in the two countries remains though these have occurred rarely in the past two decades bangladesh imports from alternative sources would also enhance food availability if another production shortfall occurs but these imports face higher transport costs and would involve far fewer importing firms given the economies of scale of shipments by sea the positive contribution of trade liberalization to short run food security in bangladesh in recent years does not minimize the importance of increased agricultural productivity and rural economic growth to provide rural poor households with sufficient incomes to acquire food nonetheless the bangladesh experience shows that trade liberalization offers potential benefits for national food security by enabling a rapid increase of food supplies following domestic production shortfalls

on the role of patience in collusive bertrand duopolies abstract this paper analyzes the role of patience in a repeated bertrand duopoly where firms bargain over which collusive price and market share to implement it is shown that the least patient firm s market share is not monotone in its own discount factor

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 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

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

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

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