analytical upper bounds for american option prices american options require numerical methods namely lattice models to provide accurate price estimates the computations can become expensive when more than one state variable is involved analytical upper bounds can therefore provide a useful guideline for how high american values can reach in this paper we derive analytical closed form upper bounds for american option prices under stochastic interest rates stochastic volatility and jumps where american option prices are difficult to compute with accuracy in a stochastic volatility model heston 1993 and scott 1997 that has two random factors we demonstrate that the upper bound only takes a very small fraction of the time that the american option needs to compute

social networks and the process of globalization we propose a stylised dynamic model to understand the role of social networks in the phenomenon we call globalization this term refers to the process by which even agents who are geographically far apart come to interact thus being able to overcome what would otherwise be a fast saturation of local opportunities a key feature of our model is that the social network is the main channel through which agents exploit new opportunities therefore only if the social network becomes global heuristically it reaches far in few steps can global interaction be steadily sustained to shed light on the conditions under which such a transformation may or may not take place is the main objective of the paper one of the main insights arising from the model is that in order for the social network to turn global the economy needs to display a degree of geographical cohesion that is neither too high for then global opportunities simply do not arise nor too low then the meeting mechanism displays too little structure for the process to take off but if globalization does materialize we show that it is a robust state of affairs that often arises abruptly as key parameters change this occurs in particular as the rate of arrival of ideas rises or when there is a high enough increase in the range at which the network transmits information

factorization of european and american option prices under complete and incomplete markets abstract in a standard option pricing model with continuous trading and diffusion processes this paper shows that the price of one european style option can be factorized into two intuitive components one robust x 0 which is priced by arbitrage and a second 0 which depends on a risk orthogonal to the traded securities this result implies the following 1 in an incomplete market these parts represent the price of a hedging portfolio which is unique and a premium which depends only on the risk premiums associated with the residual risk respectively 2 in a complete market it allows factoring the contribution of the different sources of risk to the final option price for example in a stochastic volatility model we can quantify the impact on the option price of volatility risk relative to market risk 0 and x 0 respectively hence certain misspricings in option markets can be directly related to the premium 0 3 moreover these results extend to american securities which have a third component an additional early exercise premium

classical and variance bounds tests of the production smoothing hypothesis in this paper we test the controversial production smoothing role of inventories by applying both classical econometric techniques and variance bounds tests we use seasonally unadjusted data measured in physical units for five industries the model used is a version of the familiar holt et al 1960 inventory model we also use the data on one industry disaggregated at the district level to investigate potential bias which may arise from aggregation overall the empirical evidence suggests production smoothing in the great majority of the industries examined

static hedging of exotic options this paper develops static hedges for several exotic options using standard options the method relies on a relationship between european puts and calls with different strike prices the analysis allows for constant volatility or for volatility smiles or frowns

temporal aggregation and estimation of inventory functions abstract in this paper we extend the analysis of the effects of aggregation on the estimated speed of adjustment in inventory models into two directions first we try to find out if lovell s 1993 conclusions regarding the effects of aggregation on the speed of adjustment hold a when real firm data rather than experimental data are used b when the model is modified or when models other than the flexible accelerator are used secondly we examine whether temporal aggregation also leads to underestimation when disaggregated nonseasonally adjusted data are used the evidence we provide gives strong support to mundlak s and zellner s conjectures cited in christiano and eichenbaum 1987 that temporal aggregation leads to downward bias in the estimated speed of adjustment

optimal partnership in a repeated prisoner s dilemma this paper studies informational partnerships in a repeated prisoner s dilemma with random matching assuming that players observe the play within but not across partnerships we find the surprising result that the relation between the observability of actions and the sustainability of cooperation is non monotonic increasing partnerships beyond a certain optimal size hardens cooperation although it improves observability d 2005 elsevier b v all rights reserved

street crime and street culture a model shows how reputation concerns can support widespread street crime a street culture where the direct incentives for such behavior are weak there are social benefits to street reputations but those benefits are dominated when reputation concerns draw into crime those who obtain no direct gain from it the model matches facts about violent crime that a standard model cannot easily explain including low monetary returns disproportionate victimization of the young and poor and high variance in rates across small distances the model generates novel implications for policy and social science including a negative effect of social capital

the social basis of interdependent preferences abstract most economists are sympathetic to the idea that concerns for relative position are an important aspect of many economic problems there has traditionally been a reluctance to include such concerns primarily because models that included them often allow such a broad range of behavior that there are few if any restrictions on equilibrium behavior and hence such models would have little or no predictive power in this paper we discuss how reduced form models may naturally give rise to utility functions that depend in part on relative standing there are several advantages of modelling concern for relative standing in reduced form utility functions even when there is no similar concern in the deep preferences it provides structure and constraints on the way that relative standing affects utility and further it can yield testable implications about the way that changes in the underlying environment affect the concern for relative standing we discuss the advantages and disadvantages of modelling social concerns in this way and provide examples that illustrate how concerns for relative standing can affect savings investment and labor choice decisions

simulating the inventory cycle abstract simulations of the inventory cycle utilizing a model based on 84 interacting firms in 21 industries reveals that the ratio of the variance of sales to the variance of output is an unreliable indicator of how seriously firms attempt to smooth production or whether such efforts in the aggregate even out economic fluctuations it is also shown that the two slow estimates of the speed of adjustment reported in many econometric studies of united states data may result in part from aggregation bias rather than from limitations of the flexible accelerator model itself

rational behavior and economic theory abstract nowadays it seems almost universally presumed that the fundamental characteristic of homo oeconomicus is his rationality we analyze the role played by the concept of rationality in economic theory and demonstrate that it is necessarily constrained to be an essentially contentless notion we show that the main body of economic theory is firmly grounded and that some contrasting approaches to rationality although leading to heated debates and vivid confusion have no fundamental significance for economics with a refereshed view on the essence of economics we argue that the principles of economic theory form an essential methodological guide for the emergent line of research based on the use of so called evolutive models

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

cooperation among strangers with limited information about reputation abstract the amount of institutional intervention necessary to secure efficiency enhancing cooperation in markets and organizations in circumstances where interactions take place among essentially strangers depends critically on the amount of information informal reputation mechanisms need transmit models based on subgame perfection find that the information necessary to support cooperation is recursive in nature and thus information generating and processing requirements are quite demanding models that do not rely on subgame perfection on the other hand suggest that the information demands may be quite modest the experiment we present indicates that even without any reputation information there is a non negligible amount of cooperation that is however quite sensitive to the cooperation costs for high costs providing information about a partner s immediate past action increases cooperation recursive information about the partners previous partners reputation further promotes cooperation regardless of the cooperation costs

seasonality aggregation and the testing of the production smoothing hypothesis one of the leading hypotheses concerning the dynamics of production over time is the production smoothing hypothesis given a planning horizon which spans a number of production periods the firm need not produce in each period an amount equal to expected sales rather resorting to inventory accumulation and liquidation the firm may follow a production plan temporally smoother than the path of demand if firms faced with convex cost functions chose to smooth the rate of output in order to minimize costs one would expect to observe that the rate of output would vary less than the rate of sales with variations in inventory stocks absorbing some of the fluctuations in sales recently work on the testing of the production smoothing hypothesis has cast doubt on its empirical validity the evidence presented by alan blinder seems to indicate that the variance of production exceeds that of sales in seven out of eight two digit retail industries 1981 and in eighteen out of twenty two digit manufacturing industries 1983 and 1986 the purpose of this paper then is to examine the validity of such tests when seasonally adjusted aggregated data are used the evidence presented show that the relative size of the variances of the seasonally adjusted production and sales does not provide valid tests of the production smoothing hypothesis in addition aggregating over firms where the seasonal patterns differ may also distort tests of production smoothing blinder realized that the use of seasonally adjusted data may not provide an adequate test of the hypothesis stating had they been available i would have preferred to use data that were not seasonally adjusted since the production smoothing model presumably applies to seasonal fluctuations in sales however such data are not available 1983 fn 19 in this paper i focus on the cement industry because the unadjusted disaggregated data are available for the direct testing of the conjecture that aggregate seasonally adjusted data mask production smoothing phenomenon aggregate monthly data on five other industries will also be examined

the sensitivity of american options to suboptimal exercise strategies the value of american options depends on the exercise policy followed by option holders market frictions risk aversion or a misspecified model for example can result in suboptimal behavior we study the sensitivity of american options to suboptimal exercise strategies we show that this measure is given by the gamma of the american option at the optimal exercise boundary more precisely if b is the optimal exercise price but exercise is either brought forward when or delayed until a price b has been reached the cost of suboptimal exercise is given by b b b 2 where b denotes the american option gamma therefore the cost of suboptimal exercise is second order in the bias of the exercise policy and depends on gamma this result provides new insights on american options

an experimental test of the efficacy of a simple reputation mechanism to solve social dilemmas abstract the evolution of cooperation has been the focus of intense research in the social sciences natural sciences especially biology and even computer science it has long been recognized that the possibility of future consequences is crucial to the emergence of rational cooperation it was thought that random matching was isomorphic to one shot play but kandori 1992 showed that a reputation labeling mechanism can be used to support cooperation in the random matching prisoner dilemma we designed an experiment to test this result we found that while the level of cooperation steadily declined without a reputation mechanism with our color coded reputation mechanism the level of cooperation steadily increased with experience an econometric mixture model consisting of four reputation conditioned strategies as well as a level 0 type was fitted to the data we cannot reject the hypothesis that the majority of subjects used one of these strategies and learned with experience

effects of rotation scheme on fishing behaviour with price discrimination and limited durability theory and evidence abstract this paper examines how rotation arrangement between two groups of fishers with different institutional arrangements affects fishing behaviour and economic outcomes in a particular economic environment characterised by price discrimination and product durability in one group fishers cooperate and maximise the extraction of rents while members in the second group behave non cooperatively applying a model of alternating duopoly we show that the cooperating group behaves like a price discriminating monopolist and tends to uphold prices when the two groups rotate fishing days the cooperating group tends to produce more which prevents the non cooperating group from unprofitable demand preemption

social norms and money abstract in an economy where there is no double coincidence of wants and without public record keeping of past transactions money is usually seen as the only mechanism that can support exchange in this paper we show that as long as the population is finite and agents are sufficiently patient a social norm establishing gift exchange can substitute for money however for a given discount factor population growth eventually leads to the breakdown of the social norm additionally increases in the degree of specialization in the economy can also undermine the social norm by contrast monetary equilibrium exists independent of the population size we conclude that money is essential as a medium of exchange when the population is large

social status and economic performance a survey abstract this survey combines ideas and results from sociology and economics recognizing that economic decisions are often shaped by social concerns and influences based on the sociological literature we define social status and describe its measurement we then describe the role of social status in economic analysis of saving and consumption wages and economic growth we review recent work on status determination in equilibrium including evolutionary models we conclude with some remarks on the need for further interaction between sociology and economics

social norms and random matching games abstract nash equilibrium has been tremendously useful in understanding economic problems in which strategic behavior is important the theoretical foundations of the solution concept often include the assumption that the game to be played is common knowledge an unrealistic assumption in games with many players we introduce the concept of norm equilibrium for random matching games a norm equilibrium is a nash equilibrium that relies on substantially less information than common knowledge of the game we use norm equilibria to provide a folk theorem for random matching games and to analyze increasing numbers of players in a random matching game journal of economic literature classification numbers c70 c72

asymmetry of customer loss and recovery under endogenous partnerships theory and evidence this article is inspired by real world phenomena that firms lose customers based on imprecise information and take a long time to recover if consumers are playing an ordinary repeated game with fixed partners there is no clear reason why recovery happens slowly however if consumers are playing an endogenously repeated game a class of simple efficient equilibria exhibits the asymmetry of fast loss and slow recovery of customers after a bad signal exit is systematic but formation of a new partnership is random we also give empirical evidence of our equilibria at an individual firm level

ostracism and forgiveness many communities rely upon ostracism to enforce cooperation if an individual shirks in one relationship her innocent neighbors share information about her guilt in order to shun her while continuing to cooperate among themselves however a strategic victim may herself prefer to shirk rather than report her victimization truthfully if guilty players are to be permanently ostracized then such deviations are so tempting that cooperation in any relationship is bounded by what the partners could obtain through bilateral enforcement ostracism can improve upon bilateral enforcement if tempered by forgiveness through which guilty players are eventually readmitted to cooperative society

observations on cooperation we study environments in which agents are randomly matched to play a prisoner s dilemma and each player observes a few of the partner s past actions against previous opponents we depart from the existing related literature by allowing a small fraction of the population to be commitment types the presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation we present a novel intuitive combination of strategies that sustains cooperation in various environments moreover we show that under an additional assumption of stationarity this combination of strategies is essentially the unique mechanism to support full cooperation and it is robust to various perturbations finally we extend the results to a setup in which agents also observe actions played by past opponents against the current partner and we characterize which observation structure is optimal for sustaining cooperation

option bounds in discrete time extensions and the pricing of the american put in a recent paper perrakis and ryan 1984 upper and lower bounds on european option prices were derived in discrete time these bounds were based on an extension of the discrete time derivation of black scholes pricing first presented in the work of black and scholes 1973 the bounds are functions of the stock and exercise prices the riskless rate of interest the time to maturity and the entire distribution of stock returns in other words they need more information than black scholes for their computation and the derived results are weaker on the other hand they are significantly more general in their assumptions insofar as they do not rely on the continuous time riskless hedge of the original black scholes derivations or on the assumption of a binomial distribution of stock returns used in cox ross and rubinstein 1979 and rendleman and bartter 1979 for this reason they are likely to be particularly useful in valuing options on assets for which the black scholes methodology is clearly this paper generalizes and tightens the discrete time bounds for european options and develops similar bounds for american puts the stock return has a distribution with a finite range and is subject to the restriction that the stock be nonnegative beta the bounds are derived from arbitrage portfolios using the stock the option and the riskless asset they converge to the previous ones when the range coincides with the nonnegative real line and they both become equal to the binomial option model under a two state stock return upper and lower bounds for the american put are derived recursively by the same method with arbitrage portfolios involving the stock the riskless asset and american and european puts an example is provided with a trinomial return distribution part of this research was done while i was a visiting professor 1983 84 ecole superieure de commerce et d administration des entreprises reims france i wish to thank peter ryan albert madansky and a referee of this journal for helpful advice and comment while retaining all responsibility for any remaining errors or omissions 1 note however that this is also true of other blackscholes generalizations such as merton 1976

the saga of the american put abstract the american put is one of the oldest problems in mathematical finance we review the development of the relevant literature over the last 40 years today the mainstream computational problems have been solved satisfactorily and the target of research is shifting towards the development of further insights into the value of timing investment decisions

voluntarily separable repeated prisoner s dilemma ordinary repeated games do not apply to real societies where one can cheat and run away from partners we formulate a model of endogenous relationships which one can unilaterally end and start with a randomly assigned new partner with no information flow focusing on two person two action prisoner s dilemma we show that the endogenous duration of partnerships gives rise to a significantly dierent evolutionary stability structure from the ordinary evolutionary games monomorphic equilibria require initial trust building while a polymorphic equilibrium includes early cooperators than any strategy in monomorphic equilibria and is thus more ecient this

social rewards externalities and stable preferences this paper examines the role of social rewards as a corrective mechanism for activities which generate externalities the focus of this paper is on the circumstances under which social rewards provide effective and feasible incentive mechanism that may replace laws and regulations in particular social mechanism is effective only in a society in which individuals who care about their standing in the society can survive in the long run we show that the nature of economic interaction between matched players influences whether the socially minded individuals survive in the long run and restricts the effectiveness of social rewards however circumstances exist where the socially minded survive even though relative fitness is determined only by economic payoff 1998 elsevier science s a all rights reserved

dress to impress brands as status symbols abstract we analyzed the market for indivisible pure status goods firms produce and sell different brands of pure status goods to a population that is willing to signal individual abilities to potential matches in another population individual status is determined by the most expensive status good one has there is a stratified equilibrium with a finite number of brands under constant tax rates a monopoly sells different brands to social classes of equal measure while in contestable markets social classes have decreasing measures under optimal taxation contestable markets have progressive tax rates while a monopoly faces an adequate flat tax rate to all brands in contrast with extant literature subsidies may be socially optimal depending on the parameters in both market structures

tight bounds on american option prices in contrast to the constant exercise boundary assumed by broadie and detemple 1996 broadie m detemple j 1996 american option valuation new bounds approximations and comparison of existing methods review of financial studies 9 1211 1250 we use an exponential function to approximate the early exercise boundary then we obtain lower bounds for american option prices and the optimal exercise boundary which improve the bounds of broadie and detemple 1996 with the tight lower bound for the optimal exercise boundary we further derive a tight upper bound for the american option price using the early exercise premium integral of kim 1990 kim i j 1990 the analytic valuation of american options review of financial studies 3 547 572 the numerical results show that our lower and upper bounds are very tight and can improve the pricing errors of the lower bound and upper bound of broadie and detemple 1996 by 83 0 and 87 5 respectively the tightness of our upper bounds is comparable to some best accurate efficient methods in the literature for pricing american options moreover the results also indicate that the hedge ratios deltas and gammas of our bounds are close to the accurate values of american options

bounds and prices of currency cross rate options abstract this paper derives the pricing bounds of a currency cross rate option using the option prices of two related dollar rates via a copula theory and presents the analytical properties of the bounds under the gaussian framework our option pricing bounds are useful because 1 they are general in the sense that they do not rely on the distribution assumptions of the state variables or on the selection of the copula function 2 they are portfolios of the dollar rate options and hence are potential hedging instruments for cross rate options and 3 they can be applied to generate bounds on deltas the empirical tests suggest that there are persistent and stable relationships between the market prices and the estimated bounds of the cross rate options and that our option pricing bounds obtained from the market prices of options on two dollar rates and the historical correlation of two dollar rates are highly informative for explaining the prices of the cross rate options moreover the empirical results are consistent with the predictions of the analytical properties under the gaussian framework and are robust in various aspects

comments on money is privacy by charles kahn james mcandrews and william roberds monetary theory and game theory three classes of models on money closely related to game theoretic models are i search theoretic models ii repeated games in a narrow sense and iii trading post games this note tries to point out the sense of affinity between the theory of microfoundations of money and the theory of repeated games in a broad sense of the term

social capital and social quilts network patterns of favor exchange we examine the informal exchange of favors in societies such that any two individuals interact too infrequently to sustain exchange but such that the social pressure of the possible loss of multiple relationships can sustain exchange patterns of exchange that are locally enforceable and renegotiation proof necessitate that all links are supported any two individuals exchanging favors have a common friend in symmetric settings such robust networks are social quilts tree like unions of completely connected subnetworks examining favor exchange networks in 75 villages in rural india we find high levels of support and identify characteristics that correlate with support

economics and identity this paper considers how identity a person s sense of self affects economic outcomes we incorporate the psychology and sociology of identity into an economic model of behavior in the utility function we propose identity is associated with different social categories and how people in these categories should behave we then construct a simple game theoretic model showing how identity can affect individual interactions the paper adapts these models to gender discrimination in the workplace the economics of poverty and social exclusion and the household division of labor in each case the inclusion of identity substantively changes conclusions of previous economic analysis

american garch employee stock option valuation abstract we implement a flexible simulation based approach for the fair value of employee stock option eso that accounts for the vesting period departure risk and voluntary suboptimal early exercise we introduce garch effects on the underlying asset and we analyze the price bias with respect to the constant volatility case we also perform a sensitivity analysis with respect to changes in several eso characteristics we compare this valuation with fas 123 method revealing a fas overvaluation finally we value a real eso plan providing the confidence intervals for the estimated eso prices

why the west became wild informal governance with incomplete networks settlers flocking to boomtowns on the american western frontier were faced with the same task that communities in weak states across the globe face in contemporary times self governance peer sanctions can enforce cooperation in these environments but their efficacy depends on the social networks that transmit information from peer to peer the author uses a game theoretic model to show that peripheral network positions can generate such strong incentives to misbehave that persistent cheating occurs in equilibrium the model reveals that groups maintaining high levels of cooperation that face shocks to their strategic environment or to their network can ratchet down into less cooperative equilibria in which the most peripheral become ostracized furthermore population change that features rapid growth high turnover and enclave settlements can undermine cooperation the insights from this article help to explain the trajectory of cooperation in the mining towns of the wild west in which high levels of cooperation deteriorated as the population surged and help to make sense of why only certain nonwhite settlers were targets of hostility and racism

an fft network for levy option pricing abstract this paper develops a simple network approach to american exotic option valuation under levy processes using the fast fourier transform fft the forward shooting grid fsg technique of the lattice approach is then generalized to expand the fft network to accommodate path dependent variables this network pricing approach is applicable to all levy processes for which the characteristic function is readily available in other words the log value of the underlying asset can follow finite activity or infinite activity levy processes with the powerful computation of fft the proposed network has a negligible additional computational burden compared to the binomial tree approach the early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach numerical examples using american style barrier lookback and asian options demonstrate that the fft network is accurate and efficient

the two money theorem in this article i consider environments in which all shocks have finite support and any transfer of resources is ex post voluntary consider an allocation that is achievable when potential trading partners know each others histories the one money theorem says that the allocation is achievable using only one money if that money is divisible and money holdings are observable the two money theorem says that the allocation is achievable using two divisible monies even if money holdings are concealable copyright economics department of the university of pennsylvania and the osaka university institute of social and economic research association

an improved method for pricing and hedging long dated american options abstract the majority of quasi analytic pricing methods for american options are efficient near maturity but are prone to larger errors when time to maturity increases we introduce a new methodology to increase the accuracy of almost any existing quasi analytic approach in pricing long maturity american options the new methodology called the extension method relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches so that the maturity range for which small errors are attainable is extended our method retains the quasi analytic nature of the methods it improves generic quasi analytic formulae for the price of an american put as well as for its hedging parameter are derived our scenarios based numerical study indicates that our method considerably improves both the pricing and the hedging performance of a number of established approaches for a wide range of maturities the superiority of this approach is illustrated with real financial data by considering s p 100 tm leaps options traded from january 2008 to may 2015

more on the speed of adjustment in inventory models when empirical stock adjustment models of manufacturers inventories of finished goods are estimated there appear to be two local minima in the sum of squared residuals functions at one local minimum the estimated adjustment speed is typically quite high at the other it is typically quite low furthermore finding two sets of estimates that fit the data almost equally well does not appear to be a quirk of this particular application rather it stems from a fundamental identification problem that afflicts partial adjustment models of all kinds in the specific context of manufacturers inventories of finished goods the estimation procedure employed by maccini and rossana seems to pick out the solution with rapid adjustment and high serial correlation in the disturbances whereas the solution with slow adjustment and little serial correlation is more often the global minimum this abstract was borrowed from another version of this item

competition and norms a self defeating combination this paper investigates the effects of information feedback mechanisms on electricity and heating usage at a student hall of residence in london in a randomised control trial we formulate different treatments such as feedback information and norms as well as prize competition among subjects we show that information and norms lead to a sharp more than 20 reduction in overall energy consumption because participants do not pay for their energy consumption this response cannot be driven by cost saving incentives interestingly when combining feedback and norms with a prize competition for achieving low energy consumption the reduction effect while present initially disappears in the long run this could suggest that external rewards reduce and even destroy intrinsic motivation to change behaviour

durable goods and conformity a consumer s demand for a durable good is governed not only by his individual preferences but also by preferences of other market participants this interdependence of preferences arises from the inevitable resale of durable goods if most people prefer goods with certain features original buyers conform and choose goods with these features even if they do not like them using a matching model we show there is always conformity in equilibrium the incentive to conform is strongest for long lived durables and for people who trade frequently if average preferences are sufficiently strong there is always too little conformity in equilibrium

the effects of community characteristics on community social behavior abstract the purpose of this paper is to examine the impact of a community s economic characteristics on its ability to generate adherence to socially efficient norms these norms prescribe a behavior for an individual when his her preferred behavior imposes a negative externality on others this paper explores social norms as a mechanism of how neighborhood characteristics can affect individual behavior understanding the mechanism through which community characteristics affect individual behavior is important in that it enables the development of a testable structural empirical model which is purged of the omitted variable bias arising from the potential endogeneity of the neighborhood choice

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

robust pricing of the american put option a note on richardson extrapolation and the early exercise premium this paper presents a detailed analysis of the numerical implementation of the american put option decomposition into an equivalent european option plus an early exercise premium kim 1990 jacka 1991 carr et al 1992 it subsequently introduces a new algorithm based upon this decomposition and richardson extrapolation this new algorithm is based upon a the derivation of the correct order for the error term when applying richardson extrapolation which is used to control the error of the extrapolated prices b an innovative adjustment of kim s 1990 discrete time early exercise premium so that these premiums monotonically converge and therefore it is appropriate to use them in extrapolation and c the optimal exercise frontier can be quickly computed through newton s method permitting the efficient implementation of the decomposition formula in practice numerical experiments show that this new algorithm is accurate efficient easy to implement and competitive in comparison with other methods finally it can also be applied to other american exotic securities

social norms and trust among strangers we study the development of a social norm of trust and reciprocity among a group of strangers via the contagious strategy as defined in kandori 1992 over an infinite horizon the players anonymously and randomly meet each other and play a binary trust game in order to provide the investors with proper incentives to follow the contagious strategy there is a sufficient condition that requires that there exists an outside option for the investors moreover the investors payoff from the outside option must converge to the payoff from trust and reciprocity as the group size goes to infinity we show that this sufficient condition is also a necessary condition to sustain any sequential equilibrium in which the trustees adopt the contagious strategy our results imply that a contagious equilibrium only supports trust if trust contributes almost nothing to the investors payoffs