the valuation of american options with stochastic interest rates a generalization of the geske johnson technique the geske johnson approach provides an efficient and intuitively appealing technique for the valuation and hedging of american style contingent claims here we generalize their approach to a stochastic interest rate economy the method is implemented using options exercisable on one of a finite number of dates we illustrate how the value of an american style option increases with interest rate volatility the magnitude of this effect depends on the extent to which the option is in the money the volatilities of the underlying asset and the interest rates as well as the correlation between them

re examination of uniform commodity taxes under a non linear income tax system and its implication for production efficiency abstract this paper shows that the result of uniform commodity tax under nonlinear income taxation by atkinson and stiglitz 1976 no longer holds if the production side of an economy is taken into the consideration in particular imposing a non uniform commodity tax can pareto improve welfare even under nonlinear income taxation in addition the paper shows that if the government uses a nonlinear income tax system for income redistribution then the introduction of distortions in the public sector can pareto improve welfare contrary to the results in diamond and mirrlees 1971

50th anniversary article option pricing valuation models and applications this paper surveys the literature on option pricing from its origins to the present an extensive review of valuation methods for european and american style claims is provided applications to complex securities and numerical methods are surveyed emphasis is placed on recent trends and developments in methodology and modeling

the spatial and temporal diffusion of house prices in the uk abstract this paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system we use changes in real house prices within the uk economy at the level of regions to illustrate its use adjustment to shocks involves both a region specific and a spatial effect shocks to a dominant region london are propagated contemporaneously and spatially to other regions they in turn impact on other regions with a delay we allow for lagged effects to echo back to the dominant region london in turn is influenced by international developments through its link to new york and other financial centers it is shown that new york house prices have a direct effect on london house prices we analyse the effect of shocks using generalised spatio temporal impulse responses these highlight the diffusion of shocks both over time as with the conventional impulse responses and over space

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

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

the propagation of regional recessions this paper develops a framework for inferring common markov switching components in a panel data set with large cross section and time series dimensions we apply the framework to studying similarities and dierences across u s states in the timing of business cycles we hypothesize that there exists a small number of cluster designations with individual states in a given cluster sharing certain business cycle characteristics we nd that although oil producing and agricultural states can sometimes experience a separate recession from the rest of the united states for the most part dierences across states appear to be a matter of timing with some states entering recession or recovering before others jel c11 c32 e32

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

explaining the spatial variation in housing prices an economic geography approach housing prices vary geographically even between neighbouring municipalities local differences can be attributed to differences in socio economic variables and real estate characteristics this article argues that one should additionally take into account the geographical location of municipalities in particular housing prices are affected by distance and travel time to important economic centres offering jobs and extensive services following the economic geography literature we develop a model showing the explicit impact of geographical barriers on housing prices as such we distinguish ourselves from the existing literature on the dynamics of housing prices since geographical elements are fairly constant over time we estimate our model on municipality level housing prices for all 589 belgian municipalities in 2001 we also differentiate between the two main regions of belgium flanders and wallonia our empirical results confirm expectations geographical barriers have significantly negative eff

the spatial dimension of us house prices spatial heterogeneity and spatial dependence are two well established aspects of house price developments however the analysis of differences in spatial dependence across time and space has not gained much attention yet this paper jointly analyses these three aspects of spatial data a panel smooth transition regression model is applied that allows for heterogeneity across time and space in spatial house price spillovers and for heterogeneity in the effect of the fundamentals on house price dynamics evidence is found for heterogeneity in spatial spillovers of house prices across space and time house prices in neighbouring regions spill over more in times of increasing neighbouring house prices then when neighbouring house prices are declining this is interpreted as evidence for the disposition effect moreover heterogeneity in the effect of the fundamentals on house price dynamics could not be detected for all variables real per capita disposable income and the unemployment rate have a homogeneous

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

optimal taxation in theory and practice the optimal design of a tax system is a topic that has long fascinated economic theorists and flummoxed economic policymakers this paper explores the interplay between tax theory and tax policy it identifies key lessons policymakers might take from the academic literature on how taxes ought to be designed and it discusses the extent to which these lessons are reflected in actual tax policy we begin with a brief overview of how economists think about optimal tax policy based largely on the foundational work of ramsey 1927 and mirrlees 1971 we then put forward eight general lessons suggested by optimal tax theory as it has developed in recent decades 1 optimal marginal tax rate schedules depend on the distribution of ability 2 the optimal marginal tax schedule could decline at high incomes 3 a flat tax with a universal lump sum transfer could be close to optimal 4 the optimal extent of redistribution rises with wage inequality 5 taxes should depend on personal characteristics as well as income 6 only final goods ought to be taxed and typically they ought to be taxed uniformly 7 capital income ought to be untaxed at least in expectation and 8 in stochastic dynamic economies optimal tax policy requires increased sophistication for each lesson we discuss its theoretical underpinnings and the extent to which it is consistent with actual tax policy to preview our conclusions we find that there has been considerable change in the theory and practice of taxation over the past several decades although the two paths have been far from parallel overall tax policy has moved in the y n gregory mankiw is professor of economics matthew weinzierl is assistant professor of business administration and danny yagan is a ph d candidate in economics all at harvard university cambridge massachusetts their e mail addresses are ngmankiw

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

changes of numeraire for pricing futures forwards and options a change of numeraire argument is used to derive a general option parity or equivalence result relating american call and put prices and to obtain new expressions for futures and forward prices the general parity result unifies and extends a number of existing results the new futures and forward pricing formulas are often simpler to compute in multifactor models than existing alternatives we also extend previous work by deriving a general formula relating exchange options to ordinary call options a number of applications to diffusion models including stochastic volatility stochastic interest rate and stochastic dividend rate models and jump diffusion models are examined a self financing portfolio is called a numeraire if security prices measured in units of this portfolio admit an equivalent martingale measure the most commonly used numeraire is the reinvested short rate process the corresponding equivalent martingale measure is the risk neutral measure geman el karoui and rochet 1995 show that other numeraires can simplify many asset pricing problems in this article we build on their results and using the reinvested asset price as the numeraire unify and extend the literature on option parity or equivalence results relating american call and put prices for asset and futures options the same numeraire change is used to obtain new pricing formulas for futures and forwards that are often simpler to compute in multifactor models finally we use a numeraire change to simplify exchange option pricing extending a similar result in geman el karoui and rochet to dividend paying assets the change of numeraire method is most intuitive in the context of foreign currency derivative securities as discussed by grabbe 1983 an american call option to buy 1 dm with dollar price process s for k dollars is equivalent to an american put option to sell k dollars with dm price process k s for a strike price of 1 dm the dollar price of the call must therefore equal the product of the current exchange rate s0 and the dm price of the put the call price is computed using the dollar value of a u s i am grateful to kerry back the editor and costis skiadas for their many helpful suggestions thanks also to peter demarzo matt jackson naveen khanna david marshall robert mcdonald jim moser phyllis payette and an anonymous referee for their comments this article subsumes schroder 1992

time changed levy processes and option pricing abstract the classic black scholes option pricing model assumes that returns follow brownian motion but return processes differ from this benchmark in at least three important ways first asset prices jump leading to non normal return innovations second return volatilities vary stochastically over time third returns and their volatilities are correlated often negatively for equities time changed levy processes can simultaneously address these three issues we show that our framework encompasses almost all of the models proposed in the option pricing literature and it is straightforward to select and test a particular option pricing model through the use of characteristic function technology

the finite moment log stable process and option pricing we document a surprising pattern in s p 500 option prices when implied volatilities are graphed against a standard measure of moneyness the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years this behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem clt we develop a parsimonious model which deliberately violates the clt assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon calibration exercises demonstrate its superior performance against several widely used alternatives

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

optimal income taxation an example with a u shaped pattern of optimal marginal tax rates comment using the mirrlees optimal income tax model with quasi linear preferences the paper examines conditions for marginal tax rates to be rising at high income levels and declining in an interval containing the modal skill it examines conditions for the marginal tax rate to be higher at a low skill level than at the high skill level with the same density an argument only holding for skill levels above a cutoff where resources of a worker are marginally of the same value as resources of the government data on earnings rates are presented copyright 1998 by american economic association

real options and american derivatives the double continuation region we study the nonstandard optimal exercise policy associated with relevant capital investment options and with the prepayment option of widespread collateralized borrowing contracts like the gold loan option exercise is optimally postponed not only when moneyness is insufficient but also when it is excessive we extend the classical optimal exercise properties for american options early exercise of an american call with a negative underlying payout rate can occur if the option is moderately in the money we fully characterize the existence the monotonicity the continuity the limits and the asymptotic behavior at maturity of the double free boundary that separates the exercise region from the double continuation region we find that the finite maturity nonstandard policy conspicuously differs from the infinite maturity one this paper was accepted by jerome detemple finance

dynamic relationship between house prices in malaysia s major economic regions and singapore house prices fereidouni h g al mulali u lee j y m and mohammed a h dynamic relationship between house prices in malaysia s major economic regions and singapore house prices regional studies the purpose of this study is to examine house price diffusion among malaysia s major economic regions kuala lumpur selangor pulau pinang and johor and between each of these regions and neighbouring singapore by using the quarterly data from 2000 q1 to 2011 q1 by applying multivariate co integration approach the results show the existence of ripple effects among malaysia s major economic regions moreover it is found that house price diffusion observed within a country can be extended across the border implications are offered along with the findings of this research

the american put option and its critical stock price we derive an expression for the critical stock price for the american put we start by expressing the put price as an integral involving first passage probabilities this approach yields intuition for merton s result for the perpetual put we then consider the finite lived case using 1 the fact that the put value ceases to depend on time when the critical stock price is reached and 2 the result that an american put equals a european put plus an early exercise premium we derive the critical stock price we approximate the critical stock price function to compute accurate put prices kim 1990 jacka 1991 and carr jarrow and myneni 1992 showed that the american put price is equal to the corresponding european put price plus an integral representing the early exercise premium however to use their approach one needs to know the critical stock price which may be defined in three equivalent ways 1 it is the value of the stock price at which one is indifferent between exercising and not exercising the put

optimal indirect and capital taxation we consider an environment in which agents skills are private information and follow arbitrary stochastic processes we prove that it is typically pareto optimal for an individual s marginal benefit of investing in capital to exceed his marginal cost of doing so this wedge is consistent with a positive tax on capital income we also prove that it is pareto optimal for the marginal rate of substitution between any two consumption goods to equal the marginal rate of transformation this lack of a wedge is consistent with uniform taxation of consumption goods within a period

modeling regional house prices we develop a panel model for regional house prices for which both the cross section and the time series dimension is large the model allows for stochastic trends cointegration cross equation correlations and most importantly latent class clustering of regions class membership is fully data driven and based on the average growth rates of house prices and the relationship of house prices with economic growth we apply the model to quarterly data for the netherlands the results suggest that there is convincing evidence for the existence of two distinct clusters of regions with pronounced differences in house price dynamics

asset pricing under the quadratic class we identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector we label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application we consider asset pricing in general and derivative pricing in particular under the quadratic class we provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semi closed form we further illustrate how the quadratic model and the transform methods can be applied to more general settings i introduction we identify and characterize a class of term structure models where bond yields are quadratic functions of the markov process we label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application we identify the necessary and sufficient conditions for the quadratic class and consider the general asset pricing problem under the quadratic framework in particular we propose two transform methods to price a wide variety of interest rate derivatives in closed or semi closed form we further illustrate how the pricing methods can be applied to more general settings examples include option pricing for currencies or stocks with quadratic stochastic volatilities our interests in the quadratic class come mainly from concerns on empirical application recent empirical research within the affine framework of duffie and kan 1996 indicates an inherent tension between i delivering good empirical performance in matching salient features of the interest rate data and ii excluding positive probabilities of having negative interest rates for example backus telmer and wu 1999 and dai and singleton 2000 find that incorporating gaussian state variables in the affine framework significantly increases the flexibility for model design and greatly improves its empirical performance in capturing the conditional dynamics of interest rates dai and singleton 2001

stochastic risk premiums stochastic skewness in currency options and stochastic discount factors in international economies abstract we develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options we estimate the models using time series returns and option prices on three currency pairs that form a triangular relation estimation shows that the average risk premium in japan is larger than that in the us or the uk the global risk premium is more persistent and volatile than the country specific risk premiums and investors respond differently to different shocks we also identify high frequency jumps in each economy but find that only downside jumps are priced finally our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals

the valuation of american options for a class of diffusion processes we present an integral equation approach for the valuation of american style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic our contribution is fourfold first we show that the exercise region is determined by a single exercise boundary under very general conditions on the interest rate and the dividend yield second based on this result we derive a recursive integral equation for the exercise boundary and provide a parametric representation of the american option price third we apply the results to models with stochastic volatility or stochastic interest rate and to american bond options in one factor models for the cases studied explicit parametric valuation formulas are obtained finally we extend results on american capped options to general diffusion prices numerical schemes based on approximations of the optimal stopping time such as approximations based on a lower bound or on a combination of lower and upper bounds are shown to be valid in this context