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

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

commercial land use regulation and local government finance land use regulation in american cities is pervasive taken together these rules probably represent the most significant market intervention undertaken by state and local governments land use regulation includes a wide variety of rules governing the physical location of economic activities within jurisdictions regulations governing the design height or capital intensity of commercial and industrial property rules regarding the minimum lot sizes for residential parcels the number of bedrooms in new dwellings or other restrictions on residential density and rules delineating developer responsibilities for infrastructure provided in newly subdivided areas by international standards regulations in the united states are adopted by rather small units of government i e by towns rather than regional authorities whose objectives are typically confined to narrowly defined geographical portions of metropolitan areas the small scale at which regulations are promulgated and the existence of substitutable sites within metropolitan areas for residential commercial and industrial activity suggest that recognition of competition across jurisdictions is crucial to understanding the impact of land use rules as they affect the quality of life or the fiscal health of the residents of any jurisdiction many economic models ignore these competitive forces concentrating instead upon the case of the regulatory monopolist in consequence there is considerable theoretical uncertainty about the impact of locally adopted regulations upon the utilities of local citizens or their economic wealth a selective review is provided by j m pogodzinski and tim sass 1989 land use regulations in urban areas are motivated by two conceptually distinct concerns the control of externalities and the pursuit of fiscal objectives these mixed objectives make it more difficult to understand the effects of regulation especially since externality arguments are notoriously difficult to confirm in empirical analyses fiscal arguments on the other hand are more easily tested in this paper we investigate a new but increasingly popular form of land use control limitations on the growth of commercial property in one instance we provide bounds on the fiscal implications of controls on commercial property this in turn bounds the magnitude of the implied efficiency gains when the land use policy is viewed as a rational choice by citizens

displaced diffusion option pricing this paper develops a new option pricing formula that pushes the underlying source of risk back to the risk of individual assets of the firm the formula simultaneously encompasses differential riskiness of the assets of the firm their relative weights in determining the value of the firm the effects of firm debt and the effects of a dividend policy with both constant and random components although this setting considerably generalizes the black scholes 1 analysis it nonetheless produces a formula via riskless arbitrage arguments that given estimated inputs is as easy to use as the black scholes formula

foreign aid and economic growth an econometric study of bangladesh bangladesh is one of the poorest countries in the world since independence in 1971 bangladesh has received a large inflow of foreign capital from various countries for rapid economic progress bangladesh thus provides a test case for examining the effectiveness of foreign capital in promoting economic growth focussing on the supply side of the economy an econometric model is developed to quantify the effects of foreign aid and its various components on economic growth the model is tested using available time series data on bangladesh from 1972 to 1988 keeping data limitations measurement problems and other econometric problems in mind the empirical results indicate the domestic resources exert a stronger impact on growth than foreign resources foreign resources in its highly aggregative form do not show any significant contribution to growth however its decomposition into various components show that loans are more effective than grants and food aid is more effective than commodity or period

the effects of health aid on child health promotion in developing countries cross country evidence although epidemiological knowledge in relation to child health has improved in the last few decades around 3 million children die each year in developing countries from preventable diseases the international development community views increased immunization coverage for children as an important step in eliminating or reducing these deaths many developing countries have very limited resources to tackle major health problems and have to rely on external finance this article examines the impact of foreign aid devoted to the health sector on child health promotion in developing countries two proxies for child health promotion are used a immunization against measles and b immunization against diphtheria pertussis tetanus dpt a range of model specifications and panel data econometric techniques are applied to data covering the period 1990 to 2005 this article finds a positive and statistically significant link between health aid and the measures of child health promotion

real investment options with multiple sources of rare events abstract we value real investment options when the underlying asset follows a mixed jump diffusion process involving various types sources of rare events jumps these jumps are assumed independent of each other with each type having a log normally distributed jump size and a random poisson distributed arrival time they may represent uncertainties about the arrival and impact on the underlying investment of new information concerning technological innovation competition political risk regulatory effects and other sources an analytic solution is presented for european claims call or put options with multiple sources of jumps a discrete time markov chain methodology implemented within a finite difference scheme is proposed for the valuation of american as well as european options the approach is also applicable to financial options with multiple types of rare events the approach is illustrated through valuing complex real options with compound features involving interactions between optimal investment and subsequent operating decisions specifically we value a growth option and an extension option

the use of the control variate technique in option pricing this paper presents a generalized version of the lattice approach to pricing options it shows how the control variate technique can produce significant improvements in the effi ciency ofthe approach the control variate technique is illustrated using american puts on dividend and nondividend paying stocks

on the theory of growth controls numerous empirical studies have examined the effect of growth controls on housing prices these studies have used many different techniques ranging from hedonic price model estimation to paired comparisons but have all come to the same conclusion growth controls raise the price of housing in theory there are both demand and supply side explanations which need not be mutually exclusive for these observed price differences on the supply side housing caps zoning restrictions limitations on the amount of developable land and other forms of growth control may reduce the supply of housing over time this in turn may produce scarcity effects which manifest as shifts or other changes in the housing supply curve and attendant price increases on the demand side to the extent that growth controls may reduce or internalize expected negative externalities and or congestion costs associated with growth controls may also produce amenity effects such amenity effects manifest as changes in the demand curve and likewise may be capitalized in land values and wages e g the price of a house rises as commute time falls

foreign aid and economic growth in cameroon cameroon is classified as a lower middle income country since it became a unified and independent country in 1961 cameroon has received significant amounts of foreign aid most of it from france and the european economic community since the 1960s economic growth in the country has been quite significant between 1965 and 1980 the gross domestic product grew at an average annual rate of 5 1 and at a rate of 2 3 between 1980 and 1990 cameroon seems a good test case for determining the effects of foreign aid on economic growth in developing countries an econometric model based on the neoclassical production function is developed and used to test the relationship between foreign aid and eonomic growth the model is tested using time series datd on the country from 1971 to 1990 the results show that domestic resources have a stronger impact on economic growth in cameroon than foreign resources these results however must be taken with the understanding that the data suffer from measurement probl

distributive politics ward representation and the spread of zoning this analysis examines two alternative explanations for the adoption of comprehensive zoning ordinances in the years immediately following its initial adoption in new york city the market failure explanation predicts zoning adoption in cities where externality problems represented by heavy incidence of manufacturing exist the distributive policymaking model treats zoning as a form of regulation that is most likely to be found in cities where local legislators are elected from geographically concentrated constituencies e g wards and therefore try to target policy benefits to their own constituencies while spreading the policy costs over all constituencies some support is found for each model especially striking is the interactive effect of ward representation and of economic interest i e levels of home ownership

the impact of default risk on the prices of options and other derivative securities abstract this paper presents a model for valuing derivative securities when there is default risk the holder of a security is assumed to recover a proportion of its no default value in the event of a default by the counterparty both the probability of default and the size of the proportional recovery are random the paper shows how data on bonds issued by the counterparty can be used to provide information about model parameters

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

convergence from discrete to continuous time contingent claims prices this article generalizes the cox ross and rubinstein 1979 binomial option pricing model and establishes a convergence from discrete time multivariate multinomial models to continuous time multidimensional diffusion models for contigent claims prices the key to the approach is to approximate the n dimensional diffusion price process by a sequence of n variate n 1 nomial processes it is shown that contingent claims prices and dynamic replicating portfolio strategies derived from the discrete time models converge to their corresponding continuous time limits article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

competing interests and the political market for smart growth policy the broad intent of smart growth is to reduce development in environmentally sensitive areas by limiting the outward expansion of development and redirecting private investment to urban areas local decisions that shape and constrain land uses can pit narrow economic interests against broader based environmental organisations and impact decisions on smart growth based on the political market framework this study specifically examines the influence of pro growth and smart growth interest groups on smart growth policies adopted by local governments in the state of massachusetts usa the results suggest both real estate interests and environmental groups influence local policy decisions and depending on the policy the characteristics of local political institutions mediate these influences

aid growth nexus empirical evidence from fiji foreign aid to the island economies is a major source for foreign exchange and resource needs this paper presents an empirical analysis of the relationship between foreign aid and economic growth in the case of fiji a neoclassical production function is applied to estimate the aid growth nexus since the data employed are time series for the period 1968 to 1996 the autoregressive distributed lag approach to cointegration is utilized to estimate the models components of total aid such as grant aid loan aid technical cooperation bilateral and multilateral aid flows are also utilized to estimate a disaggregated short run and long run relationship between foreign aid and economic growth the results show that total aid flows and its various forms i e bilateral aid grant aid and technical cooperation grant aid has a significant impact on economic growth in fiji as for domestic resources only exports and private investments in two equations show positive contribution to growth

a note on the convergence of binomial pricing and compound option models the binomial pricing model of cox ross and rubinstein 2 and the compound option model of geske 3 are both elegant and self contained frameworks for the valuation of american options and related contingent claims each providing us with a distinctive valuation procedure flexible enough to be adapted to a wide variety of problems for american type options on assets with a prices following a lognormal diffusion process and b a continuous time exercise policy such as put options on individual stocks calls and puts on foreign exchange and calls and puts on futures contracts the binomial pricing model approximates both the stochastic process and the exercise opportunity set the latter by restricting exercise to a discrete set of dates the compound option model on the other hand approximates only the exercise opportunity set however it pays for this with a high price in computational requirements specifically with n exercise dates allowed multivariate normal probabilities of every order up to and including n must be evaluated in their article on the valuation of put options geske and johnson 4 provide an ingenious solution to this problem by applying acceleration techniques common in numerical analysis but new to the finance literature letting t be the time to expiration of the option and p the value of a compound option with exercise permitted at the n uniformly spaced dates t n 2t n t they generate the sequence of compound option values p1 p2 pn polynomial extrapolation is then used to estimate p lim n x oo pn they found this procedure to be very accurate over a limited sample of put options with low values of n though not discussed by geske and johnson the reasons for the effectiveness of acceleration techniques in a compound option model are apparent from a cursory examination an acceleration technique will perform best when the approximating sequence converges uniformly on the true value of the contingent claim and worst when convergence includes complex and unpredictable oscilla

an analytic approximation for the american put price black and scholes 1 derived the pricing equation for a european put when the stock price follows geometric brownian motion for this same case merton 5 derived the pricing equation for an american put with infinite time to maturity brennan and schwartz 2 rubinstein and cox 7 and parkinson 6 have developed numerical solutions for the price of an american put numerical solutions are expensive and do not provide much intuition naturally an analytic solution would be much preferred unfortunately pricing the american put requires solving a formidable and presumably intractable boundary value problem

testing the heath jarrow morton ho lee model of interest rate contingent claims pricing this paper presents empirical tests of the constant volatility version of the heath jarrow and morton model which is also the continuous time limit of the ho and lee model using a generalized method of moments gmm test on three years of daily data for eurodollar futures and futures options the model can be rejected for most subperiods various biases in the fitted option prices relative to the market prices are documented through a regression study the small sample properties and power of the gmm framework to this setting are also studied through simulations

are convertible bonds underpriced an analysis of the french market we investigate the pricing of convertible bonds on the french convertible bond market using daily market prices for a period of 18 months instead of a firm value model as used in previous studies we use a stock based binomial tree model with exogenous credit risk that accounts for all important convertible bond specifications and is therefore well suited for pricing convertible bonds the empirical analysis shows that the theoretical values for the analyzed convertible bonds are on average more than 3 higher than the observed market prices this result applies to both the standard convertibles and the exchangeable bonds in our sample the difference between market and model prices is greater for out of the money convertibles than for at or in the money convertibles a partition of the sample according to maturity indicates that there is a positive relationship between underpricing and maturity with decreasing mispricing for bonds with shorter time to maturity

german aid and trade versus namibian gdp and labour productivity this paper examines the effects of german foreign aid to and net trade with namibia on namibia s recent 1985 95 economic performance the analysis suggests significant benefits for namibia from trade with and assistance from germany however domestic capital is found to determine namibian economic growth more than net trade with germany and german foreign aid to namibia while the effect of german capital tends be larger than that of german aid a need for direct foreign investment from germany to namibia is inferred two types of further investigations are required a joint determination of economic growth aid trade and capital formation and a disaggregation of german aid to namibia with an analysis of its individual impacts compared with similar effects of aid from other donors

the value of early exercise in option prices an empirical investigation previous studies in the valuation of american options apparently undervalue the right of early exercise this study uses actual prices from the cboe s s p 100 option instead of model generated values deviations from the theoretical put call parity relationship are caused by the possibility of early exercise these deviations are used to infer the value of early exercise the actual value of early exercise is both statistically and economically significant as expected from theoretical considerations the value of early exercise for put options is greater than for call options

option pricing when the variance is changing the monte carlo method is used to solve for the price of a call when the variance is changing stochastically

politics institutions and local land use regulation summary this article investigates the factors that account for second generation land use restrictions that result from comprehensive planning processes after a review of the evolution of growth management policy in the us variation among florida counties in the adoption of development impact fees and regulatory complexity is examined political system institutions were found to be related to growth management policies as predicted by distributive theories of urban politics in particular elected mayor commission government was linked to growth management these results indicate that second generation land use regulation may be driven as much by the political incentives of local actors as the preferences of the median voter

an analytic approximation for the american put price for options on stocks with dividends in a recent paper johnson 7 has given an analytic approximation to the american put price that delivers values that are very close to numerical solutions the limitation to the johnson approximation is that it is only applicable to put options on stocks without cash dividends this study modifies the johnson approximation to value options on stocks that have one exdividend date prior to the option expiration date and these approximation values are compared to the analytic solutions provided by the geske and johnson 6 american put option pricing model the approximation values are generally very close to the analytic solutions

community power and population increase an empirical test of the growth machine model attempts to relate community power to policy outputs have been criticized for lacking theoretical relevance and statistical significance to overcome these criticisms this research employs a power policy model based on a political economy framework which utilizes molotch s conpetion of the community as a growth machine analysis of the permanent community sample provides strong power policy relationships that support the major tenets of the growth machine explanation as members of the business elite gain power they can successfully promote population growth that provides them with greater profits through higher property values the most widely cited common good for growth lower unemployment does not accrue this supports the relevance of a political economy approach to community phenomena and suggests different directions for community power research

a lattice approach for pricing of multivariate contingent claims abstract the lattice approach developed by boyle evnine and gibbs beg is hitherto one of the most appealing when it comes to pricing multivariate contingent claims the beg approach has however some problems two of the major ones being that the method can lead to negative jump probabilities and has a slow rate of convergence in this paper a lattice approach the nek approach is developed which avoids both of the aforementioned problems of the beg approach it is shown that the nek approach has a very fast rate of convergence the results are accurate enough for most needs with as few as ten time steps and the results are astonishingly accurate with twenty time steps moreover the nek approach is simple and easy to understand and also easy to implement the latter property follows from the fact that all jump probabilities are equal and that the formulas for the jump sizes are extremely simple

growth in africa does the source of investment financing matter this paper examines empirical evidence for 11 sub saharan african countries on the relationship between economic growth and three principal sources of investment funds foreign aid foreign direct investment and domestic saving in light of the shortcomings of traditional cross section analyses the time series approach is used instead modern time series methods are rigorously applied beginning with unit root tests and followed by model specifications that reflect the revealed temporal behaviours of the variables in each of the 11 countries domestic saving seems to play a somewhat more important role in generating economic growth than foreign direct investment or foreign aid however the mixture of results across the 11 countries implies that in general it is not possible to rank one source of investment financing ahead of any other

the impact of foreign aid on economic growth in papua new guinea this article investigates the impact of foreign aid on economic growth in papua new guinea png using time series data for the period 1965 to 1999 following the most recent literature the article examines whether aid effectiveness is conditional on levels of economic policy and governance an empirical model is estimated using the autoregressive distributed lag ardl approach to cointegration proposed by pesaran and shin 1995 results provide little evidence that aid and its various components have contributed to economic growth in png there is some evidence that aid is more effective during periods when the country has undertaken a world bank structural adjustment program sap an alternative interpretation is that a sap may be more effective at spurring growth when supported by foreign aid

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

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