majority voting and corporate control the rule of the dominant shareholder this paper incorporates a model of corporate control into a general equilibrium framework for production economies with incomplete markets the classical objective of value maximization is extended but is indeterminate instead firms are viewed as being subject to shareholder control via some decision mechanism as long as this decision mechanism is responsive to a unanimous preference by shareholders shareholder control is consistent with but stronger than value maximization next the particular institution of majority voting by shareholders is examined it is shown that for generic economies a majority rule equilibrium for a firm implies that production is optimal for the largest or dominant shareholder finally a more realistic control mechanism is considered in which majority voting by shareholders is constrained by a group of shareholders or board of directors who control the voting agenda the result is that shareholders not on the board have no influence on the equilibrium production choice of the firm

analytical evaluation of volatility forecasts estimation and forecasting for realistic continuous time stochastic volatility models is hampered by the lack of closed form expressions for the likelihood in response andersen bollerslev diebold and labys econometrica 71 2003 579 625 advocate forecasting integrated volatility via reduced form models for the realized volatility constructed by summing high frequency squared returns building on the eigenfunction stochastic volatility models we present analytical expressions for the forecast efficiency associated with this reduced form approach as a function of sampling frequency for popular models like garch multifactor affine and lognormal diffusions the reduced form procedures perform remarkably well relative to the optimal infeasible forecasts

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

answering the skeptics yes standard volatility models do provide accurate forecasts a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using arch and stochastic volatility models while most of these studies have documented highly significant in sample parameter estimates and pronounced intertemporal volatility persistence traditional ex post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts contrary to this contention we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications new methods for improved ex post interdaily volatility measurements based on high frequency intradaily data are also discussed

models of stock returns a comparison in this paper a discrete mixture of normal distributions is proposed to explain the observed significant kurtosis fat tails and significant positive skewness in the distribution of daily rates of returns for a sample of common stocks and indexes stationarity tests on the parameter estimates of this discrete mixture of normal distributions model revealed significant differences in the mean estimates that can explain the observed skewness and significant differences in the variance estimates that can explain the observed kurtosis an alternative explanation for the observed fat tails is the symmetric student model the result of a comparison between the models is that the discrete mixture of normal distributions model has substantially more descriptive validity than the student model for many years both financial economists and statisticians have been concerned with the description of stock market returns the form of the distribution of stock returns is a crucial assumption for mean variance portfolio theory theoretical models of capital asset prices and the prices of contingent claims for example understanding the behavior of the variance is essential to option pricing models empirical tests of asset pricing models and the efficient markets hypothesis draw statistical inferences that are also conditional on distributional assumptions the most convenient assumption for financial theory and empirical methods is that the distribution of security rates of return be multivariate normal with parameters that are stationary over time since the normal distribution is stable under addition any arbitrary portfolio of stocks will also be normally distributed with the additional assumption of risk aversion mean variance theory follows furthermore the assumptions of normality and parameter stationarity are required for most of the econometric techniques typically used in empirical research tests of the normality hypothesis on the daily returns of the dow jones industrial stocks by fama 121 revealed more kurtosis fatter tails than that predicted from a sample of independent and identically distributed normal variates fama concluded from this evidence that the distribution of price changes conforms better to the stable paretian distribution with characteristic exponent

approximate option valuation for arbitrary stochastic processes abstract we show how a given probability distribution can be approximated by an arbitrary distribution in terms of a series expansion involving second and higher moments this theoretical development is specialized to the problem of option valuation where the underlying security distribution if not lognormal can be approximated by a lognormally distributed random variable the resulting option price is expressed as the sum of a black scholes price plus adjustment terms which depend on the second and higher moments of the underlying security stochastic process this approach permits the impact on the option price of skewness and kurtosis of the underlying stock s distribution to be evaluated

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

computational economics and economic theory substitutes or complements abstract this essay examines the idea and potential of a computational approach to theory discusses methodological issues raised by such computational methods and outlines the problems associated with the dissemination of computational methods and the exposition of computational results we argue that the study of a theory need not be confined to proving theorems that current and future computer technologies create new possibilities for theoretical analysis and that by resolving these issues we will create an intellectual atmosphere in which computational methods can make substantial contributions to economic analysis

determinacy and identification with taylor rules the new keynesian taylor rule theory of inflation determination relies on explosive dynamics by raising interest rates in response to inflation the fed induces ever larger inflation unless inflation jumps to one particular value on each date however economics does not rule out explosive inflation so inflation remains indeterminate attempts to fix this problem assume that the government will choose to blow up the economy if alternative equilibria emerge by following policies we usually consider impossible the taylor rule is not identified without unrealistic assumptions thus taylor rule regressions do not show that the fed moved from passive to active policy in 1980

valuation of power options under heston s stochastic volatility model abstract we derive semi analytic solutions for power option prices under the heston model specifically the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment unlike the majority of stochastic volatility models there remains a significant problem to check the existence of moments of assets prices of order higher than one fortunately the moment explosion property under the heston model is examined systematically in andersen and piterbarg 2000 incorporating with their results we present explicit formulas for moment generating function of log price and for power option prices under the circumstances when the corresponding moments are finite in case that the corresponding moment explodes we provide two numerical methods to derive prices of power put and capped power call options in spite of a simple idea numerical examples show that the approximations are extremely accurate and efficient

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

information time option pricing theory and empirical evidence abstract with a stochastic time change from calendar time to information time we derive a parsimonious option pricing formula with stochastic volatility as a risk neutral poisson sum of merton s 1973 prices over the option s information time maturity domain the formula contains two unobservable parameters information arrival intensity and information time asset volatility with stochastic volatility induced by random information arrival when the information arrival rate intensifies the option price increases and vice versa we test the formula in pricing hedging and excess profits capture empirically using currency and the s p 500 futures options transaction data

computing equilibria when asset markets are incomplete existence of equilibrium with incomplete markets is problematic because demand functions are typically not continuous discontinuities occur at prices for which a marketed asset suddenly becomes redundant we show that this discontinuity disappears if we allow an agent in the economy to introduce a new asset when such redundancies occur this enables us to prove existence with incomplete markets using a standard path following argument hence available algorithms for path following in r k can be applied to compute equilibria in the gei case we demonstrate this by computing equilibrium for a numerical example

on jumps in common stock prices and their impact on call option pricing the black scholes call option pricing model exhibits systematic empirical biases the merton call option pricing model which explicitly admits jumps in the underlying security return process may potentially eliminate these biases we provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of nyse listed common stocks however we find no operationally significant differences between the black scholes and merton model prices of the call options written on the sampled common stocks

self fulfilling recessions at the zero lower bound abstract we highlight an overlooked source of equilibrium multiplicity in monetary economies subject to a zero bound on nominal interest rates in environments with sufficient endogenous propagation depressed contemporary economic conditions must directly lower expectations of future output and inflation a current recession followed by gradual convergence back to steady state may then be an equilibrium outcome without any exogenous impulse we present this mechanism heuristically in partial equilibrium and in two computed examples of new keynesian economies expansionary fiscal policy makes the recessionary equilibrium more severe at the margin but commitment to a sufficiently large expansion can rule out multiplicity

stochastic volatility option pricing this paper examines alternative methods for pricing options when the underlying security volatility is stochastic we show that when there is no correlation between innovations in security price and volatility the characteristic function of the average variance of the price process plays a pivotal role it may be used to simplify fourier option pricing techniques and to implement simple power series methods we compare these methods for the alternative mean reverting stochastic volatility models introduced by stein and stein 1991 and heston 1993 we also examine the biases in the black scholes model that are eliminated by allowing for stochastic volatility and we correct some errors in the stein and stein 1991 analysis of this issue empirical evidence on underlying asset prices and on their derivatives strongly suggests that asset price volatility is stochastic the pricing of options under this condition is therefore an important problem in this paper we study alternative option pricing methods that account for stochastic volatility we are particularly concerned with power series methods which we show to be quite accurate and easy to implement for alternative volatility specifications we point out their relation with recently proposed exact methods this permits a precise assessment of the approximation involved in the simple power series approach and of the impact of stochastic volatility on option prices following garman 1976 stochastic volatility option prices must satisfy a bivariate fundamental partial differential equation pde in the two state variables security price and volatility since volatility is not spanned by assets in the econ omy the volatility risk may not be eliminated by arbitrage methods therefore its market price explicitly enters into the pde the associated risk premium is owen graduate school of management vanderbilt university nashville tn 37203 and universita di siena facolta di scienza economiche e bancarie 53100 siena italy respectively part of this research was supported from a grant from the dean s fund and the financial markets research center at the owen school of management vanderbilt university some of this research was completed while roma was visiting the anderson graduate school of management ofthe university of california at los angeles we thank participants of the finance accounting and economics workshop at the owen school of management vanderbilt university for useful comments we appreciate the suggestions of roger huang craig lewis ron masulis and walter torous we thank joanne ball for editorial

common factors and local factors implications for term structures and exchange rates this paper studies a multi factor two country term structure and exchange rate model when a diversification effect for an international bond portfolio is expected it shows that the diversification gain calls upon certain restrictions on the process of the stochastic discount factor in a factor structured economy existence of local factors is shown to be a necessary condition for the gains from investing in foreign bonds further the exchange rate risk premia are shown to be a function of the differentials of the risk premia of the factors in bond returns empirical results reveal the tendency for investors to respond sensitively to rare shocks which is shown to be a potential solution to the forward premium puzzle

option valuation and hedging strategies with jumps in the volatility of asset returns we develop a model in which the volatility of risky assets is subject to random and discontinuous shifts over time we derive prices of claims contingent on such assets and analyze options based trading strategies to hedge against the risk of jumps in the return volatility unsystematic and systematic events such as takeovers major changes in business plans or shifts in economic policy regimes may drastically alter firms risk profiles our model captures the effect of such events on options markets lumpy arrival of information has long been recognized as a phenomenon of considerable importance in financial markets following merton 1976 1 much of the literature on contingent claims valuation under discontinuous information arrival has studied the case where jumps occur in asset values in this article we model the discontinuous resolution of uncertainty in a new way we allow for the volatility of an asset s return to change randomly and discretely we then derive and analyze valuation equations for claims contingent on such an asset we also show how certain traded options together with the underlying stock and a riskless bond can be used to insure against jumps in the volatility of an asset s returns stock price movements in our model fluctuate randomly between low and high volatility regimes discontinuous changes in the volatility of stock prices may be a result of significant changes in a firm s operating and financial structure its competitive environment or its corporate plan reorganizations caused by takeovers and mergers may also occasion such volatility shifts changes in uncertainty in our model could also be systematic and a result of aggregate supply shocks or shifts in economic policies and political regimes our model can also be interpreted as a model of a market where from time to time firms face the release of an important piece of information that may affect their stock prices significantly the market participants may be aware

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

a hybrid stock trading system using genetic network programming and mean conditional value at risk abstract this paper describes a hybrid stock trading system based on genetic network programming gnp and mean conditional value at risk model gnp cvar the proposed method combining the advantages of evolutionary algorithms and statistical model has provided useful tools to construct portfolios and generate effective stock trading strategies for investors with different risk attitudes simulation results on five stock indices show that model based on gnp and maximum sharpe ratio portfolio performs the best in bull market and that based on gnp and the global minimum risk portfolio performs the best in bear market the portfolios constructed by markowitz s mean variance model performs the same as mean cvar model it is clarified that the proposed system significantly improves the function and efficiency of original gnp which can help investors make profitable decisions

the pricing of stock index options in a general equilibrium model this paper analyzes the pricing of stock index options in a simple general equilibrium model in this model the volatility of the stock index and the spot rate of interest are functions of a stochastic variable the paper investigates the biases that arise when using the black scholes model with the assumed volatility and interest rate dynamics it is shown that the model can in principle explain the biases observed in empirical work on stock index options

speed limit policies the output gap and optimal monetary policy in a standard new keynesian model a myopic central bank concerned with stabilizing inflation and changes in the output gap will implement a policy under discretion that replicates the optimal timeless perspective precommitment policy by stabilizing output gap changes the central bank imparts inertia into output and inflation that is absent under pure discretion even a fully optimizing i e non myopic central bank operating in a discretionary policy environment achieves better social outcomes if it focuses on inflation and changes in the output gap than are achieved under inflation targeting this abstract was borrowed from another version of this item

the risk premium of volatility implicit in currency options this article provides an empirical investigation of the risk neutral variance process and the market price of variance risk implied in the foreign currency options market there are three principal contributions first the parameters of heston s mean reverting square root stochastic volatility model are estimated using dollar mark option prices from 1987 to 1992 second it is shown that these implied parameters can be combined with historical moments of the dollar mark exchange rate to deduce an estimate of the market price of variance risk these estimates are found to be nonzero time varying and of sufficient magnitude to imply that the compensation for variance risk is a significant component of the risk premia in the currency market finally the out of sample test suggests that the historical variance and the hull and white implied variance contain no more information than that imbedded in the heston implied variance

implied volatilities and transaction costs using data that contain bid and ask quotes for both options and stocks the analysis investigates the constant volatility assumption of the black scholes model the analysis adjusts for bid ask spreads and finds evidence that is inconsistent with the constant volatility assumption instead the results reveal a strong negative correlation between volatility and stock price and they suggest that using a nonconstant volatility model such as the cev model would be more appropriate to price long term options finally transaction costs associated with the dynamic hedge tend to increase with an option s maturity but decrease as a percentage of the option s price

inflation determination with taylor rules is new keynesian analysis critically flawed abstract cochrane 2007 has strongly questioned the basic economic logic of current monetary policy analysis arguing that new keynesian nk models imply rational expectations paths with explosive inflation that do not imply explosions in real variables relevant for transversality conditions consequently the usual logic does not rule out solutions with explosive inflation that result does not however justify negative conclusions about nk analysis for a different criterion is logically satisfactory it is that to be plausible a re solution must satisfy the property of least squares learnability adoption of this criterion serves to justify in principle the bulk of current mainstream analysis

pricing and hedging in incomplete markets abstract we present a new approach for positioning pricing and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable by assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure we derive a counterpart to the first fundamental theorem of asset pricing we also derive a counterpart to the second fundamental theorem which leads to unique derivative security pricing and hedging even though markets are incomplete for products that are not spanned by the liquid assets of the economy we show how our methodology provides more realistic bid ask spreads

small dimension pde for discrete asian options abstract this paper presents an efficient method for pricing discrete asian options in presence of smile and non proportional dividends using an homogeneity property we show how to reduce an n 0 dimensional problem to a one or two dimensional one we examine different numerical specifications of our dimension reduced pde using a crank nicholson method interpolation method grid boundaries time and space steps as well as the extension to the case of non proportional discrete dividends using a jump condition we benchmark our results with quasi monte carlo simulation and a multi dimensional pde

an analytical approximation formula for european option pricing under a new stochastic volatility model with regime switching abstract in this paper an analytical approximation formula for pricing european options is obtained under a newly proposed hybrid model with the volatility of volatility in the heston model following a markov chain the adoption of which is motivated by the empirical evidence of the existence of regime switching in real markets we first derive the coupled pde partial differential equation system that governs the european option price which is solved with the perturbation method it should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved and numerical experiments confirm that our formula could provide quite accurate option prices especially for relatively short tenor ones finally empirical studies are carried out to show the superiority of our model based on s p 500 returns and options with the time to expiry less than one month

optimal simple and implementable monetary and fiscal rules welfare maximizing monetary and fiscal policy rules are studied in a model with sticky prices money and distortionary taxation the ramsey optimal policy is used as a point of comparison the main findings are the size of the inflation coefficient in the interest rate rule plays a minor role for welfare it matters only insofar as it affects the determinacy of equilibrium optimal monetary policy features a muted response to output interest rate rules that feature a positive response to output can lead to significant welfare losses the welfare gains from interest rate smoothing are negligible optimal fiscal policy is passive the optimal monetary and fiscal rule combination attains virtually the same level of welfare as the ramsey optimal policy

computing equilibria in the general equilibrium model with incomplete asset markets abstract we present an intuitive homotopy algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets the central concept is the introduction of utility maximization problems for all but one agent with penalties for transactions on the asset markets we compute equilibria with homotopy path following techniques using the first order conditions of the agents optimization problems and gradually lifting the penalty restriction as the algorithm proceeds finally we present computational results from an implementation of the algorithm showing convincingly that the algorithm is very reliable in general and suitable for large scale computations

increasing returns in infinite horizon economies this paper shows that in a general equilibrium model with an infiniite holizonl in whichi productionl may exhibit increasing returns to scale or non conivexities marginal cost pricing equilibria exist anid are essential that is stable witlh respect to small perturbationis of the economily as in many important models of mairket imperfections marginal cost pricinig equilibria need not be pareto optimal in the presence of noni convexities so the systematic approaches to equilibrium analysis in infinite dimenisionial commodity spaces which rely crucially oln the first welfare theorem cainnot be used instead this paper introduces leray schauder degree theory the extension of degree theor y to banacih and locally convex spaces as the natural methodology for showinlg that equilibria exist and for anialyzing qualitative features of equilibria such as local uniqueness or essentiality

general equilibrium models and homotopy methods abstract our purpose is to argue the inevitable and lasting role which homotopy methods will play in both theoretical and applied economic analysis the essence of our position is that large equilibrium models are needed to anticipate adjustments in the economy following policy changes or shock events and that homotopy methods are needed to analyze these equilibrium models in addition to the computation of equilibria homotopy methods will play an important role in the study of multiplicity of equilibria t tonnement comparative statics and market instability

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

a note on parental and child risk valuation the paper develops a model that allows the estimation of parent s valuation of own and child health in an endogenous risk framework where parents can employ multiple activities to protect themselves and their children from a health risk these risk reducing activities may differ in their effectiveness and their intensity of use we suggest how to estimate the parent s ex ante marginal willingness to pay for a reduction in the ambient level of health risk unencumbered by expected utility terms

on the number of state variables in options pricing in this paper we investigate the methodological issue of determining the number of state variables required for options pricing after showing the inadequacy of the principal component analysis approach which is commonly used in the literature we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and maturities as proxies for the transformed state variables the methodology is applied to the prices of s p 500 index options from the period 1996 2005 we find that in addition to the index value itself two state variables approximated by the first two nonlinear principal components are adequate for pricing the index options and fitting the data in both time series and cross sections

determining optimal monetary speed limits abstract the proposal by walsh 2003 that policy should include a speed limit by having the change in the output gap as an additional term in a taylor type rule is shown to be exactly optimal given an appropriate parameterization

stock price volatility mean reverting diffusion and noise abstract using weekly call option prices on twenty five stocks over a ten year period 1975 1985 and calls on the s p 500 stock index futures we find that ex ante market volatility follows a mixed mean reverting diffusion with noise process changes in volatility are correlated across stocks and a marketwide volatility effect is found strong forces pull the volatility back to its long term value the findings suggest the development of new option pricing models

an empirical comparison of continuous time models of implied volatility indices abstract we explore the ability of alternative popular continuous time diffusion and jump diffusion processes to capture the dynamics of implied volatility indices over time the performance of the various models is assessed under both econometric and financial metrics to this end data are employed from major european and american implied volatility indices and the rapidly growing cboe volatility futures market we find that the addition of jumps is necessary to capture the evolution of implied volatility indices under both metrics mean reversion is of second order importance though the results are consistent across the various metrics markets and construction methodologies

hedging options under transaction costs and stochastic volatility in this paper we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility extensive research has clearly demonstrated that the volatility of most stocks is not constant over time as small changes of the volatility can have a major impact on the value of contingent claims hedging strategies should try to eliminate this volatility risk we propose a stochastic optimization model for hedging contingent claims that takes into account the effects of stochastic volatility transaction costs and trading restrictions simulation results show that our approach could improve performance considerably compared to traditional hedging strategies

option values under stochastic volatility theory and empirical estimates abstract this paper numerically solves the call option valuation problem given a fairly general continuous stochastic process for return volatility statistical estimators for volatility process parameters are derived and parameter estimates are calculated for several individual stocks and indices the resulting estimated option values do not differ dramatically from black scholes values in most cases although there is some evidence that for longer maturity index options black scholes overvalues out of the money calls in relation to in the money calls

variances of security price returns based on high low and closing prices in a recent paper garman and klass 1980 studied the problem of estimating capital asset price volatility parameters developing an idea first introduced by parkinson 1980 they argue that improved volatility measures can be obtained by taking into account the daily high low and opening prices in addition to the traditionally used closing prices this paper is concerned mainly with testing the empirical validity of different volatility estimators based on high low and closing prices

option arbitrage and strategy with large price changes abstract arbitrage pricing theorems are derived for options on stocks with jumps as a well as local movements the resulting valuation formulas depend on observable variables only closed form valuation expressions are obtained in the case of large positive and negative jumps these results translate into a simple algebra for characterizing the risk of arbitrage and investment portfolios a continuous time formulation of the infinite variance hypothesis leads to isomorphic pricing expressions

valuation of american futures options theory and empirical tests this paper reviews the theory of futures option pricing and tests the valuation principles on transaction prices from the s p 500 equity futures option market the american futures option valuation equations are shown to generate mispricing errors which are systematically related to the degree the option is in the money and to the option s time to expiration the models are also shown to generate abnormal risk adjusted rates of return after transaction costs the joint hypothesis that the american futures option pricing models are correctly specified and that the s p 500 futures option market is efficient is refuted at least for the sample period january 28 1983 through december 30 1983 futures option contracts now trade on every major futures exchange and on a wide variety of underlying futures contracts the chicago mercantile exchange the chicago board of trade the new york futures exchange and the commodity exchange now collectively have more than twenty options written on futures contracts where the underlying spot commodities are financial assets such as stock portfolios bonds notes and eurodollars foreign currencies such as west german marks swiss francs and british pounds precious metals such as gold and silver livestock commodities such as cattle and hogs and agricultural commodities such as corn and soybeans moreover new contract applications are before the commodity futures trading commission and should be actively trading in the near future with the markets for these new contingent claims becoming increasingly active it is appropriate that the fundamentals of futures option valuation be reviewed and tested black 5 provides a framework for the analysis of commodity futures options although his work is explicitly directed at pricing european options on forward contracts it applies to european futures contracts as well if the riskless rate of interest is constant during the futures option life 1 the options currently

option pricing and implicit volatilities abstract this paper demonstrates that black scholes implied volatilities can be used to value options in many situations where the assumptions of the black scholes model are violated including i alternative stock processes ii stochastic interest rates and iii market frictions given its computational simplicity this procedure provides an attractive alternative to the more complex models with a direct estimation procedure

an extension of the modigliani miller theorem to stochastic economies with incomplete markets and interdependent securities the modigliani miller theorem is shown to hold in a general model of a multiperiod stochastic economy with incomplete markets and perfect foresight in the model firms are allowed to trade all available securities thus share prices and dividends become fully interdependent also several mechanisms of corporate control are considered including value maximization and shareholder voting it is demonstrated that firms have no incentive to trade securities in equilibrium further any such trading does not alter the set of equilibrium allocations this is done by establishing that agents are able to adjust their own portfolios and neutralize corporate policy journal of economic literature classification numbers 021 022 this paper extends the modigliani miller argument on the irrelevance of corporate financial policy to an economy with incomplete markets and fully interdependent securities the approach taken is a general equilibrium model incorporating multiple periods and uncertain states the market is idealized in that there are no transaction costs short sales restrictions or limited liability constraints also agents are assumed to have fully rational expectations regarding future events within this context it is shown that value maximizing firms have no incentive to change the composition of their portfolios and that any such changes have no effect on equilibrium prices and allocations within the economy finally the theory is shown to

tariffs as insurance optimal commercial policy when domestic markets are incomplete free trade is not optimal for a small country that faces uncertain terms of trade if some factors are immobile ex post and markets for contingent claims are incomplete the government can improve social welfare by using commercial policy that serves as a partial substitute for missing insurance markets using a combination of analytical and simulation techniques we demonstrate that optimal policy for this purpose will often have an anti trade bias we also show that the usual preference by economists for factor or product taxes and subsidies over tariffs and export subsidies may not be justified in this context this abstract was borrowed from another version of this item

a risk reserve model for hedging in incomplete markets abstract this paper presents a new approach to the pricing and hedging problem for contingent claims in incomplete markets we assume that traders wish to maximize the expected final payoff of the hedging portfolio and the claims and we avoid the use of utility functions instead we model how traders are punished when taking excessive risks in practice to do so we introduce an extra reserve bank account which earns a smaller rate of return than a standard deposit bank account the reserve account should always contain a minimal amount of money which depends on the risk that the trader s portfolio is exposed to we focus on a specific example which uses option price sensitivities the greeks to specify the risk the resulting optimization problem can then be solved in a rather explicit form and we show how the solution naturally leads to bid ask spreads prices which depend on the trader s current position and implied volatility smiles

a bayesian approach to modeling stock return volatility for option valuation new measures of stock return volatility are developed to increase the precision of stock option price estimates with bayesian statistical methods volatility estimates for a given stock are developed using prior information on the cross sectional patterns in return volatil ities for groups of stocks sorted on size financial leverage and trading volume call option values computed with the bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility standard historical volatility or even the actual ex post volatility that occurred during each option s life although the bayesian methods produce biased call price estimators they do reduce the systematic tendency of standard pricing approaches to overprice underprice options on high low volatility stocks little bias improvement is observed with respect to the time to maturity and moneyness of the call options

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

hedging derivative securities and incomplete markets an e arbitrage approach given a european derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based we solve the optimal replication problem find a self financing dynamic portfolio strategy involving only the underlying securities that most closely approximates the payoff function at maturity by applying stochastic dynamic programming to the minimization of a mean squared error loss function under markov state dynamics we derive recursive expressions for the optimal replication strategy that are readily implemented in practice the approximation error or e of the optimal replication strategy is also given recursively and may be used to quantify the degree of market incompleteness to investigate the practical significance of these e arbitrage strategies we consider several numerical examples including path dependent options and options on assets with stochastic volatility and jumps