robust stochastic discount factors when the market is incomplete a new non redundant derivative security cannot be priced by no arbitrage arguments alone moreover there will be a multiplicity of stochastic discount factors and each of them may give a different price for the new derivative security this paper develops an approach to the selection of a stochastic discount factor for pricing a new derivative security the approach is based on the idea that the price of a derivative security should not vary too much when the payoff of the primitive security is slightly perturbed i e the price of the derivative should be robust to model misspecification the paper develops two metrics of robustness the first is based on robustness in expectation the second is based on robustness in probability and draws on tools from the theory of large deviations we show that in a stochastic volatility model the two metrics yield analytically tractable bounds for the derivative price as the underlying stochastic volatility model is perturbed the bounds can be readily used for numerical examination of the sensitivity of the price of the derivative to model misspecification

a tale of two regimes theory and empirical evidence for a markov modulated jump diffusion model of equity returns and derivative pricing implications abstract we provide closed form solutions for a continuous time markov modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications we further demonstrate that the two state model provides the leptokurtic return features volatility smile and volatility clustering observed empirically for the dow jones industrial average djia and its component stocks using 10 years of stock return data we confirm the existence of jump intensity switching and clustering illustrate transition probabilities and verify superior empirical fit over competing poisson style models

property market efficiency an institutional economics perspective this paper reassesses the debate around property market efficiency and introduces an institutional perspective it considers property market efficiency in terms of the specific characteristics of property itself and the processes through which property is used and traded it argues that the institutional dimension fundamentally alters the concept of efficiency and leads to a partial and contingent judgement on achieved efficiency instead of seeking a judgement on whether the property market as an entity is efficient the institutional approach allows the possibility that property market process may be efficient for some market participants but not for others it also introduces a time dimension suggesting the need to assess the adaptability of property market process as economic and social conditions change

rationality and deterrence this essay explores the relationship between deterrence theory and two distinct notions of rationality associated with it the author argues that the concept of procedural irrationality which is the basis of many critiques of contemporary deterrence theory is not necessarily inconsistent with the instrumental definition of rationality implicit in many models of deterrence he also argues that some recent rational choice models of deterrence are nonetheless deficient in their application of the rationality postulate finally he provides an outline of a possible resolution of the paradox of deterrence

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 term structure of volatility implied by foreign exchange options this paper illustrates regression and kalman filtering methods for estimating the time varying term structure of volatility expectations revealed by options prices short and long term expectations are estimated for four currencies using daily phlx options prices from 1985 to 1989 throughout this period there were important differences between shortand long term expectations the slope of the term structure changed frequently and there were significant variations in long term volatility expectations the expectation estimates can be used to value otc options to improve hedging strategies and to test the hypothesis that the options market overreacts

informational efficiency of markets for stumpage this paper examines the weak form informational efficiency of markets for pine sawtimber stumpage in the u s south analyses of annual and quarterly rates of price change generally indicate that stumpage markets are efficient when viewed over monthly intervals stumpage markets do not pass the tests for weak form efficiency this failure is attributed to friction in the market due to the time and cost involved in consumating timber sales the results have implications for price responsive timber harvest scheduling for the application of asset pricing models to forestry investments and for policies governing sales of timber from public lands

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

volatility swaps and volatility options on discretely sampled realized variance abstract volatility swaps and volatility options are financial products written on discretely sampled realized variance actively traded in over the counter markets these products are often priced by continuously sampled approximations to simplify the computations this paper presents an analytical approach to efficiently and accurately price discretely sampled volatility derivatives under a general stochastic volatility model we first obtain an accurate approximation for the characteristic function of the discretely sampled realized variance this characteristic function is then applied to price discrete volatility derivatives through either semi analytical pricing formulae up to an inverse fourier transform or an efficient fourier cosine series method numerical experiments show that our approximation is more accurate in comparison to the approximations in the literature we remark that although discretely sampled variance swaps and options are usually more expensive than their continuously sampled counterparts discretely sampled volatility swaps are more prone to be cheaper than the continuously sampled counterparts an analysis is then provided to explain why this is the case in general for realistic contract specifications and reasonable model parameters

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

reading the smile the message conveyed by methods which infer risk neutral densities abstract in this study we compare the quality and information content of risk neutral densities obtained by various methods we consider a non parametric method based on a mixture of log normal densities the semi parametric ones based on an hermite approximation or based on an edgeworth expansion the parametric approach of malz which assumes a jump diffusion for the underlying process and heston s approach assuming a stochastic volatility model we apply those models on ff dm exchange rate options for two dates models differ when important news hits the market here anticipated elections the non parametric model provides a good fit to options prices but is unable to provide as much information about market participants expectations than the jump diffusion model

pricing options under generalized garch and stochastic volatility processes in this paper we develop an efficient lattice algorithm to price european and american options under discrete time garch processes we show that this algorithm is easily extended to price options under generalized garch processes with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases we establish one unifying algorithm that can price options under almost all existing garch specifications as well as under a large family of bivariate diffusions in which volatility follows its own perhaps correlated process through an equilibrium argument duan 1995 shows that options can be priced when the dynamics for the price of the underlying instrument follows a general autoregressive conditionally heteroskedastic garch process the theory of pricing under such processes is now well understood however the design of efficient numerical procedures for pricing them is lacking most applications resort to large sample simulation methods with a variety of variance reduction techniques the complexity of pricing arises from the massive path dependence inherent in garch models this path dependence causes typical lattice based procedures to grow exponentially in the number of time increments the lack of efficient numerical schemes hinders empirical tests among the wide array of competing garch models most tests of garch models limit themselves to the use of high frequency data on spot assets with little attention placed on the information content of options 1

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

pricing hang seng index options around the asian financial crisis a garch approach abstract this paper investigates how well the hang seng index options the most important class of option contracts traded in hong kong are priced using the garch approach we calibrated the garch parameters using the call and put option data and used them to price options in the subsequent weeks we found the garch model performs very well in comparison with the black scholes model even after allowing for a smile smirk adjustment its superior performance was also evident both before and during the recent asian financial turmoil

optimizing bounds on security prices in incomplete markets does stochastic volatility specification matter we extend and generalize some results on bounding security prices under two stochastic volatility models that provide closed form expressions for option prices in detail we compute analytical expressions for benchmark and standard good deal bounds for both models our findings show that our benchmark results generate much tighter bounds a deep analysis of the properties of option prices and bounds involving a sensitivity analysis and analytical derivation of greeks for both option prices and bounds is also presented these results provide strong practical applications taking into account the relevance of pricing and hedging strategies for traders financial institutions and risk managers

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

stock price distributions with stochastic volatility an analytic approach we study the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter we use analytic techniques to derive an explicit closed form solution for the case where volatility is driven by an arithmetic ornstein ublenbeck or ar1 process we then apply our results to two related problems in the finance literature 1 options pricing in a world of stochastic volatility and 2 the relationship between stochastic volatility and the nature of fat tailes in stock price distributions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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 continuous time arbitrage pricing model with stochastic volatility and jumps we formulate and test a continuous time asset pricing model using u s equity market data we assume that stock returns are driven by common factors including random jump size poisson processes and brownian motions with stochastic volatility the model places overidentifying restrictions on the mean returns allowing one to identify risk neutral probability distributions useful in pricing derivative securities we test for the restrictions and decompose moments of the asset returns into the contributions made by different factors our econometric methods take full account of time aggregation

on calibration of stochastic and fractional stochastic volatility models abstract in this paper we study optimization techniques for calibration of stochastic volatility models to real market data several optimization techniques are compared and used in order to solve the nonlinear least squares problem arising in the minimization of the difference between the observed market prices and the model prices to compare several approaches we use a popular stochastic volatility model firstly introduced by heston 1993 and a more complex model with jumps in the underlying and approximative fractional volatility calibration procedures are performed on two main data sets that involve traded dax index options we show how well both models can be fitted to a given option price surface the routines alongside models are also compared in terms of out of sample errors for the calibration tasks without having a good knowledge of the market e g a suitable initial model parameters we suggest an approach of combining local and global optimizers this way we are able to retrieve superior error measures for all considered tasks and models

how important is the correlation between returns and volatility in a stochastic volatility model empirical evidence from pricing and hedging in the s p 500 index options market abstract this paper examines the importance of allowing for correlation between returns and volatility in a continuous time stochastic volatility option pricing model specifically it tests the closed form stochastic volatility model of heston review of financial studies 6 1993 327 343 that allows for non zero correlation in terms of pricing and hedging options on the s p 500 index it is found that non zero correlation in the stochastic volatility model leads to significant improvements in mispricing of out of the money options and overall pricing performance compared to if correlation is constrained to be zero in terms of hedging non zero correlation results in significantly lower hedging errors for out of the money options

the price of a smile hedging and spanning in option markets the volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed to accommodate that change deterministic volatility models allow for more flexible volatility surfaces but refrain from introducing additional risk factors thus options are still redundant securities alternatively stochastic models introduce additional risk factors and options are then needed for spanning of the pricing kernel we develop a statistical test based on this difference in spanning using daily s p 500 index options data from 1986 95 our tests suggest that both in and out of the money options are needed for spanning the findings are inconsistent with deterministic volatility models but are consistent with stochastic models that incorporate additional priced risk factors such as stochastic volatility interest rates or jumps article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

misspecification of capital asset pricing this study documents empirical anomalies which suggest that either the simple one period capital asset pricing model capm is misspecified or that capital markets are inefficient in particular portfolios based on firm size or earnings price e p ratios experience average returns systematically different from those predicted by the capm furthermore the abnormal returns persist for at least two years this persistence reduces the likelihood that these results are being generated by a market inefficiency rather the evidence seems to indicate that the equilibrium pricing model is misspecified however the data also reveals that an e p effect does not emerge after returns are controlled for the firm size effect the firm size effect largely subsumes the e p effect thus while the e p anomaly and value anomaly exist when each variable is considered separately the two anomalies seem to be related to the same set of missing factors and these factors appear to be more closely associated with firm size than e p ratios

overreactions in the options market this paper examines the term structure of options implied volatilities using data on s p 100 index options because implied volatility is strongly mean reverting the implied volatility on a longer maturity option should move by less than one percent in response to a one percent move in the implied volatility of a shorter maturity option empirically this elasticity turns out to be larger than suggested by rational expectations theory long maturity options tend to overreact to changes in the implied volatility of short maturity options are investors rational do they behave like bayesian statisticians when it comes to incorporating new information into asset prices proponents of the efficient markets hypothesis would answer this question in the affirmative many others however believe that bayesian rationality is a poor description of investor behavior and that as a consequence asset prices tend to be informationally inefficient one way in which inefficiencies might arise is through the overreactions of traders to the arrival of new information 1 this possibility is raised by experimental and survey findings which indicate that people have a systematic tendency to overemphasize recent data at the expense of other information when making projections 2 the objective of this paper is to search for evidence of such overreactive behavior in a semingly peculiar place the options market options may appear to be unlikely candidates for overreaction because unlike primary securities their prices are closely tied down by arbitrage considerations as black and scholes 1973 demonstrate if stock price volatility is known options prices are completely determined any deviation from the prescribed value implies a riskless profit opportunity however given that volatility is in fact unknown and changing options do retain something of an independent nature not wholly redundant with their underlying stocks options can be thought of as reflecting a speculative market in volatility the implied volatility on a given option obtained by inverting a

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

equilibrium valuation of foreign exchange claims this article studies the equilibrium valuation of foreign exchange contingent claims within a continuous time lucas 1982 two country model exchange rates interest rates and in particular factor risk prices are all endogenously and jointly determined this guarantees the internal consistency of these price processes with a general equilibrium in the same model closed form valuation formulas are presented for currency options and currency futures options common to these formulas is that stochastic volatility and stochastic interest rates are admitted hedge ratios and other comparative statics are also provided analytically it is shown that most existing currency option models are included as special cases this article studies the equilibrium valuation and hedging of foreign exchange contingent claims the framework for analysis is the continuous time counterpart of the well known two country monetary model of lucas 1982 1 that is we use the modeling structure of lucas 1982 and adopt his representativeagent perfect pooling equilibrium notion rather than extending the lucas setup to a cox ingersoll and ross 1985a henceforth cir production economy as is done in nielsen and saa requejo 1993 for our purpose the lucas framework offers the desired simplicity and tractability we assume a stochastic structure for the international economy such that the resulting nominal interest rates and exchange rate dynamics exhibit similar empirically plausible features as the corresponding ones in nielsen and saa requejo 1993 for example the endogenous interest rates are positively correlated across national borders campbell and clarida 1987 and ilmanen 1995 as a predictor of future spot exchange rates the equilibrium forward exchange rate is biased in a direction consistent with the forward premium puzzle

capital structure effects on the prices of equity call options abstract we examine whether values of equity options traded on individual firms are sensitive to the firm s capital structure we estimate the compound option co model which views equity as an option on the firm compared with the black scholes model the co model with a term structure of volatility tsv reduces pricing errors by 20 on average the compound option effect is particularly strong for highly levered firms and long term options in which the pricing improvement is up to 70 of the black scholes error without a tsv the co model reduces pricing errors of in the money options by 12 74 on average and for out of the money by 9 22 we show that the co model implies a market value of firm leverage and allows imputation of the firm s implied volatility both of which have potential applications in corporate finance

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

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

american options under stochastic volatility the problem of pricing an american option written on an underlying asset with constant price volatility has been studied extensively in literature real world data however demonstrate that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on european options we consider the problem of pricing american options under stochastic volatility which has had relatively much less attention from literature first we develop a transformation procedure to compute the optimal exercise policy and option price and provide theoretical guarantees for convergence second using this computational tool we explore a variety of questions that seek insights into the dependence of option prices exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility the speed and accuracy of the procedure are compared against existing methods as well

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

efficiency of the market for residential real estate efficiency of securities markets research addressing the efficiency of the real estate market is limited the perception is widely held that such markets may not be efficient in a recent empirical study using some of the same data employed in our analysis hamilton and schwab 1985 conclude that expected appreciation rates in residential real estate markets are systematically biased by the failure of market participants to incorporate past appreciation rates into their expectations their analysis however is exclusively based on the 1974 1976 period to project appreciation rates for the 1976 1979 period as we demonstrate below their analysis though it implies systematic estimation errors ex post for the time period they study does not generalize to other periods thus their finding is not a sufficient basis for concluding that the market is not efficient ex ante

a nonparametric kernel regression approach for pricing options on stock market index abstractprevious options studies typically assume that the dynamics of the underlying asset price follow a geometric brownian motion gbm when pricing options on stocks stock indices currencies or futures however there is mounting empirical evidence that the volatility of asset price or return is far from constant this article in contrast to studies that use parametric approach for option pricing employs nonparametric kernel regression to deal with changing volatility and accordingly prices options on stock index specifically we first estimate nonparametrically the volatility of asset return in the gbm based on the nadaraya watson n w kernel estimator then based on the n w estimates for the volatility we use monte carlo simulation to compute option prices under different settings finally we compare the index option prices under our nonparametric model with those under the black scholes model and the stein stein model

model free hedge ratios and scale invariant models a price process is scale invariant if and only if the returns distribution is independent of the price measurement scale we show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale invariant are indeed so we also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model free in particular previous results on model free price hedge ratios of vanilla options based on scale invariant models are extended to any contingent claim with homogeneous pay off including complex path dependent options however model free hedge ratios only have the minimum variance property in scale invariant stochastic volatility models when price volatility correlation is zero in other stochastic volatility models and in scale invariant local volatility models model free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios

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

the persistence of volatility and stock market fluctuations this paper examines the potential influence of changing volatility in stock market prices on the level of stock market prices it demonstrates that volatility is only weakly serially correlated implying that shocks to volatility do not persist these shocks can therefore have only a small impact on stockmarket prices since changes in volatility affect expected required rates of return for relatively short intervals these findings lead us to be skeptical of recent claims that the stock market s poor performance during the 1970 s can be explained by volatility induced increases in risk premia this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item

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

a general distribution for describing security price returns this paper introduces a generalized distribution called the gb2 distribution for describing security returns the distribution is extremely flexible containing a large number of well known distributions such as the lognormal log t and log cauchy distribu tions as special or limiting cases and allowing large even infinite higher moments this flexibility allows a direct representation of different degrees of fat tails in the distribution the properties of the gb2 make it useful in empirical estimation of security returns and in facilitating the development of option pricing models and other models that depend on the specification and mathematical manipulation of distributions copyright 1987 by the university of chicago

pricing of long dated commodity derivatives do stochastic interest rates matter abstract does modelling stochastic interest rates beyond stochastic volatility improve pricing performance on long dated commodity derivatives to answer this question we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables we examine the empirical pricing performance of these models on pricing long dated crude oil derivatives estimating the model parameters from historical crude oil futures prices and option prices we find that stochastic interest rate models improve pricing performance on long dated crude oil derivatives when the interest rate volatility is relatively high furthermore increasing the model dimensionality does not tend to improve the pricing performance on long dated crude oil option prices but it matters for long dated futures prices we also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long dated crude oil option prices

a methodology for assessing model risk and its application to the implied volatility function model we propose a methodology for assessing model risk and apply it to the implied volatility function ivf model this is a popular model among traders for valuing exotic options our research is different from other tests of the ivf model in that we reflect the traders practice of using the model for the relative pricing of exotic and plain vanilla options at one point in time we find little evidence of model risk when the ivf model is used to price and hedge compound options however there is significant model risk when it is used to price and hedge some barrier options

asymmetry in the jump size distribution of the s p 500 evidence from equity and option markets this paper studies alternative distributions for the size of price jumps in the s p 500 index we introduce a range of new jump diffusion models and extend popular double jump specifications that have become ubiquitous in the finance literature the dynamic properties of these models are tested on both a long time series of s p 500 returns and a large sample of european vanilla option prices we discuss the in and out of sample option pricing performance and provide detailed evidence of jump risk premia models with double gamma jump size distributions are found to outperform benchmark models with normally distributed jump sizes

valuing futures and options on volatility abstract this paper presents simple closed form expressions for volatility futures and option prices and examines their implications for the characteristics of these securities we show that the properties of these volatility derivatives are fundamentally different from those of conventional option and futures contracts this analysis also provides insights into the role that volatility derivatives may play in managing and hedging volatility risk in financial markets

the implication of missing the optimal exercise time of an american option the optimal exercise policy of an american option dictates when the option should be exercised in this paper we consider the implications of missing the optimal exercise time of an american option for the put option this means holding the option until it is deeper in the money when the optimal decision would have been to exercise instead we derive an upper bound on the maximum possible loss incurred by such an option holder this upper bound requires no knowledge of the optimal exercise policy or true price function this upper bound is a function of only the option holder s exercise strategy and the intrinsic value of the option we show that this result holds true for both put and call options under a variety of market models ranging from the simple black scholes model to complex stochastic volatility jump diffusion models numerical illustrations of this result are provided we then use this result to study numerically how the cost of delaying exercise varies across market models and call and put options we also use this result as a tool to numerically investigate the relation between an option holder s risk preference levels and the maximum possible loss he may incur when adopting a target payoff policy that is a function of his risk preference level

a general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps abstract after the recent financial crisis the market for volatility derivatives has expanded rapidly to meet the demand from investors risk managers and speculators seeking diversification of the volatility risk in this paper we develop a novel and efficient transform based method to price swaps and options related to discretely sampled realized variance under a general class of stochastic volatility models with jumps we utilize frame duality and density projection method combined with a novel continuous time markov chain ctmc weak approximation scheme of the underlying variance process contracts considered include discrete variance swaps discrete variance options and discrete volatility options models considered include several popular stochastic volatility models with a general jump size distribution heston scott hull white stein stein hypergeometric 3 2 and 4 2 models our framework encompasses and extends the current literature on discretely sampled volatility derivatives and provides highly efficient and accurate valuation methods numerical experiments confirm our findings

volatility of aggregate volatility and hedge fund returns abstract this paper investigates empirically whether uncertainty about equity market volatility can explain hedge fund performance both in the cross section and over time we measure uncertainty via volatility of aggregate volatility vov and construct an investable version through returns on lookback straddles on the chicago board options exchange cboe volatility index vix we find that vov exposure is a significant determinant of hedge fund returns after controlling for fund characteristics we find a robust and significant negative risk premium for vov exposure in the cross section of hedge fund returns we corroborate our results using statistical and parameterized proxies of vov over a longer sample period

hedging volatility risk abstract volatility risk plays an important role in the management of portfolios of derivative assets as well as portfolios of basic assets this risk is currently managed by volatility swaps or futures however this risk could be managed more efficiently using options on volatility that were proposed in the past but were never introduced mainly due to the lack of a cost efficient tradable underlying asset the objective of this paper is to introduce a new volatility instrument an option on a straddle which can be used to hedge volatility risk the design and valuation of such an instrument are the basic ingredients of a successful financial product in order to value these options we combine the approaches of compound options and stochastic volatility our numerical results show that the straddle option is a powerful instrument to hedge volatility risk an additional benefit of such an innovation is that it will provide a direct estimate of the market price for volatility risk

underreaction overreaction and increasing misreaction to information in the options market this paper investigates options market reaction to changes in the instantaneous variance of the underlying asset there are three main findings first options market investors underreact to individual daily changes in instantaneous variance second these same investors overreact to periods of mostly increasing or mostly decreasing daily changes in instantaneous variance third they tend to underreact overreact to current daily changes in instantaneous variance that are preceded mostly by daily changes of the opposite same sign the third finding can reconcile the first two and is also consistent with well established cognitive biases