optimal policy in markov switching rational expectations models abstract in this paper we consider the optimal quadratic control problem of markov switching linear rational expectation models these models are general and flexible tools for modelling not only regime but also model or parameter uncertainty we show first how to find the solution of a markov switching linear rational expectation model based on this solution we then show how to apply dynamic programming to find the optimal time consistent policy and the resulting nash stackelberg equilibrium suitable modifications of the algorithm allow to deal with the non re case in which the policymaker and the private sector hold different beliefs or probabilities over regime change we also show how the optimisation procedure can be employed to obtain the optimal policy under commitment as an illustration we compute the optimal policy in a small open economy subject to stochastic structural breaks in some of its key parameters

it only takes a few moments to hedge options abstract we propose a novel non structural method for hedging european options relying on two model independent results first under suitable regularity conditions an option price can be disentangled into a linear combination of risk neutral moments second there exists an explicit approximate functional form linking the risk neutral moments to the futures price of the underlying asset and the related variance swap contracts we show that s p 500 call prices are mainly explained by two factors that are related to level and volatility of the underlying index we empirically compare the performance of two strategies where the vega exposure is adjusted either by a direct position in a variance swap contract or indirectly through an at the money call while both strategies ensure effective immunization in periods of market turmoil taking direct exposure on variance swaps is not optimal during extended periods of subdued volatility

how should control theory be used to calculate a time consistent government policy we study different solutions to a simple one dimensional linear quadratic game with a large number of private agents and a government a time consistent solution is defined as a solution to the hamilton jacobi bellman equation i e as a policy for which the government has noprecommitment capability this solution is compared to a policy where the government has an instantaneous pre commitment i e an equilibrium in which the government has a period by period leadership in both cases we show how control theory should be applied to calculate the equilibrium and how to relate these equilibria to the differential game literature

inflation and reputation in many macroeconomic models with rational expectations optimal policy is time inconsistent and therefore announced policy may not be credible this paper models the government s credibility explicitly using kreps and wilson s analysis time consistent optimal government policy emerges as a sequential equilibrium in a repeated game this policy is at least as good as the inconsistent optimal policy and dominates the consistent policy when reputational effects are ignored thus the analysis resolves the problem of specifying a credible optimal policy in such models the results show why attempts to disinflate may lead to recession even with perfectly flexible prices this abstract was borrowed from another version of this item

inflation and output volatility under asymmetric incomplete information abstract the assumption of asymmetric and incomplete information in a standard new keynesian model creates strong incentives for monetary policy transparency we assume that the central bank has better information about its objectives than the private sector and that the private sector has better information about shocks than the central bank transparency has the potential to trigger a virtuous circle in which all agents find it easier to make inferences and the economy is better stabilised our analysis improves upon existing work by endogenising the volatility of both output and inflation improved transparency most likely manifests itself in falling output volatility

the skew risk premium in the equity index market we develop a new method for measuring moment risk premiums we find that the skew premium accounts for over 40 of the slope in the implied volatility curve in the s p 500 market skew risk is tightly related to variance risk in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium this provides a new testable restriction for asset pricing models trying to capture in particular disaster risk premiums we base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments

the recovery theorem we can only estimate the distribution of stock returns but from option prices we observe the distribution of state prices state prices are the product of risk aversion the pricing kernel and the natural probability distribution the recovery theorem enables us to separate these to determine the market s forecast of returns and risk aversion from state prices alone among other things this allows us to recover the pricing kernel market risk premium and probability of a catastrophe and to construct model free tests of the efficient market hypothesis

product replacement bias in inflation and its consequences for monetary policy the paper examines a new keynesian model with product entry and exit and with two types of households households consume different product baskets and therefore face different inflation rates the statistical bureau used in the model measures aggregate inflation but observes product entry with a probabilistic delay consequently measured inflation suffers from product replacement bias with respect to aggregate inflation measured inflation is less volatile but more persistent than aggregate inflation and the correlation between aggregate inflation and aggregate output is lower than the correlation between measured inflation and measured output when monetary policy responds to measured variables it stabilizes aggregate inflation insufficiently nevertheless under discretionary monetary policy responding to measured variables improves welfare

recovering probability distributions from option prices this article derives underlying asset risk neutral probability distributions of european options on the s p 500 index nonparametric methods are used to choose probabilities that minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices alternative optimization specifications produce approximately the same implied distributions a new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed since the crash the risk neutral probability of a three four standard deviation decline in the index about 36 percent 46 percent over a year is about 10 100 times more likely than under the assumption of lognormality recently the increasing popularity of derivatives and some highly publicized failures to control risk have led to increased efforts to find reasonable methods to measure the sensitivity of large institutional derivatives portfolios to extreme events merely because such events are rare is not sufficient to ignore them since on the few occasions when they do occur significant amounts of money can change hands potentially wiping out profits accumulated over long prior periods a key assumption behind methods of estimation is the joint probability distribution of constituent underlying asset returns this has long been a concern of financial economists since probability assumptions are critical to much of their research during the last quarter century heretofore probability distributions of stock market returns have typically been estimated from historical time series unfortunately common hypotheses may not capture the probability of extreme events and the events of interest are rare or may not be present in the historical record even though they are clearly possible

optimal nonlinear policy signal extraction with a non normal prior the literature on optimal monetary policy typically makes three major assumptions 1 policymakers preferences are quadratic 2 the economy is linear and 3 stochastic shocks and policymakers prior beliefs about unobserved variables are normally distributed this paper relaxes the third assumption and explores its implications for optimal policy the separation principle continues to hold in this framework allowing for tractability and application to forward looking models but policymakers beliefs are no longer updated in a linear fashion allowing for plausible nonlinearities in optimal policy we consider in particular a class of models in which policymakers priors about the natural rate of unemployment are diffuse in a region around the mean when this is the case it is optimal for policy to respond cautiously to small surprises in the observed unemployment rate but become increasingly aggressive at the margin these features of optimal policy match statements by federal reserve officials and the behavior of the fed in the 1990s

leverage effect volatility feedback and self exciting market disruptions equity index volatility variation and its interaction with the index return can come from three distinct channels first index volatility increases with the market s aggregate financial leverage second positive shocks to systematic risk increase the cost of capital and reduce the valuation of future cash flows generating a negative correlation between the index return and its volatility regardless of financial leverage finally large negative market disruptions show self exciting behaviors this article proposes a model that incorporates all three channels and examines their relative contribution to index option pricing and stock option pricing for different types of companies

statistical arbitrage and securities prices this article introduces the concept of a statistical arbitrage opportunity sao in a finite horizon economy a sao is a zero cost trading strategy for which i the expected payoff is positive and ii the conditional expected payoff in each final state of the economy is nonnegative unlike a pure arbitrage opportunity a sao can have negative payoffs provided that the average payoff in each final state is nonnegative if the pricing kernel in the economy is path independent then no saos can exist furthermore ruling out saos imposes a novel martingale type restriction on the dynamics of securities prices the important properties of the restriction are that it 1 is model free in the sense that it requires no parametric assumptions about the true equilibrium model 2 can be tested in samples affected by selection biases such as the peso problem and 3 continues to hold when investors beliefs are mistaken the article argues that one can use the new restriction to empirically resolve the joint hypothesis problem present in the traditional tests of the efficient market hypothesis in a fairly general environment this article proposes a novel martingaletype restriction on the dynamics of securities prices this restriction has a number of important properties most notably the restriction may be viewed as model free because it requires no parametric assumptions about the true equilibrium model to derive the restriction we rely on the concept of statistical arbitrage a generalization of pure arbitrage a pure arbitrage opportunity pao is a zero cost trading strategy that offers the possibility of a gain with no possibility of a loss as is well known the existence of paos is incompatible with a competitive equilibrium in asset markets the fundamental theorem of the financial theory establishes a link between the absence of paos and the existence of a positive pricing kernel which supports securities prices while the absence of paos is a necessary condition for any equilibrium model this condition alone often yields pricing implications that are too weak to be practically useful for example when valuing options in incomplete markets the no arbitrage bounds on option prices are typically very wide to strengthen pricing implications several recent articles

a theory of ambiguity credibility and inflation under discretion and asymmetric information this paper develops a positive theory of credibility ambiguity and inflation under discretion and asymmetric information the monetary policymaker maximizes his own politically motivated objective function that is positively related to economic stimulation through monetary surprises and negatively related to monetary growth the relative importance he assigns to each target shifts stochastically through time his current preference trade off is known to him but not to the public when choosing the state contingent path of money growth for the present and the future the policymaker compares the benefits from current stimulation with the costs associated with higher future inflation expectations current monetary growth conveys information to the public about future money growth because there is persistence in the policymaker s objectives although expectations are rational information is imperfect because monetary control procedures are imprecise as a result the public cannot correctly distinguish persistent changes of emphasis on different policy objectives from transitory monetary control errors the public becomes aware of changes gradually by observing past monetary growth credibility is defined in terms of the speed with which the public recognizes changes in the objectives of the policymaker credibility is lower the noisier monetary control and the more stable the objectives of the policymaker looser monetary control and a higher degree of time preference on the part of the policymaker induce him to produce higher and more variable monetary growth when the policymaker is free to determine the accuracy of monetary control he does not always choose the most effective control available in spite of the fact that monetary surprises always have an expected value of zero the reason is that ambiguous control procedures enable the policymaker to generate positive surprises when he cares more than on average about economic stimulation he leaves the inevitable negative surprises for periods in which he cares more about inflation prevention this result provides an explanation for the fed s preference for ambiguity recently documented by goodfriend 1986 the policymaker is more likely to pick more ambiguous control procedures the more uncertain his objectives and the higher his time preference the paper also provides a theoretical underpinning for the well documented crosscountry positive correlation between the level and the variability of inflation

skewness preference and the popularity of technical analysis abstract we propose a simple model of how investors evaluate a trading rule and show that the market timing of technical trading rules induces lottery like trading profits therefore investors preference for positive skewness caters to the popularity of technical analysis since prospect theory implies strong skewness preference it can explain why investors trade extensively on chart patterns that are meaningless in light of the efficient market hypothesis technicians often invoke behavioral finance as its theoretical foundation contrary to this view we show that ideas from behavioral finance explain why technical analysis is popular despite the lack of theoretical foundation and empirical success

generalized risk premia abstract this paper develops an optimal trading strategy explicitly linked to an agent s preferences and assessment of the distribution of asset returns the price of this strategy is a portfolio of implied moments and its expected excess returns naturally accommodate compensation for higher order moment risk variance risk and the equity premium approximate it to first order and it nests cross sectional asset pricing models such as the linear capital asset pricing model capm an empirical study in the us index market compares the investment behavior of an agent with recursive long run risk preferences to one who merely uses an identically independently distributed time series model and takes market prices as given the two agents exhibit very similar behavior during crises and can be distinguished mostly during calm periods

the numeraire portfolio abstract a portfolio formed from a given list of assets is defined as a numeraire portfolio for the list if a it is self financing b its value is always positive and c zero is always the best conditional forecast of the numeraire dominated rate of return of every asset on the list the numeraire portfolio exists if and only if there are no profit opportunities from trading assets on the list for a sample list of heterogeneous assets nyse size quintile portfolios corporate bonds and short term bills numeraire dominated returns are similar to market model forecast errors and as abnormal return measures clearly dominate market adjusted returns

detecting money market bubbles the existence of a self financing trading strategy that replicates the money market account at a fixed future date at a lower cost than the current value of this account constitutes a money market bubble mmb understanding whether a market exhibits an mmb is crucial in particular for derivative pricing an mmb precludes the existence of a risk neutral probability measure the benchmark approach allows to study mmbs and is formulated under the real world probability measure it does not require the existence of a risk neutral probability measure using a range of well known stochastic volatility models we study the existence of an mmb in the us economy and find that the us market exhibits an mmb for all models considered that allow it this suggests that for derivative pricing and hedging care should be taken when making assumptions pertaining to the existence of a risk neutral probability measure less expensive portfolios are likely to exist for a wide range of long term derivatives as typical for pensions

robust control of forward looking models abstract this paper shows how to formulate and compute robust ramsey aka stackelberg plans for linear models with forward looking private agents the leader and the followers share a common approximating model and both have preferences for robust decision rules because both doubt the model since their preferences differ the leader s and followers decision rules are fragile to different misspecifications of the approximating model we define a stackelberg equilibrium with robust decision makers in which the leader and follower have different worst case models despite sharing a common approximating model to compute a stackelberg equilibrium we formulate a bellman equation that is associated with an artificial single agent robust control problem the artificial bellman equation contains a description of implementability constraints that include euler equations that describe the worst case analysis of the followers as an example the paper analyzes a model of a monopoly facing a competitive fringe

indicator variables for optimal policy the optimal weights on indicators in models with partial information about the state of the economy and forward looking variables are derived and interpreted both for equilibria under discretion and under commitment an example of optimal monetary policy with a partially observable potential output and a forward looking indicator is examined the optimal response to the optimal estimate of potential output displays certainty equivalence whereas the optimal response to the imperfect observation of output depends on the noise in this observation

should a monetary policymaker look at money abstract this paper examines whether monetary indicators are useful in implementing optimal discretionary monetary policy when the policymaker has incomplete information about the environment we find that money does not contain useful information for the policymaker if we calibrate the model to the u s economy if money demand were to be appreciably less variable observations on money could be useful in response to productivity shocks but would be harmful in response to money demand shocks we provide an incomplete information example where equilibrium welfare declines when the money demand volatility decreases

a nonlinear factor analysis of s p 500 index option returns growing evidence suggests that extraordinary average returns may be obtained by trading equity index options and that at least part of this abnormal performance is attributable to volatility and jump risk premia this paper asks whether such priced risk factors are alone sufficient to explain these average returns to provide an answer in as general as possible a setting i estimate a flexible class of nonlinear models using all s p 500 index futures options traded between 1986 and 2000 the results show that priced factors contribute to these expected returns but are insufficient to explain their magnitudes particularly for short term out of the money puts in a recent paper c oval and shumway 2001 examine the returns on deltahedged option positions focusing on the at the money straddle and find average returns close to minus 3 per week since over short time horizons these positions are approximately invariant to movements in the underlying index coval and shumway argue that their capm betas should be near zero and their expected returns close to the risk free rate they conclude that large deviations from the capm are the norm which they suggest is evidence that some other systematic factor such as stochastic volatility might be priced by the market similar conclusions are made by jackwerth 2000 who finds risk adjusted profitability from selling puts and by bakshi and kapadia 2003 who find that the volatility risk premium contributes significantly to higher prices for calls and puts buraschi and jackwerth 2001 concur suggesting that more than one priced risk factor is necessary to explain option prices a less direct set of evidence is the now standard observation that the black scholes implied volatilities of equity index options are upward biased predictors of future realized volatility numerous studies such as fleming ostdiek and whaley 1995 and christensen and prabhala 1998 document that implied volatilities of short term at the money equity index options are on average several percentage points higher than the volatilities realized over the option s

the term structure of currency carry trade risk premia we nd that average returns to currency carry trades decrease signicantly as the maturity of the foreign bonds increases because investment currencies tend to have small local bond term premia the downward term structure of carry trade risk premia is informative about the temporal nature of risks that investors face in currency markets we show that long maturity currency risk premia only depend on the domestic and foreign permanent components of the pricing kernels since transitory currency risk is automatically hedged by interest rate risk for long maturity bonds our

reputational and nonreputational policies under partial information abstract this paper analyses the effect of partial information on optimal policy design for stochastic macroeconomic models incorporating forward looking expectations the main theoretical result is that reputational and nonreputational policies are certainty equivalent as has previously been conjectured and it is also shown that the welfare loss does not necessarily increase with decreasing information of particular additional interest in the analysis of reputational policy design is the issue of sustainability and it is shown using an example that weak sustainability may be information dependent

the consumption based capital asset pricing model the paper provides conditions on the primitives of a continuous time economy under which there exist equilibria obeying the consumption based capital asset pricing model ccapm the paper also extends the equilibrium characterization of interest rates of cox ingersoll and ross 1985 to multi agent economies we do not use a markovian state assumption this work provides sufficient conditions on agents primitives for the validity of the consumption based capital asset pricing model ccapm of breeden 1979 as a necessary condition breeden showed that in a continuous time equilibrium satisfying certain regularity conditions one can characterize returns on securities as follows the expected instantaneous rate of return on any security in excess of the riskless interest rate the security s expected excess rate of return is a multiple common to all securities of the instantaneous covariance of this excess return with aggregate consumption increments this common multiple is the arrow pratt measure of risk aversion of a representative agent rubinstein 1976 published a discrete time precursor of this result the exis tence of equilibria satisfying breeden s regularity conditions had been an open issue we also show that the validity of the ccapm does not depend on breeden s assumption of markov state information and present a general asset pricing model extending the results of cox ingersoll and ross 1985 as well as the discrete time results of rubinstein 1976 and lucas 1978 to a multi agent environment since the ccapm was first proposed much effort has been directed at finding sufficient conditions on the model primitives the given assets the agents preferences the agents consumption endowments and in a production econ omy the feasible production sets conditions sufficient for the existence of continuous time equilibria were shown in duffie 1986 but the equilibria demonstrated were not shown to satisfy the additional regularity required for the ccapm in particular breeden assumed that all agents choose pointwise interior consumption rates in order to characterize asset prices via the first order conditions of the bellman equation interiority was also assumed by huang 1987 in demonstrating a representative agent characterization of equilibrium an approach exploited here the use of dynamic programming and the bellman equation aside from the difficulty it imposes in verifying the existence of interior 1 financial support from the national science foundation is gratefully acknowledged we thank

indicator variables for optimal policy under asymmetric information the optimal weights on indicators in models with partial information about the state of the economy and forward looking variables are derived and interpreted both for equilibria under discretion and under commitment the private sector is assumed to have more information about the state of the economy than the policymaker certainty equivalence holds for the optimal reaction function in state space form t he coefficients are independent of the degree of uncertainty about the state of the economy however in the case of commitment certainty equivalence does not hold for the reaction function in integrative form the policy instrument cannot be written as a distributed lag of past estimates of past states of the economy instead optimal policy will generally depend on new estimates of past states of the economy and in ways that depend on the information structure furthermore the usual separation principle does not hold since the estimation of the state of the economy is not independent of optimization and is in general quite complex we present a general characterization of optimal filtering and control in settings of this kind and discuss an application of our methods to the problem of the optimal use of real time macroeconomic data in the conduct of monetary policy

rational asset pricing bubbles and portfolio constraints this article shows that portfolio constraints can give rise to rational asset pricing bubbles in equilibrium even if there are unconstrained agents in the economy who can benefit from the induced limited arbitrage opportunities furthermore it is shown that bubbles can lead to both multiplicity and real indeterminacy of equilibria the general results are illustrated by two explicitly solved examples where seemingly innocuous portfolio constraints make bubbles a necessary condition for the existence of an equilibrium c 2012 elsevier inc all rights reserved

are market neutral hedge funds really market neutral one can consider the concept of market neutrality for hedge funds as having breadth and depth breadth resects the number of market risks to which a fund is neutral while depth resects the completeness of the neutrality of the fund to market risks we focus on market neutrality depth and propose ve different neutrality concepts mean neutrality nests the standard correlation based de nition of neutrality variance neutrality value at risk neutrality and tail neutrality all relate to the neutrality of the risk of the hedge fund to market risks finally complete neutrality corresponds to independence of the fund to market risks we suggest statistical tests for each neutrality concept and apply the tests to a combined database of monthly market neutral hedge fund returns from the hfr and tass hedge fund databases we nd that around one quarter of these funds exhibit some signi cant exposure to market risk

gain loss and asset pricing we develop an approach to asset pricing in incomplete markets that bridges the gap between the two fundamental approaches in finance model based pricing and pricing by no arbitrage we strengthen the absence of arbtrage assumption by precluding investment opportunities whose attractiveness to a benchmark investor exceeds a specified threshold in our framework the attractiveness of an investment opportunity is measured by the gain loss ratio we show that a restriction on the maximum gain loss ratio is equivalent to a restriction on the ratio of the maximum to minimum values of the pricing kernel by limiting the maximum gainloss ratio we can restrict the admissible set of pricing kernels which in turn allows us to restrict the set of prices that can be assigned to assets we illustrate our methodology by computing price bounds for call options in a black scholes economy without intermediate trading when we vary the maximum permitted gainloss ratio these bounds can range from the exact prices implie

consumer misperceptions uncertain fundamentals and the business cycle abstract this paper estimates the importance of shocks to consumer misperceptions noise shocks for u s business cycle fluctuations i embed imperfect information as in lorenzoni 2009 into a smets and wouters 2007 type dsge model agents only observe aggregate productivity and a signal about the permanent component contaminated with noise based on this information agents form beliefs about the temporary and the permanent component of productivity shocks to the signal noise shocks trigger aggregate fluctuations unrelated to changes in productivity bayesian estimation shows that noise shocks explain up to 14 percent of output and up to 25 percent of consumption fluctuations nominal rigidities and the specification of the monetary policy rule are crucial for the importance of noise shocks these features help to resolve conflicting results in the previous literature

a new approach to international arbitrage pricing this paper uses a nonlinear arbitrage pricing model a conditional linear model and an unconditional linear model to price international equities bonds and forward currency contracts unlike linear models the nonlinear arbitrage pricing model requires no restrictions on the payoff space allowing it to price payoffs of options forward contracts and other derivative securities only the nonlinear arbitragepricing model does an adequate job of explaining the time series behavior of a cross section of international returns the idea that a few relevant state variables explain expected returns is the main driving force of the seminal papers of merton 1973 and ross 1976 these seminal ideas have been extended to the pricing of international assets by ikeda 1991 ross and walsh 1983 solnik 1974 1983 and stulz 1981 among others the key implication of these arbitrage pricing models is that only risks related to these factors state variables are relevant in determining asset prices testable implications of these international asset pricing models have been derived either by placing restrictions on the payoff structure i e payoffs are linear in factors as in ikeda 1991 ross and walsh 1983 and solnik 1983 or on the joint distributions of the payoffs and state variables as in constantinides 1989 these restrictions lead to the testable implication that expected asset returns are linear in the conditional covariances with the factor payoffs in what follows we refer to these models as linear arbitrage models or linear models

do jumps contribute to the dynamics of the equity premium abstract this paper investigates whether risks associated with time varying arrival of jumps and their effect on the dynamics of higher moments of returns are priced in the conditional mean of daily market excess returns we find that jumps and jump dynamics are significantly related to the market equity premium the results from our time series approach reinforce the importance of the skewness premium found in cross sectional studies using lower frequency data and offer a potential resolution to sometimes conflicting results on the intertemporal risk return relationship we use a general utility specification consistent with our pricing kernel to evaluate the relative value of alternative risk premium models in an out of sample portfolio performance application

rational asset pricing bubbles this paper provides a fairly systematic study of general economic conditions under which rational asset pricing bubbles may arise in an intertemporal competitive equilibrium framework our main results are concerned with nonexistence of asset pricing bubbles in those economies these results imply that the conditions under which bubbles are possible including some well known examples of monetary equilibria are relatively fragile this paper is concerned with the conditions under which asset prices in an intertemporal competitive equilibrium are equal to the present value of the streams of future dividends to which each asset represents a claim according to a central result of the theory of finance this is very generally true in the case of economies with trading at only a finite sequence of dates as long as there are no restrictions upon transactions other than that associated with possible incom pleteness of the set of securities that are traded the result is sometimes called the fundamental theorem of asset pricing here we consider the extent to which such a result continues to be valid in the case of trading over an infinite horizon it has often been observed in the econometric literature on asset pricing bubbles that it is possible in principle for the price of a perpetuity and the dividends on that security to satisfy at all times a present value relation for one period holding returns while the security s price nonetheless does not equal the present value of the stream of dividends expected over the infinite future in such a case the price of the perpetuity is said to involve a bubble component 2 joint stochastic processes for which this component is nonzero are sometimes argued to characterize existing assets for a recent example see froot and obstfeld 1991 but such an inference depends upon aspects of the stochastic

tails fears and risk premia we show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia exploiting the special structure of the jump tails and the pricing thereof we identify and estimate a new investor fears index the index reveals large time varying compensation for fears of disasters our empirical investigations involve new extreme value theory approximations and high frequency intraday data for estimating the expected jump tails under the statistical probability measure and short maturity out of the money options and new model free implied variation measures for estimating the corresponding risk neutral expectations

endogenous persistence in an estimated dsge model under imperfect information a framework for estimating dynamic stochastic general equilibrium dsge models by bayesian methods and validation under very general information assumptions is applied to a new keynesian model the standard asssumption that private agents have perfect information observing all state variables including shocks whereas the econometrician uses only observable data is compared with both agents having the same imperfect information ii set we also generalise rational expectations to a behavioural composite model that allows some households and firms to form expectations adaptively we find significant empirical support for ii as an endogenous persistence mechanism but this is dominated by that from habit and adaptive learning

savage in the market we develop a behavioral axiomatic characterization of subjective expected utility seu under risk aversion given is an individual agent s behavior in the market assume a finite collection of asset purchases with corresponding prices we show that such behavior satisfies a revealed preference axiom if and only if there exists a seu model a subjective probability over states and a concave utility function over money that accounts for the given asset purchases

functional ross recovery theoretical results and empirical tests abstract recently ross 2015 showed that the real world probability distribution of a discrete markovian state variable can be recovered from observed option prices the so called recovery theorem follows from perron frobenius matrix theory when the pricing kernel is transition independent in this paper we generalize the recovery theorem to continuous state spaces using perron frobenius operator theory building on our theoretical results we devise a nonparametric approach to empirically estimate the recovered pricing kernel and probability density in closed form using s p 500 index options we analyze recovered pricing kernels empirically and find evidence that ross recovery is misspecified

a non structural investigation of vix risk neutral density abstract we propose a non structural method to retrieve the risk neutral density rnd implied by options on the cboe volatility index vix the methodology is based on orthogonal polynomial expansions around a kernel density and yields the rnd of the underlying asset without the need for a parametric specification the classic family of laguerre expansions is extended to include the gig and the generalized weibull kernels we show that orthogonal polynomial expansions yield accurate approximations of the rnd of vix and they generally outperform commonly used non parametric methods when controlling for accuracy based on a panel of observed vix options we retrieve the variance swap term structure the time series of vvix the vix risk neutral moments and the volatility at risk which reveal a number of stylized facts on the rnd of vix

approximating the asset pricing kernel this article tests a simple consumption based asset pricing model by approximating the true asset pricing kernel using low order orthonormal polynomials based on the model s state variables approximated kernels based solely on next period s consumption growth are not rejected by overall measures of model fit but they produce statistically and economically large pricing errors approximated kernels based on two quarters of future consumption growth and technology shocks have substantially improved overall fit in particular the best of these kernels are capable of eliminating the small firm effect a conventional approach to examining the implications of dynamic asset pricing models is to assume that markets are complete the economy is in equilibrium and that the unique state price deflator can be interpreted as the intertemporal marginal rate of substitution of a representative consumer given assumptions about the form of this unobservable utility function and on the observability of aggregate consumption the model can be tested by examining the conditional or unconditional covariation of estimated intertemporal marginal rates of substitution with measured asset returns the fact that this method of testing dynamic models requires strong assumptions is in and of itself not particularly troubling however the fact that these attempts have been almost uniformly inconsistent with the data on asset returns and consumption is problematic for example when the utility function is assumed to be time and state separable the absolute and relative levels of the real returns on risk free and risky securities see for example mehra and prescott 1985 and weil 1989 are inconsistent with the model s predictions the primary finding from a large literature testing consumption based models is that measured consumption is too smooth to rationalize the observed level and variability of asset returns for reasonable parameterizations of time separable utility functions an alternate approach pursued in this paper is to approximate the stateprice deflator or asset pricing kernel using orthonormal polynomials in a

a parametric nonlinear model of term structure dynamics recent nonparametric estimation studies pioneered by ait sahalia document that the diffusion of the short rate is similar to the parametric function r superscript 1 5 estimated by chan et al whereas the drift is substantially nonlinear in the short rate these empirical properties call into question the efficacy of the existing affine term structure models and beg for alternative models which admit the observed behavior this article presents such a model our model delivers closed form solutions for bond prices and a concave relationship between the interest rate and the yields we show that in empirical analyses our model outperforms the one factor affine models in both time series as well as cross sectional tests article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

returns of claims on the upside and the viability of u shaped pricing kernels abstract when the pricing kernel is u shaped then expected returns of claims with payout on the upside are negative for strikes beyond a threshold determined by the slope of the u shaped kernel in its increasing region and have negative partial derivative with respect to strike in the increasing region of the kernel using returns of i s p 500 index calls ii calls on major international equity indexes iii digital calls iv upside variance contracts and v a theoretical construct that we denote as kernel call we find broad support for the implications of u shaped pricing kernels a possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short selling

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

recovery of preferences from observed wealth in a single realization von neumann morgenstern preferences over terminal consumption can be inferred from wealth on a single sample path when markets are complete and returns follow a known law in a neoclassical investment problem in either a discrete time i i d binomial model or a continuous time diffusion model with a gaussian state variable numerical results suggest that useful information about preferences can be obtained from even a single noisy sample of monthly observations of a portfolio over 5 years article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

beyond arbitrage good deal asset price bounds in incomplete markets one often wants to value a risky payoff by reference to prices of other assets rather than by exploiting full fledged economic models however this approach breaks down if one cannot find a perfect replicating portfolio we impose weak economic restriction to derive usefully tight bounds on asset prices in this situation the bounds assume that investors would want to buy assets with high sharpe ratios good deals as well as pure arbitrage opportunities we show how to calculate the price bounds in one period multiperiod and continuous time contexts we show that the multiperiod problem can be solved recursively as a sequence of one period problems we calculate bounds in option pricing examples including infrequent trading and an option written on a nontraded event and we use the bounds to explore the economic significance of option pricing predictions we find that much variation in s p 500 index option prices over time and across strike prices fits within the bounds

bubbles and charges the definitions of fundamental value and speculative bubbles that are standard in macroeconomics and finance are given formal representations as the countably additive part and the purely finitely additive part a measure and a pure charge respectively of the supporting price system when the commodity space is lx examples illustrate that rational bubbles can occur in standard general equilibrium models with complete markets and a finite number of agents even in the absence of uncertainty consider an economy which includes securities or capital goods which are claims to cash flows over countably infinite time and also includes markets for all goods conduct the following thought experiment for each security add the present value of the first n elements of the cash flow and take the limit as n gets large this limit represents the fundamental value of the security the difference if any between the price of the security and its fundamental value is termed a speculative bubble this use of the terms fundamental and speculative bubble is we believe one of those that are generally accepted blanchard and fischer 1989 pp 218 221 for example used the terms precisely in this way yet confusion persists about what factors generate bubbles fads and irrationality have always figured prominently and the hypothesis that these factors are important has gained some empirical support from the literature on asset price volatility another bubbleproducing factor is the structure of information in the market in a partialequilibrium setting allen and gorton 1988 showed that rational bubbles can exist with a finite number of agents who have asymmetric information although fads and asymmetric information can undeniably produce bubbles here we focus exclusively on the phenomenon of speculative bubbles in general equilibrium models with optimizing agents rational expectations and symmetric information an important source of confusion we believe is that the term fundamental is used in connection with sunspot equilibria as well as bubble equilibria a sunspot equilibrium is one in which prices and allocations depend on irrelevant sunspots as well as exogenous variations in fundamentals preferences technology and endowments bubbles on this usage reflect the effect of extrinsic uncertainty on equilibrium prices and allocations this use of the term fundamental in connec