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31
Asset pricing at the millennium
 Journal of Finance
"... This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior ..."
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Cited by 123 (3 self)
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This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and crosssectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar* Department of Economics, Harvard University, Cambridge, Massachusetts
Term structure dynamics in theory and reality
 Review of Financial Studies
, 2003
"... This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in ..."
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Cited by 46 (8 self)
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This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in which the risk factors follow diffusions, jumpdiffusion, or have “switching regimes. ” Then the goodnessoffits of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixedincome derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads. 1
Jackknifing bond option prices
 Review of Financial Studies
, 2005
"... Prices of interest rate derivative securities depend crucially on the mean reversion parameters of the underlying diffusions. These parameters are subject to estimation bias when standard methods are used. The estimation bias can be substantial even in very large samples and much more serious than t ..."
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Cited by 21 (11 self)
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Prices of interest rate derivative securities depend crucially on the mean reversion parameters of the underlying diffusions. These parameters are subject to estimation bias when standard methods are used. The estimation bias can be substantial even in very large samples and much more serious than the discretization bias, and it translates into a bias in pricing bond options and other derivative securities that is important in practical work. This article proposes a very general and computationally inexpensive method of bias reduction that is based on Quenouille’s (1956; Biometrika, 43, 353–360) jackknife. We show how the method can be applied directly to the options price itself as well as the coefficients in the models. We investigate its performance in a Monte Carlo study. Empirical applications to U.S. dollar swap rates highlight the differences between bond and option prices implied by the jackknife procedure and those implied by the standard approach. These differences are large and suggest that bias reduction in pricing options is important in practical applications. For more than three decades continuous time models have proved to be
Do financial institutions matter
 Journal ofFinance
, 2001
"... In standard asset pricing theory, investors are assumed to invest directly in financial markets. The role of financial institutions is ignored. The focus in corporate finance is on agency problems. How do you ensure that managers act in shareholders’ interests? There is an inconsistency in assuming ..."
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Cited by 20 (0 self)
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In standard asset pricing theory, investors are assumed to invest directly in financial markets. The role of financial institutions is ignored. The focus in corporate finance is on agency problems. How do you ensure that managers act in shareholders’ interests? There is an inconsistency in assuming that when you give your money to a financial institution there is no agency problem but when you give it to a firm there is. It is argued both areas need to take proper account of the role of financial institutions and markets. Appropriate concepts for analyzing particular situations should be used. 1 DO FINANCIAL INSTITUTIONS MATTER? When I was an assistant professor my view on referees was that nine out of ten of them were complete idiots. They obviously had no idea what my papers were about or they wouldn’t have rejected them. Fortunately the remaining one out of ten was astute and sometimes would actually recommend a revise and resubmit. Over the years I learned where the problem lay and it was not with the referees. By the time I was an editor my opinion on referees had been reversed and I realized how much they could
Pricing multiname credit derivatives: heavy tailed hybrid approach
, 2002
"... In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are in ..."
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Cited by 13 (1 self)
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In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are instruments with payoffs that are contingent on the default realization in a portfolio of names. The modeling of dependent defaults is difficult because there is very little historical data available about joint defaults and because the prices of those instruments are not quoted. Therefore, the models cannot be calibrated, neither to defaults nor to prices. In this paper, we present a methodology for the estimation, simulation, and pricing of multiname contingent instruments. Our model is a hybrid of the wellknown structural and reduced form approaches for modeling defaults. The dependence structure of our model is of a tcopula that possesses nontrivial tail dependence. The tcopula allows for more joint extreme events, which have a big impact on the prices of multiname instruments, e.g. n thtodefault baskets and CDOs. We demonstrate this impact with n thtodefault baskets.
The Econometrics of Option Pricing
"... The growth of the option pricing literature parallels the spectacular developments of derivative securities and the rapid expansion of markets for derivatives in the last three decades. Writing a survey of option pricing models appears therefore like a formidable task. To delimit our focus we will ..."
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Cited by 12 (1 self)
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The growth of the option pricing literature parallels the spectacular developments of derivative securities and the rapid expansion of markets for derivatives in the last three decades. Writing a survey of option pricing models appears therefore like a formidable task. To delimit our focus we will put emphasis on the more recent contributions since there are
Inference With NonGaussian OrnsteinUhlenbeck Processes for Stochastic Volatility
, 2003
"... Continuoustime stochastic volatility models are becoming an increasingly popular way to describe moderate and highfrequency financial data. Recently, BarndorffNielsen and Shephard (2001a) proposed a class of models where the volatility behaves according to an OrnsteinUhlenbeck process, driven by ..."
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Cited by 10 (2 self)
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Continuoustime stochastic volatility models are becoming an increasingly popular way to describe moderate and highfrequency financial data. Recently, BarndorffNielsen and Shephard (2001a) proposed a class of models where the volatility behaves according to an OrnsteinUhlenbeck process, driven by a positive Lévy process without Gaussian component. These models introduce discontinuities, or jumps, into the volatility process. They also consider superpositions of such processes and we extend that to the inclusion of a jump component in the returns. In addition, we allow for leverage effects and we introduce separate risk pricing for the volatility components. We design and implement practically relevant inference methods for such models, within the Bayesian paradigm. The algorithm is based on Markov chain Monte Carlo (MCMC) methods and we use a series representation of Lévy processes. MCMC methods for such models are complicated by the fact that parameter changes will often induce a change in the distribution of the representation of the process and the associated problem of overconditioning. We avoid this problem by dependent thinning methods. An application to stock price data shows the models perform very well, even in the face of data with rapid changes, especially if a superposition of processes with different risk premiums and a leverage effect is used.
2008) Estimation of dynamic models with nonparametric simulated maximum likelihood, working paper
"... We propose a simulated maximum likelihood estimator (SMLE) for general stochastic dynamic models based on nonparametric kernel methods. The method requires that, while the actual likelihood function cannot be written down, we can still simulate observations from the model. From the simulated observa ..."
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Cited by 7 (5 self)
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We propose a simulated maximum likelihood estimator (SMLE) for general stochastic dynamic models based on nonparametric kernel methods. The method requires that, while the actual likelihood function cannot be written down, we can still simulate observations from the model. From the simulated observations, we estimate the unknown density of the model nonparametrically by kernel methods, and then obtain the SMLEs of the model parameters. Our method avoids the issue of nonidenti…cation arising from poor choice of auxiliary models in simulated methods of moments (SMM) or indirect inference. More importantly, our SMLEs achieve higher e ¢ ciency under weak regularity conditions. Finally, our method allows for potentially nonstationary processes, including timeinhomogeneous dynamics.
On simulated likelihood of discretely observed diffusion processes and comparison to closed form approximation
 Journal of Computational and Graphical Statistics
, 2007
"... This article focuses on two methods to approximate the loglikelihood function for univariate diffusions: 1) the simulation approach using a modified Brownian bridge as the importance sampler; and 2) the recent closedform approach. For the case of constant volatility, we give a theoretical justifica ..."
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Cited by 6 (0 self)
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This article focuses on two methods to approximate the loglikelihood function for univariate diffusions: 1) the simulation approach using a modified Brownian bridge as the importance sampler; and 2) the recent closedform approach. For the case of constant volatility, we give a theoretical justification of the modified Brownian bridge sampler by showing that it is exactly a Brownian bridge. We also discuss computational issues in the simulation approach such as accelerating numerical variance stabilizing transformation, computing derivatives of the simulated loglikelihood, and choosing initial values of parameter estimates. The two approaches are compared in the context of financial applications with annualized parameter values, where the diffusion model has an unknown transition density and has no analytical variance stabilizing transformation. The closedform expansion, particularly the secondorder closedform, is found to be computationally efficient and very accurate when the observation frequency is monthly or higher. It is more accurate in the center than in the tail of the transition density. The simulation approach combined with the variance stabilizing transformation is found to be more reliable than the closedform approach when the observation frequency is lower. Both methods performs better when the volatility level is lower, but the simulation method is more robust to the volatility nature of the diffusion model. When applied to two well known datasets of daily observations, the two methods yield similar parameter estimates in both datasets but slightly different loglikelihood in the case of higher volatility.
Importance sampling techniques for estimation of diffusion models
 In
, 2012
"... This article develops a class of Monte Carlo (MC) methods for simulating conditioned diffusion sample paths, with special emphasis on importance sampling schemes. We restrict attention to a particular type of conditioned diffusions, the socalled diffusion bridge processes. The diffusion bridge is t ..."
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Cited by 4 (2 self)
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This article develops a class of Monte Carlo (MC) methods for simulating conditioned diffusion sample paths, with special emphasis on importance sampling schemes. We restrict attention to a particular type of conditioned diffusions, the socalled diffusion bridge processes. The diffusion bridge is the process obtained by conditioning a diffusion to start and finish at specific values at two consecutive times t0 < t1. Diffusion bridge simulation is a highly nontrivial problem. At an even more elementary level unconditional simulation of diffusions, that is without fixing the value of the process at t1, is difficult. This is a simulation from the transition distribution of the diffusion which is typically intractable. This intractability stems from the implicit specification of the diffusion as a solution of a stochastic differential equation (SDE). Although the unconditional simulation can be carried out by various approximate schemes based on discretizations of the SDE, it is not feasible to devise similar schemes for diffusion bridges in general. This has motivated active research in the last 15 years or so for the development of MC methodology for diffusion bridges. The research in this direction has been fuelled by the fundamental role that diffusion bridge simulation plays in the statistical inference for diffusion processes. Any statistical analysis which requires the transition density of the process is halted whenever the latter is not explicitly available, which is typically the case. Hence it is challenging to fit diffusion models employed in applications to the incomplete data typically available. An interesting possibility is to approximate the intractable transition density using an appropriate MC scheme and carry