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782
Term structures of credit spreads with incomplete accounting information
 Econometrica
, 2001
"... Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of ..."
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Cited by 188 (10 self)
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Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfectinformation case, there exists a defaultarrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided. 1 We are exceptionally grateful to Michael Harrison for his significant contributions to this paper, which are noted within. We are also grateful for insightful research assistance
Numerical Valuation of High Dimensional Multivariate American Securities
, 1994
"... We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted ..."
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Cited by 95 (0 self)
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We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted expected cash flows under the modified riskneutral information process. Several efficient numerical techniques exist for pricing American securities depending on one or few (up to 3) risk sources. They are either latticebased techniques or finite difference approximations of the BlackScholes diffusion equation. However, these methods cannot be used for highdimensional problems, since their memory requirement is exponential in the
Solving ForwardBackward Stochastic Differential Equations Explicitly – a Four Step Scheme
 Prob. Th. Rel. Fields
, 1994
"... Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability ..."
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Cited by 88 (11 self)
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Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and su cient condition for the solvability of the linear FBSDEs with the processes Z (serves as a correction, see x1) being absent in the drift. Then a Riccati type equation for matrixvalued (not necessarily square) functions is derived using the idea of the FourStepScheme (introduced in [11] for general FBSDEs). The solvability of such a Riccati type equation is studied which leads to a representation of adapted solutions to linear FBSDEs. Keywords. Linear forwardbackward stochastic di erential equations, adapted solution, Riccati type equation. AMS Mathematics subject classi cation. 60H10.
An equilibrium model with restricted stock market participation
 Review of Financial Studies
, 1998
"... This article solves the equilibrium problem in a pureexchange, continuoustime economy in which some agents face information costs or other types of frictions effectively preventing them from investing in the stock market. Under the assumption that the restricted agents have logarithmic utilities, ..."
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Cited by 86 (4 self)
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This article solves the equilibrium problem in a pureexchange, continuoustime economy in which some agents face information costs or other types of frictions effectively preventing them from investing in the stock market. Under the assumption that the restricted agents have logarithmic utilities, a complete characterization of equilibrium prices and consumption/ investment policies is provided. A simple calibration shows that the model can help resolve some of the empirical asset pricing puzzles. It is well documented that even in welldeveloped capital markets, a large fraction of households does not participate in the stock market. For example, Mankiw and Zeldes (1991) report that 72.4 % of the households in a representative sample from the 1984 Panel Study of Income Dynamics held no stocks at all. 1 These households earned 62 % of the aggregate disposable income and accounted for 68 % of aggreWe thank Steve Shreve for several conversations on this topic and Kerry
Quadratic Term Structure Models: Theory and Evidence
, 1999
"... This paper theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally exible and thus encompasses the features of sever ..."
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Cited by 73 (1 self)
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This paper theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally exible and thus encompasses the features of several diverse models including the double squareroot model of Longsta (1989), the univariate quadratic model of Beaglehole and Tenney (1992), and the SquaredAutoregressiveIndependentVariable Nominal Term Structure (SAINTS) model of Constantinides (1992). We document a complete classication of admissibility and empirical identication for the QTSM, and demonstrate that the QTSM can overcome limitations inherent in ane term structure models (ATSMs). Using the Ecient Method of Moments of Gallant and Tauchen (1996), we test the empirical performance of the model in determining bond prices and compare the performance to the ATSMs. The results of the goodnessoft tests suggest that the QTSMs...
The Dynamics of Stochastic Volatility: Evidence from Underlying and Option Markets
, 2000
"... This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultane ..."
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Cited by 72 (1 self)
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This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultaneously. I conclude that the square root stochastic variance model of Heston (1993) and others is incapable of generating realistic returns behavior and find that the data are more accurately represented by a stochastic variance model in the CEV class or a model that allows the price and variance processes to have a timevarying correlation. Specifically, I find that as the level of market variance increases, the volatility of market variance increases rapidly and the correlation between the price and variance processes becomes substantially more negative. The heightened heteroskedasticity in market variance that results generates realistic crash probabilities and dynamics and causes returns to display values of skewness and kurtosis much more consistent with their sample values. While the model dramatically improves the fit of options prices relative to the square root process, it falls short of explaining the implied volatility smile for shortdated options.
Applications of Malliavin calculus to Monte Carlo methods in finance
 Finance and Stochastics
, 1999
"... This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the integrationbyparts formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin calcu ..."
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Cited by 68 (1 self)
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This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the integrationbyparts formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin calculus. The Greeks formulae, both with respect to initial conditions and for smooth perturbations of the local volatility, are provided for general discontinuous pathdependent payoff functionals of multidimensional diffusion processes. We illustrate the results by applying the formula to exotic European options in the framework of the Black and Scholes model. Our method is compared to the Monte Carlo finite difference approach and turns out to be very efficient in the case of discontinuous payoff functionals. Key words: Monte Carlo methods, Malliavin calculus, hedge ratios and Greeks JEL classification : G13 Mathematics Subject Classification (1991):60H07, 60J60, 65C05 1