8,241 research outputs found
Essays on risk and uncertainty in financial decision making: Bayesian inference of multi-factor affine term structure models and dynamic optimal portfolio choices for robust preferences
Thesis (Ph.D.)--Boston UniversityThis thesis studies model inference about risk and decision making under model uncertainty in two specific settings. The first part of the thesis develops a Bayesian Markov Chain Monte Carlo (MCMC) estimation method for multi-factor affine term structure models. Affine term structure models are popular because they provide closed-form solutions for the valuation of fixed income securities. Efficient estimation methods for parameters of these models, however, are not readily available. The MCMC algorithms developed provide more accurate estimates, compared with alternative estimation methods. The superior performance of the MCMC algorithms is first documented in a simulation study. Convergence of the algorithm used to sample posterior distributions is documented in numerical experiments. The Bayesian MCMC methodology is then applied to yield data. The in-sample pricing errors obtained are significantly smaller than those of alternative methods. A Bayesian forecast analysis documents the significant superior predictive power of the MCMC approach. Finally, Bayesian model selection criteria are discussed. Incorporating aspects of model uncertainty for the optimal allocation of risk has become an important topic in finance. The second part of the thesis considers an optimal dynamic portfolio choice problem for an ambiguity-averse investor. It introduces new preferences that allow the separation of risk and ambiguity aversion. The novel representation is based on generalized divergence measures that capture richer forms of model uncertainty than traditional relative entropy measures. The novel preferences are shown to have a homothetic stochastic differential utility representation. Based on this representation, optimal portfolio policies are derived using numerical schemes for forward-backward stochastic differential equations. The optimal portfolio policy is shown to contain new hedging motives induced by the investor's attitude toward model uncertainty. Ambiguity concerns introduce additional horizon effects, boost effective risk aversion, and overall reduce optimal investment in risky assets. These findings have important implications for the design of optimal portfolios in the presence of model uncertainty
GMM Estimation of Affine Term Structure Models
This article investigates parameter estimation of affine term structure
models by means of the generalized method of moments. Exact moments of the
affine latent process as well as of the yields are obtained by using results
derived for p-polynomial processes. Then the generalized method of moments,
combined with Quasi-Bayesian methods, is used to get reliable parameter
estimates and to perform inference. After a simulation study, the estimation
procedure is applied to empirical interest rate data
Predicting the term structure of interest rates incorporating parameter uncertainty, model uncertainty and macroeconomic information
We forecast the term structure of U.S. Treasury zero-coupon bond yields by analyzing a range of models that have been used in the literature. We assess the relevance of parameter uncertainty by examining the added value of using Bayesian inference compared to frequentist estimation techniques, and model uncertainty by combining forecasts from individual models. Following current literature we also investigate the benefits of incorporating macroeconomic information in yield curve models. Our results show that adding macroeconomic factors is very beneficial for improving the out-of-sample forecasting performance of individual models. Despite this, the predictive accuracy of models varies over time considerably, irrespective of using the Bayesian or frequentist approach. We show that mitigating model uncertainty by combining forecasts leads to substantial gains in forecasting performance, especially when applying Bayesian model averaging
A data driven equivariant approach to constrained Gaussian mixture modeling
Maximum likelihood estimation of Gaussian mixture models with different
class-specific covariance matrices is known to be problematic. This is due to
the unboundedness of the likelihood, together with the presence of spurious
maximizers. Existing methods to bypass this obstacle are based on the fact that
unboundedness is avoided if the eigenvalues of the covariance matrices are
bounded away from zero. This can be done imposing some constraints on the
covariance matrices, i.e. by incorporating a priori information on the
covariance structure of the mixture components. The present work introduces a
constrained equivariant approach, where the class conditional covariance
matrices are shrunk towards a pre-specified matrix Psi. Data-driven choices of
the matrix Psi, when a priori information is not available, and the optimal
amount of shrinkage are investigated. The effectiveness of the proposal is
evaluated on the basis of a simulation study and an empirical example
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
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A Stochastic Volatility Model With Realized Measures for Option Pricing
Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options
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