Affine and generalized affine models: Theory and applications .

摘要

The main goal of this thesis is to introduce more flexibility in discrete time financial models while maintaining tractability.;The second chapter models joint dynamics of short term rate, term spread, inflation and economic growth factor in a Vector Autoregression and Moving Average (VARMA). We combine VARMA processes with the no-arbitrage restrictions and study the fore-castability of yields and macroeconomic variables. The paper shows that adding a Moving Average [MA] component to a standard VAR process offers substantial improvements in forecasting future yields, inflation, real activity and future interest rate risk premia where our benchmarks are either a standard VAR model or a dynamic version of the Nelson-Siegel model. An important hindsight from our results is that using VARMA processes break the tight link between current value of the state variable and the current conditional expectation of the future realization of the state variable, implicit in VAR models. Moreover, we show that the state variable follows a VARMA process under the risk-neutral probability measure only if the price of risk is linear in the current value of the state variable and the current conditional expectation of the future value of the state variable.;In the third chapter, we provide results for the valuation of European style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state-space setup using the no-arbitrage principle and an equivalent martingale measure. Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional non-normal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of equivalent martingale measures for which the resulting risk-neutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a time-varying price of risk and non-normal innovations. We provide extensions of these results to more general equivalent martingale measures and to discrete time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous time models.;Finally, the fourth chapter develops a conditional arbitrage pricing theory (APT) model where factors and idiosyncratic noises are both heteroscedastic and asymmetric. The model features both stochastic volatility and conditional skewness (SVS model), as well as conditional leverage effects. We explicitly allow asset prices to be asymmetric conditional on current factors and past information, termed contemporaneous asymmetry. Conditional skewness is driven by conditional leverage effects (through factor loadings) and contemporaneous asymmetry (through idiosyncratic skewness). We estimate and test three versions of the SVS model using several equity and index daily returns, as well as daily index option data. Results suggest that contemporaneous asymmetry is particularly important in several dimensions. It helps to match sample return skewness, negative and significant cross-correlations between returns and squared returns, as well as positive and significant cross-correlations between returns are cubed returns. Further diagnostics suggest that SVS models with contemporaneous asymmetry show a better option pricing performance compared to contemporaneous normality and existing affine GARCH models, especially, but not only, for in-the-money call options and short-maturity contracts. (Abstract shortened by UMI.);The first chapter builds a new class of model termed "generalized affine models". Affine models are very popular in modeling financial time series as they allow for analytical calculation of prices of financial derivatives like treasury bonds and options. The main property of affine models is that the conditional cumulant function, defined as the logarithmic of the conditional characteristic function, is affine in the state variable. Consequently, an affine model is Markovian, like an autoregressive process, which is an empirical limitation. The chapter generalizes affine models by adding in the current conditional cumulant function the past conditional cumulant function. Hence, generalized affine models are non-Markovian, such as ARMA and GARCH processes, allowing one to disentangle the short term and long-run dynamics of the process. Importantly, the new model keeps the tractability of prices of financial derivatives. This chapter studies the statistical properties of the new model, derives its conditional and unconditional moments, as well as the conditional cumulant function of future aggregated values of the state variable which is critical for pricing financial derivatives. It derives the analytical formulas of the term structure of interest rates and option prices. Different estimating methods are discussed (MLE, QML, GMM, and characteristic function based estimation methods).