Semiparametric estimation of financial risk: corporate default, credit ratings, and implied volatility
Creators: name: Jiang, Yixiao
Publisher: name: No Publisher Supplied
Year: 2019

description: There are contexts in which it is important to estimate a model without overly assuming functional forms and distributions. For this reason, extant empirical work often considers semiparametric single-index models: that is, objects of interest depends on the explanatory vector x through a single linear index. However, as suggested by economic/financial theories, it is natural to consider models in which covariates interact more freely with each other through multiple indices. This dissertation consists of three chapters featuring the formulation and application of semiparametric, multiple-index methods in finance, spanning corporate default modeling, conflicts of interest in credit ratings, and option implied volatilities. In the first chapter, I introduce the econometric framework. As the number of indices increases, one technical difficulty that impedes statistical inference is to control bias terms of higher dimensional conditional expectation estimators. To control for this bias, I employ a differencing approach (see, Shen and Klein, 2019) which is known to reduce the bias to any order. However, there is no proof for asymptotic normality for a general multiple-index model and this result is critical for making inferences. Here, I obtain asymptotic normality (conjectured but not proven in Shen and Klein, 2019) by establishing a novel U-statistic equivalence result that utilizes the theory of empirical process developed by Eddy and Hartigan (1977). I also provide institutional background for the empirical substances of this dissertation and a brief literature review. The second chapter covers a semiparametric, ordered-response model of credit rating in which ratings are equilibrium outcomes of a stylized cheap-talk game. The proposed model allows the rating probability to be an unknown function of multiple indices permitting flexible interaction, non-monotonicity, and non-linearity in marginal effects. Based on Moody's rating data, I examine credit rating agencies' (CRAs) incentive to bias ratings when the CRA's shareholders invest in bond issuers. I find the degree of Moody's rating bias varies significantly for both rating categories as well as the institutional cross-ownership between Moody's and the bond issuer. In the third chapter, we consider an ordered-response model in which the threshold parameters are random and can correlate with some or all covariates. We use a control function approach to identify the index coefficients and provide a novel identiﬁcation and estimation strategy for the conditional threshold points up to location and scale. As a leading example, we consider estimation of the so-called "soft adjustment" --- adjustments made by CRA based on unobserved and possibly subjective criteria --- in the credit rating process. Empirically, we find a significant reduction of Moody's soft adjustment after the Dodd-Frank reform. Chapter 4 develops a Hausman type specification test for a partially linear model against a semiparametric bi-index alternative which permits interaction effects. Using recent S&amp;P 500 index traded options data, we confirm that a partially linear model permitting a flexible ``volatility smile" as well as an additive quadratic time effect is a statistically adequate depiction of the implied volatility data.