Lecturers

Levon Barseghyan (Cornell University, Department of Economics)

Topic

Estimating Risk Preferences Using Market Data: Challenges and New Methods

Abstract

We start by briefly reviewing a number of models of risk preferences including both expected utility (EU) theory and prominent non-EU models that have been estimated using field data. We then study how and when such models can be (separately) identified. In particular, we examine the role of various assumptions about underlying fundamentals in driving identification and assess how these assumptions affect inference. We then detail easy-to-implement partial identification methods that build on revealed preference argument to conduct inference at the individual level. In particular, these methods allow us to (i) classify households into various decision types (e.g. EU versus non-EU); (ii) measure how well a given model of risk preferences fits observed patterns of choices and recover its parameterizations that best fit the data; and (iii) investigate potential sources for sub-optimal behavior (such as choices of dominating options). We conclude by discussing state-of-the-art identification and inference techniques for a general model that features (i) different preference types, (ii) unobserved heterogeneity in risk attitudes within types, and (iii) unobserved heterogeneity in attention levels, whereby each market participant may pay attention only to a subset of options available to her.

Damir Filipović (Swiss Finance Institute & Ecole Polytechnique Fédérale de Lausanne)

Topic

Polynomial Models in Finance

Abstract

Financial asset pricing and portfolio management rely on dynamic stochastic models. In this course, I introduce a large class of financial models based on polynomial jump-diffusions. These are defined as jump-diffusions whose generators map polynomials to polynomials of the same or lower degree. Polynomial jump-diffusions admit closed form conditional moments, which renders them computation-ally tractable.

I show that the polynomial property of a jump-diffusion is preserved under exponentiation and subordination. These transformations allow us to easily construct polynomial jump-diffusions from simple building blocks. They also allow us to efficiently specify non-linearities in financial models, which renders them flexible in capturing many of the empirical features of financial time series. I revisit affine jump-diffusions and qualify them as special cases of polynomial jump-diffusions. The affine property is not invariant under exponentiation or subordination, which may explain why these transformations are not widely applied in affine financial models.

I present a generic method for derivatives pricing in polynomial jump-diffusion models. This method builds on the expansion of the likelihood ratio function with respect to an orthonormal basis of polynomials in some conveniently weighted L2 space. I contrast this to the Fourier transform analysis in affine models. We study applications to interest rate, credit risk, and stochastic volatility models.

This course builds on the papers (Ackerer and Filipović 2015), (Ackerer, Filipović, and Pulido 2015), (Filipović, Gourier, and Mancini 2016), (Filipović and Larsson 2016), (Filipović and Larsson 2017), (Filipović, Larsson, and Trolle 2014).

Christian Gollier (Toulouse School of Economics)

Topic

Aversion to risk of regret and preference for positively skewed risks