# Gustav Alfelt: Modeling Realized Covariance of Asset Returns

**Time: **
Thu 2019-04-11 10.00

**Location: ** Room 22, House 5, Kräftriket, Department of Mathematics, Stockholm University

**Doctoral student: **
Gustav Alfelt

**Opponent: **
Tatjana von Rosen (Department of Statistics, SU)

**Supervisor: **
Joanna Tyrcha

Abstract: In this thesis, which consists of two papers, we consider the modeling of positive definitive symmetric matrices, in particular covariance matrices of financial asset returns. The return covariance matrix describes the magnitude in which prices of financial assets tend to change over time, and how price changes between different assets are related. It is an instrumental quantity in many financial applications, and furthermore, an important component in understanding the dynamics present prior to and during times of financial turbulence, such as the 2008 financial crisis.

In the first paper, we provide several goodness-of-fit tests applicable to models driven by a centralized Wishart process. To apply such a distributional assumption has become a popular way of modeling the stochastic properties of time-series of realized covariance matrices for asset returns. The paper includes a simulation study that aims to investigate how the tests perform under model uncertainty stemming from parameter estimation. In addition, the presented methods are used to

evaluate the fit of a typical model of realized covariance adapted to real data on six stocks traded on the New York Stock Exchange.

The second paper considers positive definite and symmetric random matrices of the exponential family. Under certain conditions for this class of distributions, we derive the Stein-Haff identity. Furthermore, we determine this identity in the case of the matrix-variate gamma distribution and apply it in order to present an estimator that outperforms the maximum likelihood estimator in terms of Stein's loss function. Finally, a small simulation study is conducted to support the theoretical results.