Statistical inference for low rank volatility
Seminar in Insurance and Economics
SPEAKER: Mark Podolskij (University of Luxembourg).
TITLE: Statistical inference for low rank volatility.
ABSTRACT: In this talk we will discuss some statistical results for diffusion models with low rank volatility process. Such models appear in financial mathematics when considering joint modelling of financial instruments written on the same assets, such as e.g. bond prices with different maturities. First of all, we present a statistical procedure to estimate the maximal rank of the volatility process. This rank is equivalent to the minimal amount of Brownian motions required to model a given multivariate diffusion. The test is performed using high-frequency data. Secondly, we will consider the high-dimensional setting and investigate estimation of the matrix-valued volatility under low rank constraints. We apply the theoretical results to empirical data from Dow Jones Industrial Average.