Tennessee Hickling

Tennessee Hickling, Dennis Prangle

We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply this approach to model financial returns, capturing potentially extreme shocks that arise in such data. The trained models can be used directly to generate new synthetic sets of potentially extreme returns

Tennessee Hickling, Dennis Prangle

Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in applications to both density estimation and variational inference. A popular current solution to this problem is to use a heavy tailed base distribution. We argue this can lead to poor performance due to the difficulty of optimising neural networks, such as normalizing flows, under heavy tailed input. We propose an alternative, "tail transform flow" (TTF), which uses a Gaussian base distribution and a final transformation layer which can produce heavy tails. Experimental results show this approach outperforms current methods, especially when the target distribution has large dimension or tail weight.