Assessing Asset-Liability Risk with Neural Networks

Abstract

We introduce a neural network approach for assessing the risk of a portfolio of assets and liabilities over a given time period. This requires a conditional valuation of the portfolio given the state of the world at a later time, a problem that is particularly challenging if the portfolio contains structured products or complex insurance contracts which do not admit closed form valuation formulas. We illustrate the method on different examples from banking and insurance. We focus on value-at-risk and expected shortfall, but the approach also works for other risk measures.

Neural networks meet least squares Monte Carlo at internal model data

“…An application of neural networks for an valuation of variable annuities with guaranteed minimum income benefit with three risk factors is included in Cheridito et al [6], the example follows the previous work with a classical LSMC solution in Bauer and Ha [2].…”

“…with real-valued functions l ∶ ℝ → ℝ , which are called activation functions of the neural network and for which it is required to be monotone and Lipschitz continuous (see Definition 1 in Krah et al [19] 6 ). In our use case all l , l ∈ {1, … , L} , are equal and denoted by .…”

“…Fig 6. Box plots for the mean error resulting from 300 calculated nets for all validation points and Portfolios 1, 2 and 3 (denoted by Pf1, Pf2 and Pf3, respectively)…”

Deep treasury management for banks

“…Their problem setting is different from ours as they consider a runoff setting (no going concern), only optimize relative investment decisions (not the scale), do not consider financing decisions or constraints, and use a binary objective of whether assets are sufficient to pay all debts or not. Cheridito et al ( 2020 ) use neural networks to approximate the value and thereby the risk of a liability portfolio consisting, for instance, of options or variable annuities. This deviates from our setting since we face asset and liability portfolios that consist mainly of bonds and other deterministic as well as stochastic cash flows.…”

Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests

“…Bauer et al [2], Krah et al [23] and Floryszczak et al [11] have used Least Square Monte-Carlo (regress now) methods for the risk while Pelsser and Schweizer [25], Cambou and Filipović have developed the replicating portfolio (or regress later) approach. Recently, Cheredito et al [7] and Fernandez-Arjona and Filipović [10] have proposed to use neural networks to approximate the conditional expectation. Up to our knowledge, there are however no dedicated study on the use of multilevel Monte-Carlo estimators for the calculation of the SCR with practical application in an insurance context.…”