Insurance valuation: A two-step generalised regression approach

TL;DR

This paper introduces a novel two-step hedging method for insurance valuation that incorporates regulatory risk preferences directly into the hedging process, using generalized regression and neural networks.

Contribution

It proposes an alternative hedging approach that ensures portfolios are risk measure-neutral, integrating regulatory preferences into the valuation process.

Findings

The method satisfies yearly solvency constraints naturally.

The portfolio minimizes risk among all satisfying the constraints.

Neural network algorithm enables practical implementation with simulated risk paths.

Abstract

Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.