INSURANCE VALUATION: A TWO-STEP GENERALISED REGRESSION APPROACH

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.

A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks

This study obtains a closed-form solution for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. This extends the work of Rémillard and Rubenthaler (2013), who obtained closed-form formulas for some components of the hedging problem solution. Coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm. The author also presents a brief sensitivity analysis to determine the impact of the underlying asset drift and the hedging portfolio rebalancing frequency on the optimal hedging capital and the initial hedge ratio.