Insurance valuation: A two-step generalised regression approach

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.

Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments

“…Note thatCarbonneau (2020) demonstrates the potential of the deep hedging algorithm for global hedging long-term lookback options embedded in segregated funds guarantees with multiple hedging instruments. It is also worth highlighting thatBarigou et al (2020) developed a pricing scheme consistent with local non-quadratic hedging procedures for insurance liabilities which relies on neural networks.28 In the context of segregated funds, the short position of the embedded option is assumed to be held by an insurance company who has to provide a quote and mitigate its risk exposure. The long position is held by an unsophisticated investor who will not be hedging his risk exposure.…”