Pricing and Hedging the No-Negative-Equity Guarantee in Equity-Release Mortgages

TL;DR

This paper develops a practical superhedging strategy for the NNEG in equity-release mortgages within an incomplete market, highlighting the importance of realistic assumptions and introducing reinsurance to reduce hedging costs.

Contribution

It introduces a superhedging approach for NNEG in ERMs in an incomplete market setting, incorporating reinsurance to lower costs and providing a practical multi-period pricing model.

Findings

Market completeness assumptions undervalue NNEG.

Reinsurance significantly reduces superhedging costs.

Practical model prices are higher than complete market models but lower than regulatory thresholds.

Abstract

We provide a practical superhedging strategy for the pricing and hedging of the No-Negative-Equity-Guarantee (NNEG) found in Equity-Release Mortgages (ERMs), or reverse mortgages, using a discrete-time model. In contrast to many papers on the NNEG and industry practice we work in an incomplete market setting so that deaths and property prices are not independent under most pricing measures. We give theoretical results and numerical illustrations to show that the assumption of market completeness leads to a considerable undervaluation of the NNEG. By introducing an Excess-of-Loss reinsurance asset, we show that it is possible to reduce the cost of the superhedge for a portfolio of ERMs with the average cost decreasing rapidly as the number of lives in the portfolio increases. All the hedging assets, with the exception of cash, have a term of one year making the availability of a property hedging asset from over-the-counter derivative providers more realistic. We outline how a practical multi-period ERM pricing and hedging model can be built. Although the prices identified by this model will be higher than prices under the completeness assumption, they are considerably lower than those under the Equivalent Value Test mandated by the UK's Prudential Regulatory Authority.