Polynomial Diffusion Models for Life Insurance Liabilities

TL;DR

This paper introduces polynomial diffusion models on a compact state space for pricing and hedging life insurance liabilities, ensuring positivity and enabling explicit formulas for complex products.

Contribution

It develops a novel polynomial diffusion framework for life insurance liabilities that guarantees positivity and allows explicit pricing and hedging formulas.

Findings

Positivity of OIS short rate and mortality intensity ensured

Explicit formulas for pricing and hedging derived

Model applicable to a broad class of life insurance products

Abstract

In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model guarantees not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by explicit formulas.