Quantitative Assessment of Common Practice Procedures in the Fair Evaluation of Embedded Options in Insurance Contracts

28 Pages Posted: 18 Nov 2016 Last revised: 28 Sep 2017

See all articles by Anna Gambaro

Anna Gambaro

Università del Piemonte Orientale; University of Piemonte Orientale

Riccardo Casalini

UnipolSai Assicurazioni SpA

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa; Bayes Business School - City, University of London

Alessandro Ghilarducci

Deloitte Consulting Srl

Date Written: September 13, 2017

Abstract

This work analyses the common industry practice used to evaluate financial options written on with-profit policies issued by European insurance companies.

In the last years regulators introduced, with the Solvency II directive, a market consistent valuation framework for determining the fair value of asset and liabilities of insurance funds.

A relevant aspect is how to deal with the estimation of sovereign credit and liquidity risk, that are important components in the valuation of the majority of insurance funds, which are usually heavily invested in treasury bonds.

The common practice is the adoption of the certainty equivalent approach (CEQ) for the risk neutral evaluation of insurance liabilities, which results in a deterministic risk adjustment of the securities cash flows.

In this paper, we propose an arbitrage free stochastic model for interest rate, credit and liquidity risks, that takes into account the dependences between different government bond issuers.

We test the impact of the common practice against our proposed model, via Monte Carlo simulations.

We conclude that in the estimation of options whose pay-off is determined by statutory accounting rules, which is often the case for European traditional with-profit insurance products, the deterministic adjustment for risk of the securities cash flows is not appropriate, and that a more complete model such as the one described in this article is a viable and sensible alternative in the context of market consistent evaluations.

Keywords: Minimum Guaranteed Fund, Segregated Insurance Fund, Embedded Options, Credit Risk, Liquidity Risk

JEL Classification: C0

Suggested Citation

Gambaro, Anna and Gambaro, Anna and Casalini, Riccardo and Fusai, Gianluca and Ghilarducci, Alessandro, Quantitative Assessment of Common Practice Procedures in the Fair Evaluation of Embedded Options in Insurance Contracts (September 13, 2017). Available at SSRN: https://ssrn.com/abstract=2872184 or http://dx.doi.org/10.2139/ssrn.2872184

Anna Gambaro (Contact Author)

Università del Piemonte Orientale ( email )

Novara
Italy

University of Piemonte Orientale ( email )

Dipartimento di Studi per l'Economia e l'Impresa
Via E. Perrone, 18
Novara, 28100

Riccardo Casalini

UnipolSai Assicurazioni SpA ( email )

Via Stalingrado 45
Bologna, 40128
Italy

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone, 18
Novara, 28100
Italy

HOME PAGE: http://https://upobook.uniupo.it/gianluca.fusai

Bayes Business School - City, University of London ( email )

106 Bunhill Row
London, EC2Y 8HB
Great Britain

HOME PAGE: http:// www.cass.city.ac.uk/experts/G.Fusai

Alessandro Ghilarducci

Deloitte Consulting Srl ( email )

Via Tortona 25
Milano, 20144
Italy

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