Boudreault Mathieu - Actuarial finance : derivatives, quantitative models and risk management

Mathieu Boudreault and Jean-Franois Renaud

Universit du Qubec Montral, Canada

This edition first published 2019

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9781119137009 (hardback)

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Jolle, Justine, Raphal et Thomas

Julie, tienne et Anne-Sophie

We are deeply grateful to our families for their unconditional support.

Special thanks to Genevive Gauthier, Carole Bernard and Christiane Lemieux for their impact on our first years of teaching this material. Many thanks to colleagues from both academia and industry who took some of their precious time to review one or several chapters of earlier versions of the book: (in alphabetical order) Maciej Augustyniak, Jean-Franois Bgin, Bruno Gagnon, Ron Gebhardtsbauer, Jonathan Grgoire, Anne MacKay, Clarence Simard, Tommy Thomassin and Marie-Claude Vachon. Your comments were greatly appreciated and helped improve our book.

We also wish to thank the students who have attended our lectures for their feedback. This book is for you.

Finally, warm thanks to Jean-Mathieu Potvin for turning our handwritten plots into beautiful TikZ figures, to Christel Jackson Book for carefully reviewing each and every example and exercise, and to Adel Benlagra who also contributed to solve and revise exercises in the first half of the book. All remaining errors and typos are ours.

The work of actuaries has been strongly impacted by the deregulation of financial markets and the financial innovation that followed. Nowadays, there are embedded options in many life insurance and annuity products. Moreover, the use of weather and catastrophe derivatives in P&C insurance, to manage losses from earthquakes, hurricanes, floods and extreme weather, is constantly increasing, while longevity derivatives have been created to manage longevity risk on pools of pensioners.

As a consequence, in recent years actuarial finance has become an emerging field at the crossing of actuarial science and mathematical finance, i.e. when both actuarial and financial risks have to be taken into account. Despite its common roots with modern financial mathematics, actuarial finance has its own challenges due to:

• the very long-term nature (several years or decades) of insurance liabilities;
• the presence of mortality risk and other contingencies;
• the structure and regulations of the insurance and pension markets.

Therefore, it is now widely recognized that actuaries should have a basic knowledge of:

• derivatives and other assets to manage actuarial and financial risks;
• embedded options in actuarial liabilities.

As we are writing this book for the typical actuarial science (undergraduate) student or practitioner, our main goal is to find an appropriate balance between the level of mathematics and finance in the presentation of classical financial models such as the binomial tree and the Black-Scholes-Merton model. Given the growing complexity of many actuarial liabilities and their ties to financial markets, we also felt the need for a book with actuarial applications at the forefront.

Therefore, this book has been motivated, designed and written for actuaries (and by actuaries). This means that we spend more time on and put more energy into what matters to actuaries, i.e. topics of particular relevance for actuaries are introduced at a more accessible level and analyzed in greater depth. For example, in this book, we:

• compare pricing in insurance and financial markets;
• present credit default swaps which are largely used by insurance companies to manage credit risk and we compare them with term life insurance;
• discuss event-triggered derivatives such as weather, catastrophe and longevity derivatives and how they can be used for risk management;
• introduce equity-linked insurance and annuities (EIAs, VAs), relate them to common derivatives and describe how to manage mortality for these products;
• put more emphasis on replication in the (two-period and n-period) binomial model and in the Black-Scholes-Merton model to better grasp the origins of the so-called actuarial/real-world and risk-neutral probabilities (or the (in)famous and measures);
• implement and rebalance dynamic hedging strategies over several periods;
• introduce pricing and replication in incomplete markets and analyze the impact of market incompleteness on insurance and risk management;