Cover image for Actuarial Finance

Actuarial Finance

Author Jean-François Renaud , Mathieu Boudreault
Release Date: 2019/04/01
ISBN: 9781119137009
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Book Description

A new textbook offering a comprehensive introduction to models and techniques for the emerging field of actuarial Finance

Drs. Boudreault and Renaud answer the need for a clear, application-oriented guide to the growing field of actuarial finance with this volume, which focuses on the mathematical models and techniques used in actuarial finance for the pricing and hedging of actuarial liabilities exposed to financial markets and other contingencies. With roots in modern financial mathematics, actuarial finance presents unique challenges due to the long-term nature of insurance liabilities, the presence of mortality or other contingencies and the structure and regulations of the insurance and pension markets.

Motivated, designed and written for and by actuaries, this book puts actuarial applications at the forefront in addition to balancing mathematics and finance at an adequate level to actuarial undergraduates. While the classical theory of financial mathematics is discussed, the authors provide a thorough grounding in such crucial topics as recognizing embedded options in actuarial liabilities, adequately quantifying and pricing liabilities, and using derivatives and other assets to manage actuarial and financial risks.

Actuarial applications are emphasized and illustrated with about 300 examples and 200 exercises. The book also comprises end-of-chapter point-form summaries to help the reader review the most important concepts. Additional topics and features include:

  • Compares pricing in insurance and financial markets
  • Discusses event-triggered derivatives such as weather, catastrophe and longevity derivatives and how they can be used for risk management;
  • Introduces equity-linked insurance and annuities (EIAs, VAs), relates them to common derivatives and how to manage mortality for these products
  • Introduces pricing and replication in incomplete markets and analyze the impact of market incompleteness on insurance and risk management;
  • Presents immunization techniques alongside Greeks-based hedging;
  • Covers in detail how to delta-gamma/rho/vega hedge a liability and how to rebalance periodically a hedging portfolio.

This text will prove itself a firm foundation for undergraduate courses in financial mathematics or economics, actuarial mathematics or derivative markets. It is also highly applicable to current and future actuaries preparing for the exams or actuary professionals looking for a valuable addition to their reference shelf. 

As of 2019, the book covers significant parts of the Society of Actuaries’ Exams FM, IFM and QFI Core, and the Casualty Actuarial Society’s Exams 2 and 3F. It is assumed the reader has basic skills in calculus (differentiation and integration of functions), probability (at the level of the Society of Actuaries’ Exam P), interest theory (time value of money) and, ideally, a basic understanding of elementary stochastic processes such as random walks.

Table of Contents

  1. Cover
  2. Acknowledgments
  3. Preface
  4. Part I Introduction to actuarial finance
    1. 1 Actuaries and their environment
      1. 1.1 Key concepts
      2. 1.2 Insurance and financial markets
      3. 1.3 Actuarial and financial risks
      4. 1.4 Diversifiable and systematic risks
      5. 1.5 Risk management approaches
      6. 1.6 Summary
      7. 1.7 Exercises
      8. Notes
    2. 2 Financial markets and their securities
      1. 2.1 Bonds and interest rates
      2. 2.2 Stocks
      3. 2.3 Derivatives
      4. 2.4 Structure of financial markets
      5. 2.5 Mispricing and arbitrage opportunities
      6. 2.6 Summary
      7. 2.7 Exercises
      8. Note
    3. 3 Forwards and futures
      1. 3.1 Framework
      2. 3.2 Equity forwards
      3. 3.3 Currency forwards
      4. 3.4 Commodity forwards
      5. 3.5 Futures contracts
      6. 3.6 Summary
      7. 3.7 Exercises
      8. Notes
    4. 4 Swaps
      1. 4.1 Framework
      2. 4.2 Interest rate swaps
      3. 4.3 Currency swaps
      4. 4.4 Credit default swaps
      5. 4.5 Commodity swaps
      6. 4.6 Summary
      7. 4.7 Exercises
      8. Notes
    5. 5 Options
      1. 5.1 Framework
      2. 5.2 Basic options
      3. 5.3 Main uses of options
      4. 5.4 Investment strategies with basic options
      5. 5.5 Summary
      6. 5.6 Exercises
      7. Note
    6. 6 Engineering basic options
      1. 6.1 Simple mathematical functions for financial engineering
      2. 6.2 Parity relationships
      3. 6.3 Additional payoff design with calls and puts
      4. 6.4 More on the put-call parity
      5. 6.5 American options
      6. 6.6 Summary
      7. 6.7 Exercises
      8. Notes
    7. 7 Engineering advanced derivatives
      1. 7.1 Exotic options
      2. 7.2 Event-triggered derivatives
      3. 7.3 Summary
      4. 7.4 Exercises
      5. Note
    8. 8 Equity-linked insurance and annuities
      1. 8.1 Definitions and notations
      2. 8.2 Equity-indexed annuities
      3. 8.3 Variable annuities
      4. 8.4 Insurer’s loss
      5. 8.5 Mortality risk
      6. 8.6 Summary
      7. 8.7 Exercises
      8. Notes
  5. Part II Binomial and trinomial tree models
    1. 9 One-period binomial tree model
      1. 9.1 Model
      2. 9.2 Pricing by replication
      3. 9.3 Pricing with risk-neutral probabilities
      4. 9.4 Summary
      5. 9.5 Exercises
      6. Note
    2. 10 Two-period binomial tree model
      1. 10.1 Model
      2. 10.2 Pricing by replication
      3. 10.3 Pricing with risk-neutral probabilities
      4. 10.4 Advanced actuarial and financial examples
      5. 10.5 Summary
      6. 10.6 Exercises
    3. 11 Multi-period binomial tree model
      1. 11.1 Model
      2. 11.2 Pricing by replication
      3. 11.3 Pricing with risk-neutral probabilities
      4. 11.4 Summary
      5. 11.5 Exercises
      6. Notes
    4. 12 Further topics in the binomial tree model
      1. 12.1 American options
      2. 12.2 Options on dividend-paying stocks
      3. 12.3 Currency options
      4. 12.4 Options on futures
      5. 12.5 Summary
      6. 12.6 Exercises
      7. Note
    5. 13 Market incompleteness and one-period trinomial tree models
      1. 13.1 Model
      2. 13.2 Pricing by replication
      3. 13.3 Pricing with risk-neutral probabilities
      4. 13.4 Completion of a trinomial tree
      5. 13.5 Incompleteness of insurance markets
      6. 13.6 Summary
      7. 13.7 Exercises
      8. Notes
  6. Part III Black-Scholes-Merton model
    1. 14 Brownian motion
      1. 14.1 Normal and lognormal distributions
      2. 14.2 Symmetric random walks
      3. 14.3 Standard Brownian motion
      4. 14.4 Linear Brownian motion
      5. 14.5 Geometric Brownian motion
      6. 14.6 Summary
      7. 14.7 Exercises
      8. Notes
    2. 15 Introduction to stochastic calculus***
      1. 15.1 Stochastic Riemann integrals
      2. 15.2 Ito’s stochastic integrals
      3. 15.3 Ito’s lemma for Brownian motion
      4. 15.4 Diffusion processes
      5. 15.5 Summary
      6. 15.6 Exercises
      7. Notes
    3. 16 Introduction to the Black-Scholes-Merton model
      1. 16.1 Model
      2. 16.2 Relationship between the binomial and BSM models
      3. 16.3 Black-Scholes formula
      4. 16.4 Pricing simple derivatives
      5. 16.5 Determinants of call and put prices
      6. 16.6 Replication and hedging
      7. 16.7 Summary
      8. 16.8 Exercises
      9. Notes
    4. 17 Rigorous derivations of the Black-Scholes formula***
      1. 17.1 PDE approach to option pricing and hedging
      2. 17.2 Risk-neutral approach to option pricing
      3. 17.3 Summary
      4. 17.4 Exercises
      5. Notes
    5. 18 Applications and extensions of the Black-Scholes formula
      1. 18.1 Options on other assets
      2. 18.2 Equity-linked insurance and annuities
      3. 18.3 Exotic options
      4. 18.4 Summary
      5. 18.5 Exercises
      6. Notes
    6. 19 Simulation methods
      1. 19.1 Primer on random numbers
      2. 19.2 Monte Carlo simulations for option pricing
      3. 19.3 Variance reduction techniques
      4. 19.4 Summary
      5. 19.5 Exercises
      6. Note
    7. Hedging strategies in practice
      1. 20.1 Introduction
      2. 20.2 Cash-flow matching and replication
      3. 20.3 Hedging strategies
      4. 20.4 Interest rate risk management
      5. 20.5 Equity risk management
      6. 20.6 Rebalancing the hedging portfolio
      7. 20.7 Summary
      8. 20.8 Exercises
      9. Notes
  7. References
  8. Index
  9. End User License Agreement