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

List of Tables

1. Chapter 2
   1. Table 2.1
   2. Table 2.2
2. Chapter 4
   1. Table 4.1
3. Chapter 7
   1. Table 7.1
4. Chapter 8
   1. Table 8.1
5. Chapter 15
   1. Table 15.1
6. Chapter 17
   1. Table 17.1
7. Chapter 19
   1. Table 19.1
8. Chapter 20
   1. Table 20.1

List of Illustrations

1. Chapter 1
   1. Figure 1.1 Systematic risk
   2. Figure 1.2 Partially diversifiable risks
2. Chapter 2
   1. Figure 2.1 Typical term structure of interest rate
   2. Figure 2.2 U.S. Treasury yield curve as of December 31st, 2015. Data from Federal Reserve ...
   3. Figure 2.3 Different shapes of the term structure of interest rates
   4. Figure 2.4 Relationship between spot and forward rates
3. Chapter 3
   1. Figure 3.1 Cash flows of a forward contract at maturity
   2. Figure 3.2 Payoff of a long forward (continuous line) and a short forward (dotted line)
4. Chapter 4
   1. Figure 4.1 Periodic cash flows of a general swap
   2. Figure 4.2 Valuation of a fixed-rate bond
   3. Figure 4.3 Valuation of a floating-rate bond
   4. Figure 4.4 Swap between two parties initiated with an intermediary such as a financial ins...
   5. Figure 4.5 Cash flows of a typical credit default swap
5. Chapter 5
   1. Figure 5.1 Exchanges between the buyer and the seller of a call option at maturity for a p...
   2. Figure 5.2 Exchanges between the buyer and the seller of a call option at maturity for a c...
   3. Figure 5.3 Payoff (continuous line) and profit (dashed line) of long/short call and put op...
   4. Figure 5.4 Exchanges between the buyer and the seller of a put option at maturity for a ph...
   5. Figure 5.5 Exchanges between the buyer and the seller of a put option at maturity for a ca...
   6. Figure 5.6 Payoff (continuous line) and profit (dashed line) of various strategies involvi...
   7. Figure 5.7 Payoff (continuous line) and profit (dashed line) of a straddle
   8. Figure 5.8 Payoff of a heartbeat option
6. Chapter 6
   1. Figure 6.1 Maximum function and related functions
   2. Figure 6.2 Indicator function of the event {x > a}
   3. Figure 6.3 Asset-or-nothing and cash-or-nothing binary options
   4. Figure 6.4 Gap call and put options
7. Chapter 7
   1. Figure 7.1 Knock-in and knock-out barrier options. Shaded areas imply the option is activa...
   2. Figure 7.2 A path of the stock price along with the continuously and discretely monitored ...
   3. Figure 7.3 Fictional evolution of the stock price over a year
8. Chapter 8
   1. Figure 8.1 Evolution of a sub-account balance for a GMWB with periodic withdrawal ω
9. Chapter 13
   1. Figure 13.1 Different payoff functions and their corresponding super-replicating (continuou...
10. Chapter 14
    1. Figure 14.1 Standard normal distribution (μ = 0 and σ² = 1)
    2. Figure 14.2 Lognormal distribution with parameters μ = 0 and σ² = 1
    3. Figure 14.3 A symmetric random walk. At each time step, it moves upward or downward by 1 wi...
    4. Figure 14.4 A symmetric random walk where the process is kept constant in between time step...
    5. Figure 14.5 An accelerated symmetric random walk with n = 2
    6. Figure 14.6 Accelerated and rescaled symmetric random walks
    7. Figure 14.7 Sample path of a standard Brownian motion
    8. Figure 14.8 Sample path of a discretized standard Brownian motion (SBM)
    9. Figure 14.9 Sample path of the standard Brownian motion depicted in example 14.3.6
    10. Figure 14.10 Sample paths of linear Brownian motions (black) along with the corresponding st...
    11. Figure 14.11 Sample path of a discretized linear Brownian motion
    12. Figure 14.12 Sample path generated in example 14.4.4
    13. Figure 14.13 Sample paths of geometric Brownian motions (GBMs) with different parameters
    14. Figure 14.14 Sample path of the geometric Brownian motion depicted in example 14.5.3
11. Chapter 15
    1. Figure 15.1 Riemann integral of a given path of a stochastic process using Riemann sums
    2. Figure 15.2 Four paths of the same elementary one-step stochastic process H_t as defined in ...
    3. Figure 15.3 Two different paths of the same elementary stochastic process H
    4. Figure 15.4 A sample path H_t(ω) approximated by different step functions. For n large, the ...
12. Chapter 16
    1. Figure 16.1 An eight-period binomial tree (left panel) along with the probability mass func...
    2. Figure 16.2 Four different sample paths of the asset price in a 20-period binomial tree
    3. Figure 16.3 Illustration of a path in the binomial tree as the number of time steps increas...
    4. Figure 16.4 Convergence of a call option price in Cox-Ross-Rubinstein (CRR) binomial trees ...
    5. Figure 16.5 A highlighted sub-tree (in black) of 10 periods in a tree with 20 periods
    6. Figure 16.6 Black-Scholes formulas (solid line: call, dashed line: put) as functions of S₀,...
13. Chapter 19
    1. Figure 19.1 Histogram of 100 uniform random numbers (left panel) and the probability mass f...
    2. Figure 19.2 Histogram of 10, 000 uniform random numbers (left panel) and the probability ma...
    3. Figure 19.3 A sample path of a geometric Brownian motion (solid line) and its corresponding...
14. Chapter 20
    1. Figure 20.1 Liability tied to the life insurance business of example 20.1.1 as a function o...
    2. Figure 20.2 The price of a zero-coupon bond as a function of the interest rate (solid line)...
    3. Figure 20.3 Quality of duration and duration-convexity matching hedging strategies as a fun...
    4. Figure 20.4 Value of the 1-year call option (liability, continuous line) and of the asset p...
    5. Figure 20.5 Value of the 1-year call option (liability, continuous line) and of the investm...
    6. Figure 20.6 Initial value of a 10-year put option as a function of the risk-free rate r (so...

Guide

1. Cover
2. Table of Contents
3. Part