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…mehr
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. 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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
MATHIEU BOUDREAULT, PHD, is Professor of Actuarial Science in the Département de mathématiques at Université du Québec à Montréal (UQAM), Canada. Fellow of the Society of Actuaries and Associate of the Canadian Institute of Actuaries, his teaching and research interests include actuarial finance, catastrophe modeling and credit risk. JEAN-FRANÇOIS RENAUD, PHD, is Professor of Actuarial Science in the Département de mathématiques at Université du Québec à Montréal (UQAM), Canada. His teaching and research interests include actuarial finance, actuarial mathematics and applied probability.
Inhaltsangabe
Acknowledgments xvii Preface xix Part I Introduction to actuarial finance 1 1 Actuaries and their environment 3 1.1 Key concepts 3 1.2 Insurance and financial markets 6 1.3 Actuarial and financial risks 8 1.4 Diversifiable and systematic risks 9 1.5 Risk management approaches 15 1.6 Summary 16 1.7 Exercises 17 2 Financial markets and their securities 21 2.1 Bonds and interest rates 21 2.2 Stocks 29 2.3 Derivatives 32 2.4 Structure of financial markets 35 2.5 Mispricing and arbitrage opportunities 38 2.6 Summary 42 2.7 Exercises 44 3 Forwards and futures 49 3.1 Framework 49 3.2 Equity forwards 52 3.3 Currency forwards 59 3.4 Commodity forwards 61 3.5 Futures contracts 62 3.6 Summary 70 3.7 Exercises 72 4 Swaps 75 4.1 Framework 76 4.2 Interest rate swaps 77 4.3 Currency swaps 87 4.4 Credit default swaps 90 4.5 Commodity swaps 93 4.6 Summary 95 4.7 Exercises 96 5 Options 99 5.1 Framework 100 5.2 Basic options 102 5.3 Main uses of options 107 5.4 Investment strategies with basic options 110 5.5 Summary 114 5.6 Exercises 116 6 Engineering basic options 119 6.1 Simple mathematical functions for financial engineering 119 6.2 Parity relationships 122 6.3 Additional payoff design with calls and puts 126 6.4 More on the put-call parity 129 6.5 American options 133 6.6 Summary 136 6.7 Exercises 137 7 Engineering advanced derivatives 141 7.1 Exotic options 141 7.2 Event-triggered derivatives 150 7.3 Summary 154 7.4 Exercises 156 8 Equity-linked insurance and annuities 159 8.1 Definitions and notations 160 8.2 Equity-indexed annuities 161 8.3 Variable annuities 165 8.4 Insurer's loss 171 8.5 Mortality risk 173 8.6 Summary 177 8.7 Exercises 179 Part II Binomial and trinomial tree models 183 9 One-period binomial tree model 185 9.1 Model 185 9.2 Pricing by replication 190 9.3 Pricing with risk-neutral probabilities 195 9.4 Summary 198 9.5 Exercises 199 10 Two-period binomial tree model 201 10.1 Model 201 10.2 Pricing by replication 212 10.3 Pricing with risk-neutral probabilities 220 10.4 Advanced actuarial and financial examples 225 10.5 Summary 233 10.6 Exercises 236 11 Multi-period binomial tree model 239 11.1 Model 239 11.2 Pricing by replication 250 11.3 Pricing with risk-neutral probabilities 259 11.4 Summary 263 11.5 Exercises 265 12 Further topics in the binomial tree model 269 12.1 American options 269 12.2 Options on dividend-paying stocks 276 12.3 Currency options 279 12.4 Options on futures 282 12.5 Summary 287 12.6 Exercises 289 13 Market incompleteness and one-period trinomial tree models 291 13.1 Model 292 13.2 Pricing by replication 296 13.3 Pricing with risk-neutral probabilities 306 13.4 Completion of a trinomial tree 313 13.5 Incompleteness of insurance markets 316 13.6 Summary 319 13.7 Exercises 321 Part III Black-Scholes-Mertonmodel 325 14 Brownian motion 327 14.1 Normal and lognormal distributions 327 14.2 Symmetric random walks 333 14.3 Standard Brownian motion 336 14.4 Linear Brownian motion 347 14.5 Geometric Brownian motion 351 14.6 Summary 359 14.7 Exercises 362 15 Introduction to stochastic calculus*** 365 15.1 Stochastic Riemann integrals 366 15.2 Ito's stochastic integrals 368 15.3 Ito's lemma for Brownian motion 380 15.4 Diffusion processes 382 15.5 Summary 389 15.6 Exercises 391 16 Introduction to the Black-Scholes-Mertonmodel 393 16.1 Model 394 16.2 Relationship between the binomial and BSM models 397 16.3 Black-Scholes formula 403 16.4 Pricing simple derivatives 410 16.5 Determinants of call and put prices 414 16.6 Replication and hedging 417 16.7 Summary 428 16.8 Exercises 430 17 Rigorous derivations of the Black-Scholes formula*** 433 17.1 PDE approach to option pricing and hedging 433 17.2 Risk-neutral approach to option pricing 440 17.3 Summary 451 17.4 Exercises 452 18 Applications and extensions of the Black-Scholes formula 455 18.1 Options on other assets 455 18.2 Equity-linked insurance and annuities 463 18.3 Exotic options 473 18.4 Summary 484 18.5 Exercises 485 19 Simulation methods 487 19.1 Primer on random numbers 488 19.2 Monte Carlo simulations for option pricing 490 19.3 Variance reduction techniques 497 19.4 Summary 513 19.5 Exercises 516 20 Hedging strategies in practice 519 20.1 Introduction 520 20.2 Cash-flow matching and replication 521 20.3 Hedging strategies 523 20.4 Interest rate risk management 527 20.5 Equity risk management 533 20.6 Rebalancing the hedging portfolio 546 20.7 Summary 548 20.8 Exercises 551 References 555 Index 557
