Details

Actuarial Finance


Actuarial Finance

Derivatives, Quantitative Models and Risk Management
1. Aufl.

von: Mathieu Boudreault, Jean-François Renaud

111,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 22.03.2019
ISBN/EAN: 9781119137016
Sprache: englisch
Anzahl Seiten: 592

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Beschreibungen

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

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