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Financial Mathematics for Actuaries (Updated Edition)

Financial Mathematics for Actuaries (Updated Edition)

Author: Wai Sum Chan; Yiu Kuen Tse
Publisher: McGraw Hill Higher Education
ISBN: 9781259011481
Published In: January 2013
Format: Paperback , 348 pages
Jurisdiction: International ? Disclaimer:
Countri(es) stated herein are used as reference only

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Financial Mathematics for Actuaries: Updated Edition is an introductory textbook on the mathematics of interest rates. It is written at a level of rigor required of students who major in actuarial science and prepares them for further analysis of financial instruments. This book emphasizes an intuitive treatment of the mathematics of finance and insurance, with a particular focus on applications. Students will find many illustrative examples that apply mathematical techniques to financial products and personal financial management.

For this latest updated edition, a whole section in the chapter on bond management has been revised, extended and placed under a new heading called Immunization Strategies.

Contents About the Authors v
Preface to the Updated Edition vii
Preface to the 1st Edition ix
List of Mathematical Symbols xi

Chapter 1 Interest Accumulation and Time Value of Money 1 1.1 Accumulation Function and Amount Function 2
1.2 Simple and Compound Interest 2
1.3 Frequency of Compounding 5
1.4 Effective Rate of Interest 8
1.5 Rates of Discount 12
1.6 Force of Interest 17
1.7 Present and Future Values 20
1.8 Equation of Value 26
1.9 Summary 29
Exercises 29

Chapter 2 Annuities 39 2.1 Annuity-immediate 40
2.2 Annuity-due 43
2.3 Perpetuity, Deferred Annuity and Annuity Values at Other Times 45
2.4 Annuities under Other Accumulation Methods 49
2.5 Payment Periods, Compounding Periods and Continuous Annuities 51
2.6 Varying Annuities 57
2.7 Term of Annuity 62
2.8 Summary 66
Exercises 66

Chapter 3 Spot Rates, Forward Rates and the Term Structure 73 3.1 Spot and Forward Rates of Interest 74
3.2 The Term Structure of Interest Rates 79
3.3 Present and Future Values Given the Term Structure 80
3.4 Accumulation Function and the Term Structure 86
3.5 Summary 92
Exercises 92

Chapter 4 Rates of Return 99 4.1 Internal Rate of Return 100
4.2 One-period Rate of Return 105
4.3 Rate of Return over Multiple Periods 110
4.4 Portfolio Return 115
4.5 Short Sales 118
4.6 Crediting Interest: Investment-year Method and Portfolio Method 119
4.7 Inflation and Real Rate of Interest 121
4.8 Capital Budgeting and Project Appraisal 123
4.9 Summary 129
Exercises 130

Chapter 5 Loans and Costs of Borrowing 141 5.1 Loan Balance: Prospective and Retrospective Methods 142
5.2 Amortization 146
5.3 Sinking Fund 148
5.4 Varying Installments and Varying Interest Rates 154
5.5 Comparison of Borrowing Costs 158
5.6 Flat Rate Loan and Flat Rate Discount Loan 161
5.7 Borrowing Costs and Reference Rates 164
5.8 Summary 167
Exercises 168

Chapter 6 Bonds and Bond Pricing 181 6.1 Basic Concepts 182
6.2 Bond Evaluation 183
6.3 Bond Amortization Schedule 187
6.4 Valuation between Coupon-payment Dates 192
6.5 Callable Bonds 195
6.6 Bond Pricing under a General Term Structure 198
6.7 Summary 200
Exercises 200

Chapter 7 Bond Yields and the Term Structure 207 7.1 Some Simple Measures of Bond Yield 208
7.2 Yield to Maturity 208
7.3 Par Yield 213
7.4 Holding-period Yield 215
7.5 Discretely Compounded Yield Curve 218
7.6 Continuously Compounded Yield Curve 222
7.7 Term Structure Models 226
7.8 Summary 231
Exercises 232

Chapter 8 Bond Management 239 8.1 Macaulay Duration and Modified Duration 240
8.2 Duration for Price Correction 246
8.3 Convexity 249
8.4 Some Rules for Duration 250
8.5 Immunization Strategies 254
8.6 Some Shortcomings of Duration Matching 268
8.7 Duration under a Nonflat Term Structure 269
8.8 Passive versus Active Bond Management 273
8.9 Summary 273
Exercises 274

Chapter 9 Stochastic Interest Rates 285 9.1 Deterministic Scenarios of Interest Rates 286
9.2 Random-scenario Model 287
9.3 Independent Lognormal Model 289
9.4 Autoregressive Model 294
9.5 Dynamic Term Structure Model 296
9.6 An Application: Guaranteed Investment Income 297
9.7 Summary 300
Exercises 301

Appendix A Review of Mathematics and Statistics 307 A.1 Exponential Function 307
A.2 Logarithmic Function 307
A.3 Roots of a Quadratic Equation 308
A.4 Arithmetic Progression 308
A.5 Geometric Progression 308
A.6 Some Derivatives 309
A.7 Integration by Part 309
A.8 Taylor Series Expansion 309
A.9 Binomial Expansion 310
A.10 Expected Value and Variance of a Random Variable 310
A.11 Mean and Variance of Sum of Random Variables 310
A.12 Uniform Distribution 311
A.13 Normal Distribution 311
A.14 Lognormal Distribution 312

Appendix B Answers to Selected Exercises 313 Index 325