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by Wai-Sum Chan (Author), Yiu-Kuen Tse (Contributor)
About the Author
Wai-Sum Chan, PhD, FSA, CERA, graduated from the Chinese University of Hong Kong with a major in Accounting and a minor in Statistics. He pursued a doctorate in Applied Statistics at the Fox School of Business Management, Temple University (Philadelphia, USA), receiving his PhD in 1989. He qualified as a Fellow of the Society of Actuaries in 1995 and Chartered Enterprise Risk Analyst in 2008. Dr. Chan held teaching and research posts at the National University of Singapore, the University of Waterloo and the University of Hong Kong before his present appointment as Professor of Finance at the Chinese University of Hong Kong. Dr. Chan s research interests include Health Care Financing, Actuarial Modeling and Financial Econometrics. He has had over 90 scientific articles published in scholarly journals. Dr. Chan has been teaching financial and actuarial courses since 1992.
Yiu-Kuen Tse, PhD, FSA, graduated from the University of Hong Kong, majoring in Economics and Statistics. He obtained his MSc in Statistics and his PhD in Econometrics from the London School of Economics. He has been a Fellow of the Society of Actuaries since 1993. Dr. Tse s research interests are in Empirical Finance, Financial Econometrics and Econometric Methodology. He is Professor of Economics at the School of Economics and Social Sciences, Singapore Management University. He has published extensively in scholarly journals and is the author of the book Nonlife Actuarial Models: Theory, Methods and Evaluation (Cambridge University Press, 2009). Dr. Tse teaches undergraduate actuarial courses and has been involved in many executive training programs.
About this book
Financial Mathematics for Actuaries is a textbook for students in actuarial science, quantitative finance, financial engineering and quantitative risk management and is designed for a one-semester undergraduate course. Covering the theories of interest rates, with applications to the evaluation of cash flows, the pricing of fixed income securities and the management of bonds, this textbook also contains numerous examples and exercises and extensive coverage of various Excel functions for financial calculation. Discussions are linked to real financial market data, such as historical term structure, and traded financial securities. The topics discussed in this book are essential for actuarial science students. They are also useful for students in financial markets, investments and quantitative finance. Students preparing for examinations in financial mathematics with various professional actuarial bodies will also find this book useful for self-study. In this second edition, the recent additions in the learning objectives of the Society of Actuaries Exam FM have been covered.
Brief contents
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 EffectiveRateof Interest 9
1.5 Rates of Discount 12
1.6 Forceof Interest 16
1.7 Present and Future Values 19
1.8 Equation ofValue 24
1.9 Summary 27
Exercises 28
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 56
2.7 TermofAnnuity 60
2.8 Summary 64
Exercises 64
Chapter 3 Spot Rates, Forward Rates and the Term Structure 73
3.1 Spot andForwardRatesof Interest 74
3.2 TheTermStructure of InterestRates 79
3.3 Present and Future Values Given the Term Structure 80
3.4 Accumulation Function and theTermStructure 85
3.5 InterestRateSwaps 90
3.6 Summary 97
Exercises 98
Chapter 4 Rates of Return 105
4.1 InternalRate ofReturn 106
4.2 One-PeriodRateofReturn 112
4.3 Rate of Return over Multiple Periods 116
4.4 Portfolio Return 121
4.5 ShortSales 124
4.6 Crediting Interest: Investment-Year Method and Portfolio Method 125
4.7 Capital Budgeting and Project Appraisal 127
4.8 Summary 132
Exercises 134
Chapter 5 Loans and Costs of Borrowing 147
5.1 Loan Balance: Prospective and Retrospective Methods 148
5.2 Amortization 152
5.3 SinkingFund 154
5.4 Varying Installments andVarying InterestRates 159
5.5 Comparison ofBorrowingCosts 163
5.6 Flat Rate Loan and Flat Rate Discount Loan 165
5.7 BorrowingCosts andReferenceRates 168
5.8 Summary 170
Exercises 172
Chapter 6 Bonds and Bond Pricing 187
6.1 BasicConcepts 188
6.2 BondEvaluation 190
6.3 BondAmortization Schedule 193
6.4 Valuation between Coupon-Payment Dates 198
6.5 Callable Bonds 202
6.6 Bond Pricing under a General Term Structure 204
6.7 Summary 206
Exercises 207
Chapter 7 Bond Yields and the Term Structure 213
7.1 Some Simple Measures of Bond Yield 214
7.2 Yield to Maturity 215
7.3 ParYield 219
7.4 Holding-PeriodYield 221
7.5 Discretely Compounded Yield Curve 225
7.6 Continuously Compounded Yield Curve 228
7.7 TermStructureModels 232
7.8 Summary 236
Exercises 237
Chapter 8 Bond Management 245
8.1 Macaulay Duration and Modified Duration 246
8.2 Duration forPriceCorrection 252
8.3
8.4 SomeRules forDuration 256
8.5 Immunization Strategies 259
8.6 SomeShortcomings ofDurationMatching 272
8.7 Duration under a Nonflat Term Structure 274
8.8 Passive versus Active Bond Management 277
8.9 Summary 278
Exercises 279
Chapter 9 Interest Rates and Financial Securities 291
9.1 InterestRateDetermination 292
9.2 Financial Securities 296
9.3 Inflation andCentralBankPolicy 300
9.4 Macroeconomic Management 301
9.5 Rate of Interest in an Open Economy 302
9.6 Summary 302
Exercises 303
Chapter 10 Stochastic Interest Rates 305
10.1 Deterministic Scenarios of InterestRates 306
10.2 Random-Scenario Model 307
10.3 Independent Lognormal Model 310
10.4 Autoregressive Model 314
10.5 DynamicTermStructureModel 316
10.6 AnApplication: Guaranteed Investment Income 317
10.7 Summary 320
Exercises 320
Appendix A Review of Mathematics and Statistics 327
A.1 Exponential Function 327
A.2 Logarithmic Function 327
A.3 Roots of aQuadratic Equation 328
A.4 Arithmetic Progression 328
A.5 Geometric Progression 328
A.6 SomeDerivatives 328
A.7 Integration byPart 329
A.8 TaylorSeriesExpansion 329
A.9 BinomialExpansion 329
A.10 Expected Value and Variance of a Random Variable 330
A.11 Mean and Variance of Sum of Random Variables 330
A.12 Uniform Distribution 330
A.13 Normal Distribution 331
A.14 Lognormal Distribution 331
Appendix B Answers to Selected Exercises 333
Index 349
Pages: 372 pages
Publisher: WSPC; 2 edition, 2018 Edition
Language: English
ISBN-10: 9813224673
ISBN-13: 978-9813224674
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