Risk and Financial Management: Mathematical and Computational Methods

Risk and Financial Management: Mathematical and Computational Methods by Charles Tapiero
Publisher: Wiley (May 28, 2004) | 0470849088 | 344Pages | PDF | 2.11Mb
Financial risk management has become a popular practice amongst financial institutionsto protect against the adverse effects of uncertainty caused byfluctuations in interest rates, exchange rates, commodity prices, andequity prices. New financial instruments and mathematicaltechniques are continuously developed and introduced in financialpractice. These techniques are being used by an increasing number offirms, traders and financial risk managers across various industries.Risk and Financial Management: Mathematical and Computational Methodsconfronts the many issues and controversies, and explains thefundamental concepts that underpin financial risk management.   

・rovides a comprehensive introduction to the core topics of risk and financial management.
・Adopts a pragmatic approach, focused on computational, rather than just theoretical, methods.
・Bridges the gap between theory and practice in financial risk management
・Includes coverage of utility theory, probability, options and derivatives, stochastic volatility and value at risk.
・Suitable for students of risk, mathematical finance, and financial risk management, and finance practitioners.
・Includes extensive reference lists, applications and suggestions for further reading.

Risk and Financial Management: Mathematical and Computational Methodsis ideally suited to both students of mathematical finance with littlebackground in economics and finance, and students of financial riskmanagement, as well as finance practitioners requiring a clearerunderstanding of the mathematical and computational methods they useevery day. It combines the required level of rigor, to support thetheoretical developments, with a practical flavour through manyexamples and applications.
Contents
Preface xiii
Part I: Finance and Risk Management
Chapter 1 Potpourri 03
1.1 Introduction 03
1.2 Theoretical finance and decision making 05
1.3 Insurance and actuarial science 07
1.4 Uncertainty and risk in finance 10
1.4.1 Foreign exchange risk 10
1.4.2 Currency risk 12
1.4.3 Credit risk 12
1.4.4 Other risks 13
1.5 Financial physics 15
Selected introductory reading 16
Chapter 2 Making Economic Decisions under Uncertainty 19
2.1 Decision makers and rationality 19
2.1.1 The principles of rationality and bounded rationality 20
2.2 Bayes decision making 22
2.2.1 Risk management 23
2.3 Decision criteria 26
2.3.1 The expected value (or Bayes) criterion 26
2.3.2 Principle of (Laplace) insufficient reason 27
2.3.3 The minimax (maximin) criterion 28
2.3.4 The maximax (minimin) criterion 28
2.3.5 The minimax regret or Savage’s regret criterion 28
2.4 Decision tables and scenario analysis 31
2.4.1 The opportunity loss table 32
2.5 EMV, EOL, EPPI, EVPI 33
2.5.1 The deterministic analysis 34
2.5.2 The probabilistic analysis 34
Selected references and readings 38
viii CONTENTS
Chapter 3 Expected Utility 39
3.1 The concept of utility 39
3.1.1 Lotteries and utility functions 40
3.2 Utility and risk behaviour 42
3.2.1 Risk aversion 43
3.2.2 Expected utility bounds 45
3.2.3 Some utility functions 46
3.2.4 Risk sharing 47
3.3 Insurance, risk management and expected utility 48
3.3.1 Insurance and premium payments 48
3.4 Critiques of expected utility theory 51
3.4.1 Bernoulli, Buffon, Cramer and Feller 51
3.4.2 Allais Paradox 52
3.5 Expected utility and finance 53
3.5.1 Traditional valuation 54
3.5.2 Individual investment and consumption 57
3.5.3 Investment and the CAPM 59
3.5.4 Portfolio and utility maximization in practice 61
3.5.5 Capital markets and the CAPM again 63
3.5.6 Stochastic discount factor, assets pricing
and the Euler equation 65
3.6 Information asymmetry 67
3.6.1 ‘The lemon phenomenon’ or adverse selection 68
3.6.2 ‘The moral hazard problem’ 69
3.6.3 Examples of moral hazard 70
3.6.4 Signalling and screening 72
3.6.5 The principal–agent problem 73
References and further reading 75
Chapter 4 Probability and Finance 79
4.1 Introduction 79
4.2 Uncertainty, games of chance and martingales 81
4.3 Uncertainty, random walks and stochastic processes 84
4.3.1 The random walk 84
4.3.2 Properties of stochastic processes 91
4.4 Stochastic calculus 92
4.4.1 Ito’s Lemma 93
4.5 Applications of Ito’s Lemma 94
4.5.1 Applications 94
4.5.2 Time discretization of continuous-time
finance models 96
4.5.3 The Girsanov Theorem and martingales∗ 104
References and further reading 108
Chapter 5 Derivatives Finance 111
5.1 Equilibrium valuation and rational expectations 111
CONTENTS ix
5.2 Financial instruments 113
5.2.1 Forward and futures contracts 114
5.2.2 Options 116
5.3 Hedging and institutions 119
5.3.1 Hedging and hedge funds 120
5.3.2 Other hedge funds and investment strategies 123
5.3.3 Investor protection rules 125
References and additional reading 127
Part II: Mathematical and Computational Finance
Chapter 6 Options and Derivatives Finance Mathematics 131
6.1 Introduction to call options valuation 131
6.1.1 Option valuation and rational expectations 135
6.1.2 Risk-neutral pricing 137
6.1.3 Multiple periods with binomial trees 140
6.2 Forward and futures contracts 141
6.3 Risk-neutral probabilities again 145
6.3.1 Rational expectations and optimal forecasts 146
6.4 The Black–Scholes options formula 147
6.4.1 Options, their sensitivity and hedging parameters 151
6.4.2 Option bounds and put–call parity 152
6.4.3 American put options 154
References and additional reading 157
Chapter 7 Options and Practice 161
7.1 Introduction 161
7.2 Packaged options 163
7.3 Compound options and stock options 165
7.3.1 Warrants 168
7.3.2 Other options 169
7.4 Options and practice 171
7.4.1 Plain vanilla strategies 172
7.4.2 Covered call strategies: selling a call and a
share 176
7.4.3 Put and protective put strategies: buying a
put and a stock 177
7.4.4 Spread strategies 178
7.4.5 Straddle and strangle strategies 179
7.4.6 Strip and strap strategies 180
7.4.7 Butterfly and condor spread strategies 181
7.4.8 Dynamic strategies and the Greeks 181
7.5 Stopping time strategies∗ 184
7.5.1 Stopping time sell and buy strategies 184
7.6 Specific application areas 195
x CONTENTS
7.7 Option misses 197
References and additional reading 204
Appendix: First passage time∗ 207
Chapter 8 Fixed Income, Bonds and Interest Rates 211
8.1 Bonds and yield curve mathematics 211
8.1.1 The zero-coupon, default-free bond 213
8.1.2 Coupon-bearing bonds 215
8.1.3 Net present values (NPV) 217
8.1.4 Duration and convexity 218
8.2 Bonds and forward rates 222
8.3 Default bonds and risky debt 224
8.4 Rated bonds and default 230
8.4.1 A Markov chain and rating 233
8.4.2 Bond sensitivity to rates – duration 235
8.4.3 Pricing rated bonds and the term structure
risk-free rates∗ 239
8.4.4 Valuation of default-prone rated bonds∗ 244
8.5 Interest-rate processes, yields and bond valuation∗ 251
8.5.1 The Vasicek interest-rate model 254
8.5.2 Stochastic volatility interest-rate models 258
8.5.3 Term structure and interest rates 259
8.6 Options on bonds∗ 260
8.6.1 Convertible bonds 261
8.6.2 Caps, floors, collars and range notes 262
8.6.3 Swaps 262
References and additional reading 264
Mathematical appendix 267
A.1: Term structure and interest rates 267
A.2: Options on bonds 268
Chapter 9 Incomplete Markets and Stochastic Volatility 271
9.1 Volatility defined 271
9.2 Memory and volatility 273
9.3 Volatility, equilibrium and incomplete markets 275
9.3.1 Incomplete markets 276
9.4 Process variance and volatility 278
9.5 Implicit volatility and the volatility smile 281
9.6 Stochastic volatility models 282
9.6.1 Stochastic volatility binomial models∗ 282
9.6.2 Continuous-time volatility models 00
9.7 Equilibrium, SDF and the Euler equations∗ 293
9.8 Selected Topics∗ 295
9.8.1 The Hull and White model and stochastic
volatility 296
9.8.2 Options and jump processes 297
CONTENTS xi
9.9 The range process and volatility 299
References and additional reading 301
Appendix: Development for the Hull and White model (1987)∗ 305
Chapter 10 Value at Risk and Risk Management 309
10.1 Introduction 309
10.2 VaR definitions and applications 311
10.3 VaR statistics 315
10.3.1 The historical VaR approach 315
10.3.2 The analytic variance–covariance approach 315
10.3.3 VaR and extreme statistics 316
10.3.4 Copulae and portfolio VaR measurement 318
10.3.5 Multivariate risk functions and the
principle of maximum entropy 320
10.3.6 Monte Carlo simulation and VaR 324
10.4 VaR efficiency 324
10.4.1 VaR and portfolio risk efficiency with
normal returns 324
10.4.2 VaR and regret 326
References and additional reading 327
Author Index 329
Subject Index 333