Java Methods for Financial Engineering: Applications in Finance and Investment

Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Numerical Accuracy & Errors.................................................... 1
1.2. Core Math’s Classes ................................................................... 2
1.2.1. Root Finding - Interval Bisection.................................. 2
1.2.2. Newton’s Method........................................................... 7
1.3. Statistical Classes........................................................................ 12
1.3.1. Measures of Dispersion ................................................. 13
1.4. Application Classes..................................................................... 17
1.4.1. Internal Rate of Return .................................................. 18
1.4.2. Deriving Yield Approximations – Bisection Method ... 18
1.4.3. Deriving Yield Approximations
-the Newton Raphson Method ....................................... 21
1.4.4. Portfolio Management.................................................... 21
1.4.5. Portfolio Risk Measurement .......................................... 28
2. Interest Rate Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1. Compound Interest...................................................................... 33
2.1.1. Nominal and Effective Interest...................................... 33
2.2. Present Value (PV) ..................................................................... 37
2.2.1. Compounding Cashflows............................................... 37
2.2.2. Perpetuity and Annuity .................................................. 39
2.3. Internal Rate of Return ............................................................... 40
2.4. Term Structures........................................................................... 41
2.4.1. Rate Interchanges........................................................... 41
2.4.2. Spot Rates ...................................................................... 43
2.4.3. Deriving the Spot Curve................................................ 49
3. Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1. Bonds – Fixed Interest................................................................ 59
3.2. Bond Prices ................................................................................. 68
3.2.1. Interest Yields ................................................................ 69
3.2.2. Yield to Maturity ........................................................... 69
3.3. Static Spread ............................................................................... 70
3.4. Credit Spreads............................................................................. 74

3.5. Bond Volatility Measures........................................................... 81
3.5.1. Price Value of a Point.................................................... 85
3.6. Bond Pricing Characteristics ...................................................... 88
4. Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1. Macaulay Duration ..................................................................... 99
4.2. Effective Duration....................................................................... 105
5. Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
5.1. Forward & Futures Pricing......................................................... 108
5.2. Forward Price.............................................................................. 112
5.3. Pricing On Different Markets..................................................... 115
5.3.1. Stock Index .................................................................... 115
5.3.2. Currencies....................................................................... 117
5.4. Commodity Futures .................................................................... 118
6. Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125
6.1. Option Types............................................................................... 125
6.2. Option Specifications.................................................................. 127
6.3. Pricing Specification................................................................... 128
6.3.1. Dividends and Stock Splits............................................ 130
6.3.2. Option Quotes ................................................................ 131
6.3.3. Margin Accounts............................................................ 132
6.4. Arbitrage in Option Prices.......................................................... 133
6.4.1. Main Components of Pricing......................................... 133
6.4.2. Limits for Pricing........................................................... 136
6.5. Early Exercise of American Options.......................................... 141
6.6. Option Convexity........................................................................ 143
6.7. Put Call Parity............................................................................. 145
6.8. Strategies ..................................................................................... 149
6.8.1. Hedge with a Protected Put ........................................... 150
6.8.2. Reverse Protected Put Hedge ........................................ 150
6.8.3. Hedge with a Covered Call ........................................... 150
6.8.4. Reverse Covered Call Hedge......................................... 150
6.9. Profit Diagrams........................................................................... 155
7. Modelling Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163
7.1. The Stochastic Process ............................................................... 163
7.1.1. Random Walks............................................................... 163
7.1.2. Brownian Motion ........................................................... 164
7.1.3. Wiener Process............................................................... 164
7.1.4. Ito Differential................................................................ 168
7.2. Lognormal Modelling of Stock Prices ....................................... 170
7.2.1. Handling Empirical Data ............................................... 171
7.2.2. Simulation with Monte Carlo ........................................ 177
7.3. The Lognormal Property ............................................................ 182
Contents ix
8. The Binomial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.1. Stock Price .................................................................................. 191
8.1.1. Cox Ross Rubinstein (CRR) Model .............................. 192
8.1.2. Binomial Tree ................................................................ 193
8.2. Trees for American & European Pricing ................................... 201
9. Analytical Option Pricing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205
9.1. Black-Scholes-Merton ................................................................ 205
9.2. Pricing with Black-Scholes ........................................................ 207
9.2.1. Pricing without Dividends ............................................. 208
9.2.2. Effects of Dividends ...................................................... 209
9.2.3. Options Paying a Yield.................................................. 210
9.2.4. Stock Index Options....................................................... 211
9.2.5. Options on Futures......................................................... 212
9.2.6. Currency Options ........................................................... 213
9.3. Analytical Approximations for American Options .................... 216
9.3.1. Roll Geske Whaley (RGW) Approximation ................. 216
9.3.2. Bjerksund and Stensland (B&S) Approximation .......... 220
9.3.3. Quadratic Approximation (Barone-Adesi
Whaley Derivation) ........................................................ 223
10. Sensitivity Measures (The ‘Greeks’) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
10.1. The Black-Scholes Pde............................................................... 231
10.2. Delta Sensitivity.......................................................................... 231
10.3. Gamma Sensitivity...................................................................... 234
10.4. Theta Sensitivity ......................................................................... 238
10.5. Vega Sensitivity .......................................................................... 241
10.6. Rho Sensitivity............................................................................ 245
10.7. Option Extensions....................................................................... 247
10.7.1. Elasticity......................................................................... 247
10.7.2. Cost of Carry.................................................................. 249
11. Interest Rate Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255
11.1. Market Price of Risk................................................................... 255
11.2. Martingales.................................................................................. 257
11.3. Interest Rate Caps & Floors ....................................................... 260
11.6.2. Hull and White Model ................................................... 274
12. Conditional Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
12.1. Executive Stock Options ............................................................ 279
12.1.1. Forward Start Option ..................................................... 282
12.1.2. Indexed Stock Options................................................... 284

太长中间省略部分
18.6.1. Geometric Average Rate Option ................................... 513
18.6.2. Arithmetic Approximations ........................................... 515
18.6.3. Levy Method.................................................................. 518
18.7. Quantos ....................................................................................... 521
18.7.1. Fixed Exchange Valuation............................................. 521
18.7.2. Foreign Exchange Option .............................................. 524
Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
Appendix 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .555

 

  

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