Index
a
b
- Bid-ask spread 36
- Binary option
- Binomial model 185, 397
- American option 269
- Approximation of the Black-Scholes formula 405
- Approximation of the Black-Scholes-Merton model 398
- Continuation value 270
- Cox-Ross-Rubinstein (CRR) model 243, 405
- Currency option 280
- Discrete (dollar) dividend 228
- Dividend-paying risky asset 276
- Dynamic trading strategy 212, 250
- Guaranteed minimum withdrawal benefit (GMWB) 232
- Holding value 270
- Investment guarantee 194
- Jarrow-Rudd (JR) model 243, 402
- Market completeness 192, 218, 253, 417
- Multi-period model 239
- No-arbitrage condition 187, 205, 207, 241
- One-period model 185
- Portfolio value process 251
- Rebalancing 212
- Recombining tree 204, 241
- Replicating portfolio 190, 213
- Risk-neutral pricing formula 196, 221, 260
- Risk-neutral probability 196, 220, 260
- Self-financing strategy 215, 252
- Static trading strategy 212, 250
- Stochastic interest rate 225
- Trading strategy 190, 250
- Two-period model 201
- Black-Scholes formula 403, 450, 455
- Asian option 478
- Black’s formula 460
- Call option 404
- Currency option 459
- Dynamic version 409
- Equity-indexed annuity (EIA) 466, 468
- Exchange option 462
- Futures option 460
- Guaranteed minimum maturity benefit (GMMB) 471
- Investment guarantee 464
- Lookback option 480
- Price sensitivity 414
- Put option 406
- With dividends 457
- Black-Scholes partial differential equation, see Partial differential equation (PDE)
- Black-Scholes-Merton model 393, 455
- Asian option 474
- Barrier option 482
- Binary option 411
- Black’s formula 460
- Black-Scholes formula 403
- Black-Scholes PDE 438
- Currency option 459
- Delta 422
- Delta hedging 424
- Delta-hedging strategy 425
- Dividend-paying risky asset 455
- Equity-indexed annuity (EIA) 465
- Equity-linked insurance and annuity (ELIA) 463
- Exchange option 461
- Exotic option 473
- Forward contract 410
- Futures option 459
- Gap option 412
- Geometric Brownian motion 394
- Guaranteed minimum maturity benefit (GMMB) 470
- Investment guarantee 464
- Lookback option 479
- Market completeness 418
- Portfolio value process 418
- Price sensitivity 414
- Pricing probability measure 449
- Replicating strategy 418
- Risk-neutral probability measure 447
- Self-financing condition 437
- Self-financing strategy 418, 426
- Stop-loss transform 450
- Variable annuity 470
- Bond
- Callable bond 22
- Corporate bond 22
- Coupon bond 22
- Coupons 22
- Credit risk 90
- Definition 21
- Face value 23
- Fixed-rate bond 77, 81
- Floating-rate bond 77, 82
- Initial price 23, 26
- Maturity 22
- Municipal bond 22
- Principal 23
- Redeemable bond 22
- Sovereign bond 22
- Stripping 26
- Treasury 22
- Yield 23
- Zero-coupon bond 22, 23
- Brownian motion 327
- Diffusion coefficient 347
- Distribution of the maximum 480
- Drift coefficient 347
- Estimation 357
- Gaussian process 341
- Geometric Brownian motion 351, 386, 394
- Girsanov theorem 446
- Linear Brownian motion 347, 386, 480
- Markovian property 342, 349, 354
- Martingale property 344, 350, 355
- Maximum likelihood estimator 357
- Simulation 345, 350, 356
- Standard Brownian motion 336, 339
- Volatility coefficient 347, 354
c
d
- Delta hedging 526, 535
- Delta-gamma hedging, see Hedging
- Delta-rho hedging, see Hedging
- Delta-vega hedging, see Hedging
- Derivative
- Attainable derivative 298
- Catastrophe derivative 16, 33, 152
- Definition 8, 32
- Delta 422
- Event-triggered derivative 33, 141, 150
- Exotic option 33
- Forward contract 33, 49
- Futures contract 33, 49
- Insurance 8
- Longevity derivative 16, 33, 153
- Option 33
- Payoff 51
- Swap 33, 75
- Underlying asset 32
- Weather derivative 33, 150
- Diffusion process, see Stochastic calculus
- Digital option, see Binary option
- Diversifiable risk 10, 11
- Diversification 10
- Dividend
- Domestic currency 59
- Duration
- Duration matching, see Hedging
- Duration-convexity matching, see Hedging
e
- Early exercise
- Equity
- Definition 4
- Equity-indexed annuity (EIA) 161
- Equity-linked insurance and annuity (ELIA) 33, 159
- Event-triggered derivative 33, 141, 150
- Exotic option 33, 141
- Asian option 147, 474
- Average price Asian option 148
- Average strike Asian option 148
- Barrier option 141, 482
- Black-Scholes-Merton model 473
- Down-and-in option 142
- Down-and-out option 142
- Exchange option 148, 461
- Fixed strike lookback 146
- Floating strike lookback 146
- Knock-in option 142
- Knock-out option 142
- Lookback option 146, 479
- Monitoring frequency 146, 147, 473
- Up-and-in option 142
- Up-and-out option 142
f
g
h
- Hedging 15, 33, 519
- Asset and liability management (ALM) 519
- Black-Scholes-Merton model 424
- Definition 519
- Delta hedging 526, 535
- Delta-gamma hedging 526, 538
- Delta-rho hedging 542
- Delta-vega hedging 545
- Duration matching 526, 529
- Duration-convexity matching 526, 531
- First-order hedging strategy 526
- Full immunization 532
- Greeks 533, 541
- Hedging error 424
- Hedging strategy 519, 523
- Immunization 532
- Rebalancing 546
- Redington immunization 532
- Relative hedging error 536
- Second-order hedging strategy 526
- Self-financing strategy 546
- Sensitivity matching 525
i
l
m
- Market
- Bear market 112
- Bond market 22
- Bull market 112
- Complete market 298, 417, 418
- Exchange-traded market 35, 62
- Financial market 6, 7
- Foreign exchange market 35
- Frictionless market 38
- Frictions 37
- Incomplete market 298
- Insurance market 6, 316
- Market completeness 192
- Market incompleteness 291, 316
- Market maker 7
- Over-the-counter 62
- Over-the-counter market (OTC) 35
- Primary market 35
- Secondary market 35
- Market price of risk 453
- Marking to market 50, 62
- Maximum likelihood estimator, see Brownian motion
- Mean reversion 388
- Monte Carlo simulation, see Simulation
- Mortgage-backed security (MBS) 8
n
o
- Option
- American option 101, 133
- Asian option 147
- At the money 102
- Barrier option 141
- Bermudan option 101
- Binary option 126
- Bounds on option prices 129
- Box spread 112
- Butterfly spread 112
- Call option 100, 102
- Cap 108
- Cash settlement 103
- Collar 114
- Definition 33, 100
- Elasticity 535
- European option 101
- Exchange option 148
- Exercise price 101
- Exercise value 134
- Exotic option 141
- Floor 108
- Futures option 282
- Gap option 128
- In the money 102
- Intrinsic value 102, 134
- Long call 103
- Long put 105
- Lookback option 146
- Maturity 101
- Moneyness 102
- Out of the money 102
- Path-dependent option 141
- Payoff 101
- Physical settlement 103
- Premium 101
- Profit/loss 101
- Protective put 108
- Put option 100, 105
- Ratio spread 112
- Short call 105
- Short put 107
- Simple option 141
- Spread 110, 112
- Straddle 112
- Strangle 113
- Strike price 101
- Synthetic call 123, 124
- Synthetic put 123, 124
- Underlying asset 100
- Vanilla option 102
- Vertical spread 112
- Zero-cost ratio spread 112
- Ordinary differential equation, see Partial differential equation (PDE)
p
q
- Quantile function, see Simulation
r
- Random walk 398
- Reinsurance 14, 16
- Replication 15, 521
- Riemann integral, see Stochastic calculus
- Risks
- Actuarial risk 9
- Counterparty risk 38, 523
- Credit risk 22, 29, 368, 523
- Default risk 38, 62
- Diversifiable 10, 11
- Financial risk 9
- Interest rate risk 8, 13
- Investment risk 8
- Liquidity risk 29
- Long-term risk 8
- Longevity risk 9, 14, 153, 368
- Market risk 174
- Model risk 548
- Mortality risk 8, 174
- Partially diversifiable 14
- Short-term risk 9
- Systematic 9, 12
s
- Securitization 316
- Definition 7
- Security
- Definition 7
- Segregated fund, see Variable annuity
- Sharpe ratio 453
- Short selling
- Short-term risk 9
- Simulation
- Antithetic variates estimator 504
- Antithetic variates technique 502, 503
- Box-Muller method 490
- Brownian motion 345
- Control variates estimator 510
- Control variates method 508
- Definition 487
- Exponential distribution 489
- Geometric Brownian motion 356
- Importance sampling 513
- Inverse transform method 488, 489, 502
- Linear Brownian motion 350
- Monte Carlo estimator 491
- Monte Carlo simulation 490
- Normal distribution 490
- Normal random number 490
- Option pricing 492, 501, 505, 510
- Pseudo-random number generator (PRNG) 488
- Quantile function 488
- Quasi Monte Carlo methods 513
- Random numbers 488
- Seed 488
- Statified sampling 497
- Statified sampling estimator 501
- Strata 499
- Uniform distribution 488
- Uniform random number 488
- Variance reduction technique 497
- Speculation 33, 109
- Stochastic calculus 365
- Adapted stochastic process 374
- Diffusion coefficient 382
- Diffusion process 382
- Drift coefficient 382
- Elementary stochastic process 370, 372
- Feynman-Kač formula 435
- Geometric Brownian motion 386
- Ito’s isometry 377
- Ito’s lemma 380, 384
- Ito-integrable stochastic process 374
- Linear Brownian motion 386
- Ornstein-Uhlenbeck (OU) process 387
- Product rule 384
- Riemann sums 370
- Square-root diffusion process 388
- Stochastic differential equation (SDE) 365, 382
- Stochastic integral 365, 368
- Stochastic Riemann integral 366
- Volatility coefficient 382
- Stochastic mortality 368
- Stock
- Swap
- Commodity swap 33, 77, 93
- Credit default swap (CDS) 22, 33, 77, 90
- Cross-currency basis swap 87
- Currency swap 33, 76, 87
- Deferred swap 77
- Definition 33, 75
- Equity swap 77
- Fixed for floating 76
- Fixed leg 76
- Floating leg 76
- Foreign exchange swap 87
- Interest rate swap 33, 76, 77
- Prepaid swap 77
- Swap rate 85
- Swap term 76
- Tenor 76
- Total return swap 77
- Variable leg 76
- Systematic risk 9, 12
t
u
- Uniform random number, see Simulation
- Unit-linked contract, see Variable annuity
v
- Variable annuity 165
- Binomial model 232
- Black-Scholes-Merton model 470
- Fee rate 166, 473
- Guaranteed lifetime withdrawal benefit (GLWB) 175
- Guaranteed minimum death benefit (GMDB) 175
- Guaranteed minimum maturity benefit (GMMB) 167, 168, 470
- Guaranteed minimum withdrawal benefit (GMWB) 167, 168
- Insurer’s loss 172
- Management and expense ratio 165
- Separate account policy 165
- Sub-account 165, 166
- Variance reduction technique, see Simulation
w
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