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Baxter M., Rennie A. Ч Financial calculus
Baxter M., Rennie A. Ч Financial calculus



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Ќазвание: Financial calculus

јвторы: Baxter M., Rennie A.

јннотаци€:

The rewards and dangers of speculating in the modern financial markets have been to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investments.
At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities.
Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including the Black-Scholes) are developed.
Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided.
This unique, modern and up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world.


язык: en

–убрика: Ёкономика и финансы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1996

 оличество страниц: 233

ƒобавлена в каталог: 10.02.2006

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Adapted processes      55 62
American options      93
Arbitrage      8 39 41
Arbitrage pricing      7Ч9
Arbitrage, arbitrage price      8 86 139
Arbitrage, arbitrage-free      197
Arbitrage-free complete models      196Ч200
Autoregressive process      156
Bachelier      45
Bank account process      see УCash bondФ
Binomial representation theorem      28Ч41 77
Binomial, branch      11
Binomial, branch model      10Ч17
Binomial, distribution      42
Binomial, process      46
Binomial, tree      19
Binomial, tree model      17Ч28
Black Ч Derman Ч Toy model      157
Black Ч Karasinski model      157
Black Ч Scholes      83Ч98
Black Ч Scholes, currency model      100
Black Ч Scholes, formula      43 91 182
Black Ч Scholes, hedge      96
Black Ч Scholes, model      83 178
Black Ч Scholes,summary      90
Bond only strategy      12
Bond options      169
Bond prices      144
bonds      112Ч115
Bonds, with coupons      114 165
Brace Ч Gatarek Ч Musiela model      175
Branch      10
Branch, binomial branch process      11
Brown, Robert      46
Brownian motion      44Ч46 48 49 54
Brownian motion, as stock model      50
Brownian motion, exponential with drift      51
Brownian motion, two-dimensional      62
Brownian motion, with drift      50
Calculus, Ito      57Ч62
Calculus, Newtonian      52
Calculus, stochastic      51Ч57
Call option      9 43 90
Call option, American      93
Call option, European      90
Call option, foreign exchange      103
Call option, on bonds      169
Call option, on coupon bonds      115 170
Call option, on dividend paying stocks      109
Call option, on swaps      see УSwaptionsФ
Call option, quanto      123
Cameron Ч Martin Ч Girsanov theorem      74 75
Cameron Ч Martin Ч Girsanov theorem, and market price of risk      120
Cameron Ч Martin Ч Girsanov theorem, converse      74 105 192
Cameron Ч Martin Ч Girsanov theorem, n-factor      159 186 187
Cameron Ч Martin Ч Girsanov theorem, use in foreign exchange      102
Cameron Ч Martin Ч Girsanov theorem, use in HJM models      138 145
Cameron Ч Martin Ч Girsanov theorem, use in stock models      83 84 179
Caplet      171 176
Caps      170
Cash bond      11 18 37 136 144
Cash bond, foreign currency      100
Central limit theorem      42 47 48
Change of measure      62Ч76 145 179 187
Claim      3 20 30
Coin-tossing game      4 5
Collector's guide to, exponential martingales      79
Collector's guide to, martingales      79
Commodity      3
Complete market      197
Completeness      196Ч200
Conditional expectation      32
Conditional marginal distribution      48 69
Construction strategies      79Ч83
Contingent claim      5 (see УClaim continuous compoundingФ)
Continuous processes      44Ч51
Correlation      123 126 158 176 182 193
Coupon bonds      114 165
Coupon bonds, options on      115 170
Coupons, fixed rate      165
Coupons, floating rate      166
Covariance      124 158
Cox Ч Ingersoll Ч Ross model      156
Cross-currency contracts      see УQuantosФ
Cumulative normal integral      see УNormal distribution functionФ
Currency      see УForeign exchangeФ
Default free      129
Delta hedge      181
density      7
Derivative      3 12
Derivative pricing      181 188
Difference equation      40 80
Diffusion      61 150
Digital contract      27 123
Discount bond      112 129
Discount process      37 87
Discounted, bond      138 145
Discounted, claim      38 87 90
Discounted, expectation      20 28
Discounted, stock      38 87 90 179
Discrete model, conclusions      41
Discrete model, continuous overture      41Ч43
Distribution function, normal      43 91
Dividends      106Ч112
Dividends, continuous      107
Dividends, periodic      111
Doleans exponential      61
Dollar investor      101
Doob Ч Meyer decomposition      56
Double fork      20
Drift      52 55 83
Drift, HJM      143 158
Drift, HJM constraints on      141 148
Drift, uniqueness      56
Driftlessness      78
Equilibrium distribution      154
Equities      106Ч112
Equities, guaranteed profits example      110
Equivalent martingale measure      197Ч200 (see УMartingale measureФ)
Equivalent measures      66 74
European call option      90
Examples, pricing on tree      23
Exercise date      91
Exercise price      see УStrike priceФ
Existence of martingale measure      40
Exotic contracts      128 163
Expectation      4 9 23
Expectation, discounted claim      40
Expectation, for a branch      12
Expectation, on a tree      21
Expectation, operator      31
Expectation, pricing      3Ч7 16 86
Expectation, re-emergence      23
Expectation, regained      16
Expectation, vs arbitrage      9
Exponential Brownian motion      60 84 85
Exponential Brownian motion, with drift      51
Exponential martingale      79 85
Filtration      30 48
fixed rate      165 167 168
Floating rate      166 167
Floorlet      171
Floors      170
Foreign exchange      99Ч106 122
Foreign exchange, interest rate models      192Ч196
Forward      6 11 17
Forward measure      165 191
Forward rate      134Ч136 142
Forward rate, bond price formula      144
Forward rate, curve      134
Forward rate, drift      143 158
Forward rate, under forward measure      192
Forward rate, volatility      143 158
Forward swaps      168
Forward, foreign exchange      99 103
Forward, interest rate      133 163
Forward, quanto      123
Forward, use in option formula      169 182
Fractal      49
Fubini      143
Gaussian process      50
Harrison and Pliska      197 200
Heath Ч Jarrow Ч Morton      see УHJMФ
Hedge      94 145 180 188
Hedge, BlackЧScholes      96
Hedging strategy      see УReplicating strategyФ
history      20 30
HJM      142 158
HJM, conditions      143 148 159
HJM, equivalence to short-rate      150
HJM, multi-factor      158Ч163
HJM, single-factor      142Ч149
HJM, universality      149
Ho and Lee model      151 169 172 174
Hull and White model      see УVasicekФ
IID variables      47 58
Illustrated definitions      29
Independence      4 21 46 48
Indicator function      199
Induction      19 22
Induction, backwards      19
Induction, inductive step      22 36
Induction, result      22
Instantaneous rate      132 135 136 144
Instantaneous rate, Markovian      150
Instruments      3 11 83 100 128
Interest rate      18
Interest rate, foreign exchange model      193
Interest rate, market      128Ч135
Interest rate, multi-factor models      172Ч177
Interest rate, products      163Ч172
Interest rate, riskless      83
Interest rate, short-rate models      149Ч158
Interest rate, simple model      135Ч142
Ito calculus      57Ч62
Ito's formula      59 61 81 83
Ito's formula, n-factor      185
Jamshidian      170
Joint likelihood function      70
Kolmogorov's law of large numbers      see УStrong lawФ
Law of the unconscious statistician      7
LIBOR rate      166 168 170 175Ч176
LIBOR rate, under forward measure      191
Local martingales      79
Log-drift      60
Log-normal, call formula      103
Log-normal, distribution      6
Log-normal, models      181Ч183
Log-volatility      60
Long position      96 168 172
Marginal distribution      48
Marginal distribution, conditional      48 69
Market maker      14
Market price of risk      115Ч122
Market price of risk, definition      119
Market price of risk, in general models      179 188
Market price of risk, in HJM models      141 145 147
Markov process      144 150
Martingale      33 76
Martingale measure      34 44 76 197
Martingale measure, continuous model      85 87
Martingale measure, discrete model      34Ч39
Martingale measure, existence and uniqueness      40
Martingale representation theorem      76Ч79 94
Martingale representation theorem, and dividend payments      108 112
Martingale representation theorem, and tradable assets      116
Martingale representation theorem, n-factor      161 186 188
Martingale representation theorem, use in foreign exchange      102
Martingale representation theorem, use in HJM      139 146
Martingale representation theorem, use in stock models      83Ч85 88 180
Martingale, exponential      79
maturity      129
Mean      155 (see УExpectation mean reversionФ)
Measure      30 63
Multi-factor models      172
Multi-factor models, HJM      158
Multi-factor models, normal models      174
Multiple payment contracts      164
Newtonian calculus      52
Newtonian differentials      51
Newtonian differentials, uniqueness      53
Newtonian function      52
Node      10
Noise      41 50
Non-tradable quantity      116Ч118 120
Normal distribution, function      43 91
Normal distribution, identification      72
Numeraires      143 188Ч192
Numeraires, changing      190
Numeraires, with volatility      189
Option      9 43 90 94
Ordinary differential equation      53
Ornstein Ч Uhlenbeck process      173
Over-the-counter      163
Partial differential equation      95
Path probabilities      21
Payoff      4 15 103 147
Pliska      197 200
Poisson process      55
Portfolio      80
POSITION      96
Previsible process      32 56 78 80
Price is right, the      14
Principal      165Ч167
probability      4
Probability density function      7
Process      29
Process, stochastic      55
Product rule      62 138 189
Product rule, n-factor      185
Pull to par      114
Put option      91
Put-call parity      91 171
Quantos      122Ч127 183
Radon Ч Nikodym derivative      63Ч68 73
Radon Ч Nikodym derivative, changing numeraire      105 190Ч192 196
Radon Ч Nikodym derivative, continuous time      69 71
Random variable      7 12 32 65
Random walk      46
Recombinant tree      23
Replicating strategy      8 12 40
Replicating strategy, continuous model      82 86 180
Replicating strategy, discrete model      13 22Ч23
Replicating strategy, foreign exchange      102
Replicating strategy, HJM model      137 146 164
Riccati differential equation      156
Risk-free construction      see УReplicating strategyФ
Risk-neutral measure      120 (see УMartingale measureФ)
SDE      56
Self-financing      39Ч40 80 180
Self-financing, equation      81 89 162 189
Self-financing, in HJM model      139 147
Semimartingale      55 56
SHARE      3
Short position      80 82
Short rate      see УInstantaneous rateФ
Single-factor models HJM      142
Single-factor models HJM, short-rate models      149
Standard deviation      6
Sterling investor      104
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