Mathematical Modeling in Finance with Stochastic Processes

280 INDEX

future, 18
futures, 8, 9

Gambler’s Fallacy, 127
gambler’s ruin, 95
Gamma, 261
Gaussian processes, 60
Geometric Brownian Motion, 204
Geometric Brownian Motion
lognormal distribution, 208
mean, 209
parameters, 211
quadratic variation, 212
ruin and victory probabilities, 211
variance, 210
geometric Brownian Motion, 198
geometric Brownian motion, 12, 61

half-integer correction, 147
heat equation, 224
initial value problem, 224
hedge ratio, 29
hedge ratios, 12, 14
hedge-ratio, 260
hedging, 12, 26, 28, 29, 263
historical volatility,seevolatility, his-
torical
hitting time, 180

ideal gas, 45
ideal gas law, 46
implied volatility, see volatility, im-
plied
in the money, 265, 267
indicator random variable, 115
Itˆo’s formula, 204

jump-diffusion models, 265, 266, 271

Khinchin, Aleksandr, 126

Kolmogorov, Andrey, 127

Kronecker delta, 115

Laplace, Pierre-Simon, 139

leptokurtosis, 267

leptokutosis, 265

Liapunov’s theorem, 139

Liapunov, Aleksandr, 139

Lindeberg’s Theorem, 139

lognormal distribution, 209

Markov chain, 58

Markov process, 59, 101

Markov processes

family tree, 61

Markov’s Inequality, 124

martingale, 102

mathematical finance, 9

modern, 11

mathematical model, 39

unit analysis, 42

mathematical models, 15, 16

equations, 41

McKean, Henry, 12

Merton, Robert, 12, 13

model robustness, 68

moment, 129

moment generating function, 131

moment generating function, 129

National Longitudinal Survey of Youth,

140

New York Stock Exchange, 19

Newton’s method, 255

Nobel Prize, 12

non-risky portfolio, 219, 248

normal random variable

moment generating function, 132

normal random variables, 133