Mathematical Modeling in Finance with Stochastic Processes

INDEX 281

NYSE

seeNew York Stock Exchange, 19

option
American, 18
Asian, 19
Bermuda, 19
call, 18, 27
European, 18
factors, 21
holder, 18
intrinsic value, 21
put, 18, 19, 28
writer, 18, 21
option pricing
history, 12
options, 8, 9
in the money, 21
over-the-counter, 19
Ornstein-Uhlenbeck process, 61
out of the money, 265, 267
over the counter, 10
over the counter, 14

Perrin, Jean-Baptiste, 11
Poisson process, 60
Poisson, Simeon, 126
probability by conditioning, 180
probability space,seesample space
put option, 239
put-call parity, 237
put-call parity principle
arbitrage, 239

quadratic variation, 188
quantum randomness, 55
queuing processes, 60

random time, 181

random walk, 59, 61, 101, 156

Central Limit Theorem, 159

limiting process, 158

mean, 157

phase space, 156

probability of position, 159

variance, 157

random walk hypothesis, 217, 246

random walk theory, 53

Reflection Principle, 180

replicating portfolio, 74, 75, 218, 247

reserve ratio,seereserve requirement

reserve requirement, 114, 115

Rho, 262

risk free interest rate, 217, 246

risk management, 29

sample path, 57

sample point, 57

sample space, 57

Samuelson, Paul, 11

Scholes, Myron, 12, 13

security, 74

sensitivity analysis, 44

short selling, 29

simple random walk, 58

speculation, 26, 27

spreadsheets, 42

state space, 57

stochastic, 57

stochastic differential equation, 197

stochastic process, 57

stochastic volatility, 265, 266, 271

stock, 74

strike price, 18, 20

Strong Law of Large Numbers, 127

swaps, 8, 9

symmetries, 178