Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:stochastic_process
|
| gptkbp:application |
asset price modeling
stock price modeling |
| gptkbp:assumes |
independent increments
constant volatility no jumps constant drift |
| gptkbp:category |
gptkb:logic
gptkb:probability_theory |
| gptkbp:governingEquation |
dS = μSdt + σS dW
|
| gptkbp:hasProperty |
gptkb:log-normal_distribution
gptkb:Itô_process Markov chain continuous-time |
| https://www.w3.org/2000/01/rdf-schema#label |
geometric Brownian motion
|
| gptkbp:introducedIn |
gptkb:Paul_Samuelson
gptkb:Louis_Bachelier |
| gptkbp:namedAfter |
Brownian motion
|
| gptkbp:parameter |
Wiener process (W)
drift (μ) volatility (σ) |
| gptkbp:solutionForm |
S(t) = S(0) exp((μ - 0.5σ^2)t + σW(t))
|
| gptkbp:usedIn |
gptkb:Black-Scholes_model
mathematical finance option pricing |
| gptkbp:bfsParent |
gptkb:Black-Scholes-Merton_model
|
| gptkbp:bfsLayer |
7
|