Brownian Motion and Random Walk Models › Key Parameters
Michael BrenndoerferNovember 22, 20251 min read
Quantitative FinanceAll chapters Part 5 of 15Stochastic Calculus and Pricing Theory
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The key parameters for the Geometric Brownian Motion model are:
- : Initial asset price. The starting point for the simulation or pricing path.
- μ: Drift rate (expected return). Represents the annualized average growth rate of the asset.
- σ: Volatility. The standard deviation of the asset's logarithmic returns, measuring uncertainty.
- T: Time horizon. The total duration for which the price path is simulated.
- dt: Time step size. Smaller steps () lead to more accurate approximations of the continuous process.