Module 11GBM SimulationLesson 1 of 718 min
GBM Intuition
SDE idea in words and the exact terminal solution.
Model
dS = r S dt + σ S dW under risk-neutral measure.
Exact terminal
S_T = S_0 exp((r-½σ²)T + σ√T Z), Z~N(0,1)
Path-dependent
Need multi-step discretization for Asians, barriers, etc.
Challenge
Write the multi-step update formula as a comment in code.
Tips
- Risk-neutral drift uses r
- Exact terminal for vanilla
- Multi-step for path deps
Try it live
GBM IntuitionRust 2021
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Output
Press Run to compile and execute.