Lookang, based on model by Francisco Esquembre and Fu-Kwun β https://commons.wikimedia.org/wiki/File:Brownianmotion5particles150frame.gif · CC BY-SA 3.0 · Wikimedia Commons
Lognormal is the multiplicative cousin of the Normal β log-prices are Normal, prices are Lognormal. This is the workhorse of Black-Scholes.
β Intro Β· expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine β being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
β Try first Β· expand
Worked example
A stock price S_T at time T = 1 year follows geometric Brownian motion with drift ΞΌ = 0.05/yr and volatility Ο = 0.20/yr, starting from S_0 = 100. Specifically, ln(S_T / S_0) ~ N(ΞΌ - ΟΒ²/2, ΟΒ²). (a) Identify the distribution of S_T. (b) Compute E[S_T]. (c) Compute the median of S_T. (d) Compute P(S_T < 90).
β Worked example Β· expand
Practice 1 of 3Type a fraction, decimal, or expression β mathjs parses it.
β Practice Β· expand
Reflection
Where does this distribution sit in the story chain β what question does it answer that the previous distribution couldn't? Try to recall the key moment formulas (mean, variance) without looking them up.
