Questions / Quant research, Stochastic calculus & linear algebra
Mean and median of GBM
dS = μS dt + σS dW with S₀ = 100, μ = 8% and σ = 20%. What is E[S₁]?
Answer it in the app It's free. You get hints, a second try if you miss, and a follow-up question.
Show the answer and worked solution
Answer: 108.3 USD
- E[S_T] = S₀e^(μT).
- 100e^0.08 = 108.33.
Interview shortcut. GBM mean grows at μ: S₀e^(μT) = 100e^0.08.
Takeaway. The σ²/2 correction moves the median, not the mean.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.