Hi!My question relates to monte carlo simulation. Hull provides a standard approach that generates lognormal distributed prices by multiplying some initial price with a lognormally distributed random factor. The drift in this expression is mu – sigma^2/2. Benninga’s textbook Financial Modeling models the prices with the same logic except for one small difference: the drift is mu only, i.e. he takes the drift as it is in the geometric brownian motion of the underlying log returns, whereas Hull “corrects” it by subtracting sigma^2/2 due to Ito's Lemma. So one could say - Benninga models log return paths assuming log returns are normally distributed and then translates them into prices and does not necessarily stick to the lognormal distribution of prices. In this setup log prices are normally distributed with mu rather than mu - sigma^2/2- whereas Hull directly models lognormally distributed pricesIn the end there is no big difference in the simulated prices and derived simple returns from them. So what is the more “correct“way? I attached an Excel file with both versions implemented. Best, roomer

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Thanks, I looked it up - any other comments?

Hull's approach: is the exact solution of the SDEBenninga's approach is the discretization of the SDE according to the Euler schema. This converges to the exact (Hull) solution only for small (infinitesimal) time stepsP.

So if you had to run a simulation to get monthly prices, i.e. 12 per year how would you do it after specifying you mu p.a. and sigma p.a.Hull:St = St-1 x exp((mu-0.5xsigma^2)/12 + Z x sigma/sqrt(12))orBenninga:St = St-1 x exp((mu/12 + Z x sigma/sqrt(12))

always use the exact solution, using the Euler scheme when an easy exact solution exists is just sloppy

You can check book of Seydel R\ödiger "Tools for comp. finance", chapter no. 3.