Hi

@nicholasjalonso GARP's practice exams, um, they aren't always the best. In the practice exam, GARP is explicitly providing (u) and (d) which is available as an approach but the

**better (more sophisticated) approach** is to match volatility with (u) and (d) as even GARP's new materials state (emphasis mine) in their Chapter 14:

"Before moving on to show how these equations are used in multi-step trees, we will explain how u and d are determined. **The parameters u and d should be chosen to reflect the volatility of the stock price.** [footnote 3: See Section 3.3 for a discussion of the measurement of volatility.] If we denote the volatility per year by s, then appropriate values for the parameters are

u = exp[σ *sqrt(Δt)]

d = exp[-σ *sqrt(Δt)]

where ∆t is measured in years. The appendix to this chapter explains why these parameters match the volatility."

-- May, B. (2019). 2020 Financial Risk Management Part I: Valuation and Risk Models, 10th Edition. [[VitalSource Bookshelf version]].

If you are given explicitly u = 1.2 and d = 0.8, then of course use them; as such, they implicitly assume normally distributed arithmetic returns. However, the exam should be more likely to ask u and d to be determined by (i.e., matched to) volatility per the text above; this approach implicitly assumes normally distributed geometric returns and this binomial converges on the BSM.

**Either approach is okay**, but matching volatility is better. The question will tell you which approach. I hope that's helpful,

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