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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