1. Explain in detail the derivation of the BOPM for a call option. Include
   1. Derivation of the single-period model (use parameters)
   2. Include a single-period example where: u = 1.10, d = 0.95, R_f = 0.025, S₀ = $50, X = $50. Show an arbitrage example when the call is mispriced.
   3. Explain the mechanics for pricing a call with the multiple-period model.
   4. Include a multiple period model example with n = 2 (u = 1.0488, d = 0.9747, R_f = 0.025, S₀ = $50, and X = $50).
   5. Explain why subdividing the binomial model adds realism to the model
   6. Describe the methodology for estimating u and d. Include verbal statement, graphical picture, and math explanation.