Explain in detail the derivation of the BOPM for a call option.Include

1.Derivation of the single-period model (use parameters not numbers in your explanation)

2.Include a single-period example where: u = 1.10, d = 0.95, R_f = 0.025, S₀ = $50, X = $50. Explain or show with an example the arbitrage 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 = 0.0125, 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.