Suppose = 4, u = 2, d = 1/2, and r = 1/4. Let N = 2. Consider an American call option with strike price K = 5. Use backward algorithm to evaluate

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SO 2. Theorem 4.4.3. We have the following American pricing algorithm for the path-dependent derivative security price process given by Definition 4.4.1: Vn(wi ...WN) = max{Gn(wi...WN),0}, (4.4.10) (4.4.11) Vn/w...wn) = max {Gaw....wn), [pVu+1(w.wm) + Vn+1(w...wq7)}} 1 1+r for n = N -1,...,0. SO 2. Theorem 4.4.3. We have the following American pricing algorithm for the path-dependent derivative security price process given by Definition 4.4.1: Vn(wi ...WN) = max{Gn(wi...WN),0}, (4.4.10) (4.4.11) Vn/w...wn) = max {Gaw....wn), [pVu+1(w.wm) + Vn+1(w...wq7)}} 1 1+r for n = N -1,...,0