--------------------------------------------------- # # # Chapter 2: The Binomial Model # # and Binomial Trees # # # --------------------------------------------------- Summary: The binomial model, sometimes just refered to as binomial trees, is the easiest but nevertheless absolutely nontrivial model which allows the pricing of options through exact payoff replication. Its price dynamics is given by S_k = S_{k-1} * ( 1 + ret_k ) (1) where the returns ret_k are allowed to take on only two different values, ret_k in { ret_up , ret_down } (2) Because of that property, arbitrary option payoffs H = H(S_0,S_1,...,S_{N-1},S_N) (3) can be replicated exactly by a suitable trading strategy in the underlying S_k. That is, there are numbers delta_0,...,delta_{N-1} with delta_k being the number of stocks to be held at the end of day t_k, such that the amount of money V_N generated by that strategy is equal to the option payoff H: V_N = V_0 + sum_{k=1}^N delta_{k-1}*(S_k - S_{k-1}) = H(S_0,S_1,...,S_{N-1},S_N) . In chapter 2 the mathematical details and proofs are presented.

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