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# Chapter 2: The Binomial Model #
# and Binomial Trees #
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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.

**pdf-file:** Chapter 2: The Binomial Model