#                                                 #
#        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 

pdf-file: Chapter 2: The Binomial Model

<<previous chapter       next chapter>>