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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 7

Replication and Pricing in the Binomial Tree Model

7.1 The Standard Binomial Tree Model

By combining the probabilistic framework in Chapter 6 with the main formal concepts of derivative asset pricing presented for the single-period model in Chapter 5, we are now ready to formally discuss derivative asset pricing within the multi-period binomial tree model. Let us begin by recalling the salient features of the standard T-period (recombining) binomial tree model on the space (Ω,,,F) with two assets, namely, a risky stock S and a risk-free asset B, such as a bank account or zero-coupon bond. The model is specified as follows.

  • The time is discrete: t ∊ {0, 1, 2, ..., T}.
  • There are 2T possible market scenarios:

    ΩΩT={ω=ω1ω2ωT:ωt{

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