Financial Mathematics

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 $\left(\Omega ,\mathbb{P},ℱ,\mathbb{F}\right)$ 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:

  $\Omega \equiv {\Omega }_T=\{\omega ={\omega }_1{\omega }_2\cdots {\omega }_T:{\omega }_t\in \{$