In this chapter, we construct the geometric binomial model for stock price movement and use the model to determine the value of a general European claim. An important consequence is the Cox-Ross-Rubinstein formula for the price of a call option. Formulas for path-dependent claims are given in the last section. The valuation techniques in this chapter are based on the notion of self-financing portfolio described in Chapter 5.
7.1 Construction of the Binomial Model
Consider a (non-dividend paying) stock with initial price S0 such that during each discrete time period the price changes either by a factor u with probability p or by a factor d with probability q ≔ 1 − p, where 0 < d < u. The symbols u and d are meant ...
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