# Multi- period option

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We'll see that our results from the one-period binomial model actually extend very easily to the multi-period model, we'll see that our results from the one-period binomial model, actually extend very easily to the multi-period model. So, let's get started.

The multiperiod binomial model for pricing derivatives of a risky security is also called the Cox-Ross-Rubenstein model or CRR model for short, after those who introduced it in Advantages and Disadvantages of the model Fast real earnings disadvantages of the binomial model are: Trading times are not really at discrete times, trading goes on continuously.

Securities do not change value according to a Bernoulli two-valued distribution on a single time step, or a binomial distribution on multiple time periods, they change over a range of values with a continuous distribution.

The calculations are tedious. Developing a continuous theory will take detailed limit-taking considerations.

The advantages of the model are: It clearly reveals the construction of the replicating portfolio. It is simple to calculate, although it can get tedious.

It reveals that we need more probability theory to get a complete understanding of path dependent probabilities of security prices.

It is possible, with considerable attention to detail, to make a limiting argument and pass from the binomial tree model of Cox, Ross and Rubenstein to the Black-Scholes pricing formula. However, this approach is not the most instructive.

Instead, we will back up from derivative pricing models, multi- period option consider simpler models with only risk, that is, gambling, to get a more complete understanding of stochastic processes before returning to pricing derivatives.

The discrete models derived from the Black-Scholes model are used for simple and rapid numerical evaluation of option prices rather than for motivation.

Baxter, A. Avellaneda and P.

Laurence [ 1 ]. The scripts will output the derivative security value.

First set values of S.