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- W56354548 abstract "Having described single-step pricing models rather fully, we are ready to consider models with a finite number of consecutive trading dates. We shall see that these models behave essentially as a succession of one-step models, so that our earlier analysis can be applied repeatedly to yield explicit pricing formulae. For a simple binomial model we now describe how the use of risk-neutral probabilities implies the martingale property of discounted stock prices and thus of the discounted value process of any self-financing strategy. In this model pricing techniques for European options using replicating portfolios or risk-neutral probabilities are compared and an explicit pricing formula for the European call is then derived. Two-step example Most of the essential features of a general multi-step model can be seen in a simple example with two time steps, where we avoid cumbersome notation related to a general case. Here we take time to be 0, T , 2 T , and we simplify the notation by just specifying the number of a step, ignoring its length. We wish to build a model of stock prices with three ingredients S (0), S (1), S (2), where S (0) is a given number and the remaining quantities are random variables. The construction consists of two repetitions of the single-step dynamics. In the single-step case the core of the construction was the model of the rate of return with two possible values, which can be thought of as related to a single toss of a coin." @default.
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- W56354548 date "2012-02-23" @default.
- W56354548 modified "2023-09-30" @default.
- W56354548 title "Multi-step binomial model" @default.
- W56354548 doi "https://doi.org/10.1017/cbo9781139051583.004" @default.
- W56354548 hasPublicationYear "2012" @default.
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