Abstract
Chapter 3 examines the extent to which the properties of the simple model of Chapter 2 (a single time period, with one stock and just two future scenarios) continue to hold in more general one-step models. These involve increasing the number of scenarios at time 1 and increasing the number of stocks. The properties examined are viability and its characterization using risk-neutral probabilities, and the pricing problem for general derivatives using replication and risk-neutral probabilities.
For such models it can happen that not all derivatives can be replicated (the model may be incomplete), and there may not be a unique fair price. The chapter discusses how to identify incomplete models and how to find the range of possible fair prices for a derivative.
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© 2012 Springer-Verlag London
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Cutland, N.J., Roux, A. (2012). Single-Period Models. In: Derivative Pricing in Discrete Time. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-4408-3_3
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DOI: https://doi.org/10.1007/978-1-4471-4408-3_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4407-6
Online ISBN: 978-1-4471-4408-3
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