Titlebook: Uncertain Volatility Models; Theory and Applicati Robert Buff Book 2002 Springer-Verlag Berlin Heidelberg 2002 Mathematica.Uncertain volati

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Notation and Basic Definitionsℕ denotes the nonnegative integers. ℝ denotes the real numbers. ℝ. denotes the nonnegative real numbers. ℝ. denotes the strictly positive real numbers.

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Scenario-Based Evaluation and UncertaintyThe following problems arise in practice:

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A Lattice FrameworkNonlinear Black-Scholes models for worst-case scenarios require two kinds of algorithmic techniques:

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Algorithms for Vanilla OptionsVanilla options are standard European calls and puts on the underlying asset. Before we discuss algorithms for barrier and American options we illustrate uncertain volatility for portfolios of vanilla options with an example.

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Algorithms for Barrier OptionsWe consider barrier options that knock out the first time the price .. of the underlying asset crosses a predetermined knock-out barrier .. This is one flavor of barrier options; a timing feature is added in [29], where options loose a fraction of their value for every day they spend above (or below) ..

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Exotic Volatility ScenariosIn Chapters 7 and 8, algorithms have been discussed that compute (best) worst-case prices under uncertain volatility scenarios in which ∂(..,.) and ∂..,.) are independent for .. In this chapter we extend the notion of uncertain volatility scenarios to include evolutions of the spot volatility that depend on its past history.