Book ChapterDOI
A Didactic Note on Affine Stochastic Volatility Models
Jan Kallsen
- pp 343-368
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In this article, the authors take a look at affine Markov processes from the point of view of semimartingales and time changes, and explain the intuition behind these properties.Abstract:
Many stochastic volatility (SV) models in the literature are based on an affine structure, which makes them handy for analytical calculations. The underlying general class of affine Markov processes has been characterized completely and investigated thoroughly by Duffie, Filipovic, and Schachermayer (2003). In this note, we take a look at this set of processes and in particular affine SV models from the point of view of semimartingales and time changes. In the course of doing so, we explain the intuition behind semimartingale characteristics.read more
Citations
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Analysis of Fourier Transform Valuation Formulas and Applications
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On using shadow prices in portfolio optimization with transaction costs
Jan Kallsen,Johannes Muhle-Karbe +1 more
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Exponentially affine martingales, affine measure changes and exponential moments of affine processes
Jan Kallsen,Johannes Muhle-Karbe +1 more
TL;DR: In this article, the authors consider local martingales of exponential form M = e X or E (X ), where X denotes one component of a multivariate affine process and give a weak sufficient criterion for M to be a true martingale.
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On the duality principle in option pricing: semimartingale setting
TL;DR: This paper considers models where prices evolve as general exponential semimartingales and provides a complete characterization of the dual process under the dual measure.
References
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Journal ArticleDOI
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Book
Limit Theorems for Stochastic Processes
Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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Markov Processes: Characterization and Convergence
TL;DR: In this paper, the authors present a flowchart of generator and Markov Processes, and show that the flowchart can be viewed as a branching process of a generator.
Book
Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.