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Recent work by Nualart and Schoutens (2000), where a kind of chaotic property for Lévy processes has been proved, has enabled us to develop a Malliavin calculus for Lévy processes. For simple Lévy processes some useful formulas for computing Malliavin derivatives are deduced. Applications for...
Persistent link: https://www.econbiz.de/10005390667
Consider a model of a financial market with a stock driven by a Lévy process and constant interest rate. A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formula for perpetual American put options...
Persistent link: https://www.econbiz.de/10005390677
We derive the density process of the minimal entropy martingale measure in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard [2]. The density is represented by the logarithm of the value function for an investor with exponential utility and no claim issued, and a...
Persistent link: https://www.econbiz.de/10005390692
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The Lévy term structure model due to Eberlein and Raible is extended to non-homogeneous driving processes. The classes of equivalent martingale and local martingale measures for various filtrations are characterized. It turns out that in a number of standard situations the martingale measure is...
Persistent link: https://www.econbiz.de/10005390742
In the spirit of Kyprianou and Ott (in Acta Appl. Math., to appear, <CitationRef CitationID="CR11">2013</CitationRef>) and Ott (in Ann. Appl. Probab. 23:2327–2356, <CitationRef CitationID="CR15">2013</CitationRef>) we consider an option whose payoff corresponds to a capped American lookback option with floating strike and solve the associated pricing problem (an optimal stopping...</citationref></citationref>
Persistent link: https://www.econbiz.de/10010997079
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Models driven by Lévy processes are attractive because of their greater flexibility compared to classical diffusion models. First we derive the dynamics of the LIBOR rate process in a semimartingale as well as a Lévy Heath-Jarrow-Morton setting. Then we introduce a Lévy LIBOR market model. In...
Persistent link: https://www.econbiz.de/10005613406
Except for the geometric Brownian model and the geometric Poissonian model, the general geometric Lévy market models are incomplete models and there are many equivalent martingale measures. In this paper we suggest to enlarge the market by a series of very special assets (power-jump assets)...
Persistent link: https://www.econbiz.de/10005613439