The valuation of American options in a multidimensional exponential Lévy model |
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Authors: | Tomasz Klimsiak Andrzej Rozkosz |
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Affiliation: | 1. Institute of Mathematics, Polish Academy of Sciences, Warszawa, Poland;2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland |
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Abstract: | We consider the problem of valuation of American options written on dividend‐paying assets whose price dynamics follow a multidimensional exponential Lévy model. We carefully examine the relation between the option prices, related partial integro‐differential variational inequalities, and reflected backward stochastic differential equations. In particular, we prove regularity results for the value function and obtain the early exercise premium formula for a broad class of payoff functions. |
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Keywords: | American option backward stochastic differential equation exponential Lé vy model obstacle problem optimal stopping |
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