Abstract
This paper considers the valuation of exotic path-dependent options in Lévy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener–Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a Lévy process. Combined with general results on Fourier methods for option pricing, we provide formulas for the valuation of one-touch options, lookback options, and equity default swaps in Lévy models.
K. Glau would like to thank the DFG for financial support through project EB66/11-1, and the Austrian Science Fund (FWF) for an invitation under grant P18022. A. Papapantoleon gratefully acknowledges the financial support from the Austrian Science Fund (FWF grant Y328, START Prize).
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Notes
- 1.
The historical reasons leading to the adoption of the terminology “Wiener–Hopf” are outlined in Sect. 6.6 in [33].
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Eberlein, E., Glau, K., Papapantoleon, A. (2011). Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_8
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