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Lookback option prices under a spectrally negative tempered-stable model. (English) Zbl 1269.91085

Summary: We perform a Laplace transform inversion in the time parameter on the two Wiener-Hopf factors for a spectrally negative tempered stable Lévy process. This yields the issuing price of continuously monitored lookback options. We also propose a simulation technique for the purpose of Monte-Carlo valuation and discuss the convergence rate to continuous prices when the number of discretization steps (i.e. monitoring dates) goes to infinity.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
60G51 Processes with independent increments; Lévy processes
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