Lookback option prices under a spectrally negative tempered-stable model
Résumé
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.