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Motivated by the pricing of lookback options in exponential L\'evy models, westudy the difference between the continuous and discrete supremum of L\'evyprocesses. In particular, we extend the results of Broadie et al. (1999) tojump-diffusion models. We also derive bounds for general exponential L\'evymodels.

Connecting discrete and continuous lookback or hindsight options in exponential L\'evy models