Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options
We deal with the finite time distribution of the discrete extrema for a Lvy process We propose a procedure based on the combined use of Hilbert- and z-transforms Our results solve in an efficient and accurate way a long-standing problem Our results are relevant in many fields: OR, finance, insurance, engineering, physics As a concrete application, we contribute to the option pricing literature
spitzer identity wiener-hopf factorization discrete monitoring lvy process z-transform barrier options lookback options hilbert transform fourier transform fft sinc functions euler summation