Efficient Inverse Z-Transform and Pricing Barrier and Lookback Options With Discrete Monitoring
Efficient Inverse Z-Transform and Pricing Barrier and Lookback Options With Discrete Monitoring
We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse $Z$-transform, the Fourier/Laplace inversion and Wiener-Hopf factorization, and discuss efficient numerical methods for realization of these formulas. As applications, the cumulative probability distribution …