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This paper extends the Singular Fourier--Pad\'e (SFP) method proposed by Chan(2018) to pricing/hedging early-exercise options--Bermudan, American anddiscrete-monitored barrier options--under a L\'evy process. The current SFPmethod is incorporated with the Filon--Clenshaw--Curtis (FCC) rules invented byDom\'inguez et al. (2011), and we call the new method SFP--FCC. The mainpurpose of using the SFP--FCC method is to require a small number of terms toyield fast error convergence and to formulate option pricing and option Greekcurves rather than individual prices/Greek values. We also numerically showthat the SFP--FCC method can retain a global spectral convergence rate inoption pricing and hedging when the risk-free probability density function ispiecewise smooth. Moreover, the computational complexity of the method is$\mathcal{O}((L-1)(N+1)(\tilde{N} \log \tilde{N}) )$ with $N$ a (small) numberof complex Fourier series terms, $\tilde{N}$ a number of Chebyshev series termsand $L$, the number of early-exercise/monitoring dates. Finally, we show thatour method is more favourable than existing techniques in numericalexperiments.

An SFP--FCC Method for Pricing and Hedging Early-exercise Options under L\'evy Processes