An SFP–FCC method for pricing and hedging early-exercise options under Lévy processes

This paper extends the singular Fourier–Padé (SFP) method proposed by Chan [Singular Fourier–Padé series expansion of European option prices. Quant. Finance, 2018, 18, 1149–1171] for pricing/hedging early-exercise options–Bermudan, American and discrete-monitored barrier options–under a Lévy process. The current SFP method is incorporated with the Filon–Clenshaw–Curtis (FCC) rules invented by Domínguez et al. [Stability and error estimates for Filon–Clenshaw–Curtis rules for highly oscillatory integrals. IMA J. Numer. Anal., 2011, 31, 1253–1280], and we call the new method SFP–FCC. The main purpose of using the SFP–FCC method is to require a small number of terms to yield fast error convergence and to formulate option pricing and option Greek curves rather than individual prices/Greek values. We also numerically show that the SFP–FCC method can retain a global spectral convergence rate in option pricing and hedging when the risk-free probability density function is piecewise smooth. Moreover, the computational complexity of the method is $\mathcal {O}((L-1)(N+1)(\tilde {N} \log \tilde {N}) ) $O((L−1)(N+1)(N~log⁡N~)) with N, a (small) number of complex Fourier series terms, $\tilde {N} $N~, a number of Chebyshev series terms and L, the number of early-exercise/monitoring dates. Finally, we compare the accuracy and computational time of our method with those of existing techniques in numerical experiments.