Closed-form pricing formulae and option Greeks are obtained for European-type options using an orthogonal polynomial series -- complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and stochastic volatility models. We provide a succinct error analysis to...

This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend 2014a), to pricing/hedging European-type, early-exercise and discrete- monitored barrier options under a Lévy process. The paper employs Chebfun (cf. Trefethen...

We introduce a new numerical method called the complex Fourier series (CFS) method proposed by Chan (2017) to price options with an early-exercise feature — American, Bermudan and discretely monitored barrier options — under exponential Lévy asset dynamics. This new method allows us to...