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...

In this paper we extend the complex Fourier series expansion method proposed in Chan 2016a and 2016b to derive a closed-form pricing formula of options with early-exercise features − American options, barrier options and Bermuda options. We implement the method to price options under...

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...

This paper will demonstrate how European and American option prices can be computed under the jump-diffusion model using the radial basis function (RBF) interpolation scheme. The RBF interpolation scheme is demonstrated by solving an option pricing formula, a one-dimensional partial...

This paper develops a complex Fourier series (CFS) expansion pricing formula for evaluating European-type (call/put) options -- asset-or-nothing options, cash-or-nothing options, forward-start options, ratchet options and vanilla options -- when these risky assets are driven by Levy processes,...

We apply a new numerical method, the singular Fourier-Pade (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in Levy and affine processes. The motivation behind this application is to reduce the ineffciency of current Fourier techniques when they are...

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...