FFT-network for bivariate Lévy option pricing

Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes

“…Currently, there are fve popular numerical methods to price options under Lévy processes, binomial tree methods (BTMs, see [3,8,9]), fnite diference methods (FDMs, see [10][11][12][13]), Monte Carlo methods (MCM, see [14]), FFTbased transformation methods (see [15][16][17][18]), and cosine-willow tree methods (see [19]). For BTMs and WTMs, computing transition probabilities (TPs) is an insurmountable barrier.…”

“…Te COS method employs a cosine series expansion on the riskneutral return density and estimates the European option price based on the numerical integration on (− ∞, +∞). However, it is hard to determine a proper fnite interval [a, b] to truncate (− ∞, +∞) for the integration (see [15,18,20]) and is hard to be extended to path-dependent options. Te PROJ method overcomes these shortcomings and is extendable to Asian options, variance swaps, and American options but its extendability is still limited compared to the Cosine-willow tree method.…”

“…Tis algorithm is unifed and suitable for all GH subclass models. (2) In FFT-based transformation methods (see [15,18,20,21]), it is hard to fnd a proper fnite interval [a, b] to truncate the integration over (− ∞, +∞). While in the WT method, we propose an adaptive integration method in which the appropriate integral interval [a, b] is automatically found.…”