Fourier methods for pricing early-exercise options under levy dynamics

[摘要] ENGLISH ABSTRACT: The pricing of plain vanilla options, including early exercise options, such as Bermudanand American options, forms the basis for the calibration of financial models.As such, it is important to be able to price these options quickly and accurately.Empirical studies suggest that asset dynamics have jump components which can bemodelled by exponential Lévy processes. As such models often have characteristicfunctions available in closed form, it is possible to use Fourier transform methods,and particularly, the Fast Fourier Transform, to price such options efficiently. Inthis dissertation we investigate and implement four such methods, dubbed the Carr-Madan method, the convolution method, the COS method and the Fourier spacetimestepping method. We begin by pricing European options using these Fouriermethods in the Black-Scholes, Variance Gamma and Normal Inverse Gaussian models.Thereafter, we investigate the pricing of Bermudan and American options inthe Black-Scholes and Variance Gamma models. Throughout, we compare the fourFourier pricing methods for accuracy and computational efficiency.

[发布机构] Stellenbosch University