The Characteristic Function of the Time-Integral of Geometric Brownian Motion and its Application in Asian Option Pricing

In this research a new method for pricing continuous Arithmetic averaged Asian options is proposed. The computation is based on Fourier-cosine expansion, namely the COS method. Therefore, we derive the characteristic function of Integrated Geometric Brownian Motion based on Bougerol's identity. <br/><br/>Extensive numerical error analysis on the...

Generalized Variant Support Vector Machine

With the advancement in information technology, datasets with an enormous amount of data are available. The classification task on these datasets is more time- and memory-consuming as the number of data increases. The support vector machine (SVM), which is arguably the most popular classification technique, has disappointing performance in...

Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European style and American-style Asian options and for discretely and continuously monitored versions. In the present paper...

Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions. Part II. Early-exercise features and GPU implementation

In this article, we propose an efficient pricing method for Asian options with early–exercise features. It is based on a two–dimensional integration and a backward recursion of the Fourier coefficients, in which several numerical techniques, like Fourier cosine expansions, Clenshaw–Curtis quadrature and the Fast Fourier transform (FFT) are...

Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions Part I: European-style products

We propose an efficient pricing method for arithmetic, and geometric, Asian options under Levy processes, based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European–style and American–style Asian options, and for discretely and continuously monitored versions. In the present paper we...