Pricing of early-exercise Asian options under L\'evy processes based on Fourier cosine expansions

In this article, we propose a 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 employed. Rapid convergence of the pricing method is illustrated by an error analysis. Its performance is further demonstrated by various numerical examples, where we also show the power of an implementation on Graphics Processing Units (GPUs)

Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility

We propose a highly efficient and accurate valuation method for exotic-style options based on the novel Shannon wavelet inverse Fourier technique (SWIFT). Specifically, we derive an efficient pricing methods for power options under a more realistic double exponential jump model with stochastic volatility and jump intensity. Inclusion of such innovations may accommodate for the various stylised facts observed in the prices of financial assets, and admits a more realistic pricing framework as a result. Following the derivation of our SWIFT pricing method for power options, we perform extensive numerical experiments to analyse both the method's accuracy and efficiency. In addition, we investigate the sensitivities in the resulting prices, as well as the inherent errors, to changes in the underlying market conditions. Our numerical results demonstrate that the SWIFT method is not only more efficient when benchmarked to its close competitors, such as the Fourier- cosine (COS) and the widely-acclaimed fast-Fourier transform (FFT) methods, but it is also robust across a range of different market conditions exhibiting exponential error convergence

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alter- native to Hagan’s analytic formula for short maturities that may be employed for model calibration purposes

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 we focus on the European-style Asian options. The exponential convergence rates of Fourier cosine expansions and Clenshaw–Curtis quadrature reduces the CPU time of the method to milliseconds for geometric Asian options and a few seconds for arithmetic Asian options. The method’s accuracy is illustrated by a detailed error analysis and by various numerical examples.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

On an efficient multiple time step Monte Carlo simulation of the SABR model

In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options