Accelerating the calibration of stochastic volatility models

This paper compares the performance of three methods for pricing vanilla options in models with known characteristic function: (1) Direct integration, (2) Fast Fourier Transform (FFT), (3) Fractional FFT. The most important application of this comparison is the choice of the fastest method for the calibration of stochastic volatility models, e.g. Heston, Bates, Barndor®-Nielsen-Shephard models or Levy models with stochastic time. We show that using additional cache technique makes the calibration with the direct integration method at least seven times faster than the calibration with the fractional FFT method.Stochastic Volatility Models; Calibration; Numerical Integration; Fast Fourier Transform

Accelerating the calibration of stochastic volatility models

This paper compares the performance of three methods for pricing vanilla options in models with known characteristic function: (1) Direct integration, (2) Fast Fourier Transform (FFT), (3) Fractional FFT. The most important application of this comparison is the choice of the fastest method for the calibration of stochastic volatility models, e.g. Heston, Bates, Barndorff-Nielsen-Shephard models or Levy models with stochastic time. We show that using additional cache technique makes the calibration with the direct integration method at least seven times faster than the calibration with the fractional FFT method. --Stochastic Volatility Models,Calibration,Numerical Integration,Fast Fourier Transform

Pricing of reinsurance contracts in the presence of catastrophe bonds

A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process. Within the proposed methodology, an appropriate financial pricing formula is derived, under a market implied risk neutral probability measure for both a catastrophe bond and an aggregate excess of loss reinsurance contract, using a generalised Fourier transform. Efficient numerical methods for the evaluation of this formula, such as the Fast Fourier transform and Fractional Fast Fourier transform, are considered. The methodology is illustrated on several examples including Pareto and Gamma claim severities

New sampling theorem and multiplicative filtering in the FRFT domain

Having in consideration a fractional convolution associated with the fractional Fourier transform (FRFT), we propose a novel reconstruction formula for bandlimited signals in the FRFT domain without using the classical Shannon theorem. This may be considered the main contribution of this work, and numerical experiments are implemented to demonstrate the effectiveness of the proposed sampling theorem. As a second goal, we also look for the designing of multiplicative filters. Indeed, we also convert the multiplicative filtering in FRFT domain to the time domain, which can be realized by Fast Fourier transform. Two concrete examples are included where the use of the present results is illustrated.publishe

Programmable two-dimensional optical fractional Fourier processor

A flexible optical system able to perform the fractional Fourier transform (FRFT) almost in real time is presented. In contrast to other FRFT setups the resulting transformation has no additional scaling and phase factors depending on the fractional orders. The feasibility of the proposed setup is demonstrated experimentally for a wide range of fractional orders. The fast modification of the fractional orders, offered by this optical system, allows to implement various proposed algorithms for beam characterization, phase retrieval, information processing, etc