FFT Based Option Pricing

Efficient Options Pricing Using the Fast Fourier Transform

We review the commonly used numerical algorithms for option pricing under Levy process via Fast Fourier transform (FFT) calculations. By treating option price analogous to a probability density function, option prices across the whole spectrum of strikes can be obtained via FFT calculations. We also show how the property of the Fourier transform of a convolution product can be used to value var...

Fast Fourier Transform for Option Pricing: Improved Mathematical Modeling and Design of Efficient Parallel Algorithm

The Fast Fourier Transform (FFT) has been used in many scientific and engineering applications. The use of FFT for financial derivatives has been gaining momentum in the recent past. In this thesis, i) we have improved a recently proposed model of FFT for pricing financial derivatives to help design an efficient parallel algorithm. The improved mathematical model put forth in our research bridg...

Option Pricing Using the Fractional Fft

This paper shows how the recently developed fractional fft algorithm (frft) can be used to retrieve option prices from the corresponding characteristic functions. The frft algorithm has the advantage of using the characteristic function information in a more efficient way than the straight fft. Therefore less function evaluations are typically needed and substantial savings in computational tim...

Option Pricing via the FFT and its Application to Calibration

Pricing Asian option by the FFT with higher-order error convergence rate under Lévy processes

Pricing Asian options is a long standing hard problem since there is no analytical formula for the probability density of its payoff even when the process of the underlying asset follows the simple lognormal diffusion process. It is known that the option payoff can be expressed as a recursive function of sums of independent random variables. As a result, the density function of the option payof...