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Fabien Le Floc'h

Publications and source records attributed to Fabien Le Floc'h.

23 records · Page 2Linked to original sources
arXiv2021

More stochastic expansions for the pricing of vanilla options with cash dividends

There is no exact closed form formula for pricing of European options with discrete cash dividends under the model where the underlying asset price follows a piecewise lognormal process with jumps at dividend ex-dates. This paper presents alternative expansions based on the technique of Etore and Gobet, leading to more robust first, second and third-order expansions across the range of strikes and the range of dividend dates.

q-fin.CP↗
arXiv2021

Entropy of Mersenne-Twisters

The Mersenne-Twister is one of the most popular generators of uniform pseudo-random numbers. It is used in many numerical libraries and software. In this paper, we look at the Komolgorov entropy of the original Mersenne-Twister, as well as of more modern variations such as the 64-bit Mersenne-Twisters, the Well generators, and the Melg generators.

cs.DS↗
arXiv2020

An arbitrage-free interpolation of class $C^2$ for option prices

This paper presents simple formulae for the local variance gamma model of Carr and Nadtochiy, extended with a piecewise-linear local variance function. The new formulae allow to calibrate the model efficiently to market option quotes. On a small set of quotes, exact calibration is achieved under one millisecond. This effectively results in an arbitrage-free interpolation of class $C^2$. The paper proposes a good regularization when the quotes are noisy. Finally, it puts in evidence an issue of the model at-the-money, which is also present in the related one-step finite difference technique of Andreasen and Huge, and gives two solutions for it.

q-fin.PR↗
arXiv2020

Notes on the SWIFT method based on Shannon Wavelets for Option Pricing

This note shows that the cosine expansion based on the Vieta formula is equivalent to a discretization of the Parseval identity. We then evaluate the use of simple direct algorithms to compute the Shannon coefficients for the payoff. Finally, we explore the efficiency of a Filon quadrature instead of the Vieta formula for the coefficients related to the probability density function.

q-fin.CP↗