no code implementations • 27 Feb 2024 • Fabien Le Floc'h
We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters.
no code implementations • 3 Jan 2024 • Fabien Le Floc'h
This note revisits the SWIFT method based on Shannon wavelets to price European options under models with a known characteristic function in 2023.
no code implementations • 1 Sep 2023 • Fabien Le Floc'h
This note explores in more details instabilities of explicit super-time-stepping schemes, such as the Runge-Kutta-Chebyshev or Runge-Kutta-Legendre schemes, noticed in the litterature, when applied to the Heston stochastic volatility model.
no code implementations • 23 May 2023 • Fabien Le Floc'h
This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function.
no code implementations • 26 Apr 2023 • Fabien Le Floc'h, Winfried Koller
In the Black-Scholes model, the absence of arbitrages imposes necessary constraints on the slope of the implied variance in terms of log-moneyness, asymptotically for large log-moneyness.
no code implementations • 18 Nov 2022 • Fabien Le Floc'h
What kind of implied volatility extrapolation is appropriate?
no code implementations • 11 Jul 2022 • Fabien Le Floc'h
The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data.
no code implementations • 16 Mar 2022 • Fabien Le Floc'h
The classic Brennan-Schwartz algorithm to solve the linear complementary problem, which arises from the finite difference discretization of the partial differential equation related to American option pricing does not lead to the exact solution under negative interest rates.
no code implementations • 6 Sep 2021 • Fabien Le Floc'h, Cornelis W. Oosterlee
This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary.
no code implementations • 22 Jun 2021 • Fabien Le Floc'h
This paper presents the Runge-Kutta-Legendre finite difference scheme, allowing for an additional shift in its polynomial representation.
1 code implementation • 22 Jun 2021 • Fabien Le Floc'h
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.
no code implementations • 27 Jan 2021 • Fabien Le Floc'h
The Mersenne-Twister is one of the most popular generators of uniform pseudo-random numbers.
Data Structures and Algorithms
1 code implementation • 27 May 2020 • Fabien Le Floc'h
We present an alternative formula to price European options through cosine series expansions, under models with a known characteristic function such as the Heston stochastic volatility model.
no code implementations • 27 May 2020 • Fabien Le Floc'h
This note shows that the cosine expansion based on the Vieta formula is equivalent to a discretization of the Parseval identity.
no code implementations • 18 Apr 2020 • Fabien Le Floc'h
This paper presents simple formulae for the local variance gamma model of Carr and Nadtochiy, extended with a piecewise-linear local variance function.
