arXiv subjects

Cyril Coste

Publications and source records attributed to Cyril Coste.

5 recordsLinked to original sources

arXiv2018

Series representation of the pricing formula for the European option driven by space-time fractional diffusion

In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. The series formula can be obtained from the Mellin-Barnes representation of the option price with help of residue summation in $\mathbb{C}^2$. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

q-fin.MF↗

arXiv2017

Non-Gaussian analytic option pricing: a closed formula for the Lévy-stable model

We establish an explicit pricing formula for the class of Lévy-stable models with maximal negative asymmetry (Log-Lévy model with finite moments and stability parameter $1<α\leq 2$) in the form of rapidly converging series. The series is obtained with help of Mellin transform and the residue theory in $\mathbb{C}^2$. The resulting formula enables the straightforward evaluation of an European option with arbitrary accuracy without the use of numerical techniques. The formula can be used by any practitioner, even if not familiar with the underlying mathematical techniques. We test the efficiency of the formula, and compare it with numerical methods.

q-fin.PR↗

arXiv2016

Distributional Mellin calculus in $\mathbb{C}^n$, with applications to option pricing

We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in $\mathbb{C}^n$ and its connection to residue expansion or evaluation of Laplace integrals. These mathematical concepts are demonstrated on several option-pricing models. This includes European option models such as Black-Scholes or fractional-diffusion models, as well as evaluation of quantities related to the optimal exercise price of American options.

q-fin.PR↗

arXiv2016

Regularization and analytic option pricing under $α$-stable distribution of arbitrary asymmetry

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $α$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the Lévy propagator. Using distributional and $\mathbb{C}^n$ tools, we derive an analytic closed formula for the option price, valid for any stability $α\in]1,2]$ and any asymmetry. This formula is very efficient and recovers previous cases (Black-Scholes, Carr-Wu); we calibrate the formula on market datas, make numerical tests, and discuss its many interesting properties.

q-fin.PR↗

arXiv2009

The StressVaR: A New Risk Concept for Superior Fund Allocation

In this paper we introduce a novel approach to risk estimation based on nonlinear factor models - the "StressVaR" (SVaR). Developed to evaluate the risk of hedge funds, the SVaR appears to be applicable to a wide range of investments. Its principle is to use the fairly short and sparse history of the hedge fund returns to identify relevant risk factors among a very broad set of possible risk sources. This risk profile is obtained by calibrating a collection of nonlinear single-factor models as opposed to a single multi-factor model. We then use the risk profile and the very long and rich history of the factors to asses the possible impact of known past crises on the funds, unveiling their hidden risks and so called "black swans". In backtests using data of 1060 hedge funds we demonstrate that the SVaR has better or comparable properties than several common VaR measures - shows less VaR exceptions and, perhaps even more importantly, in case of an exception, by smaller amounts. The ultimate test of the StressVaR however, is in its usage as a fund allocating tool. By simulating a realistic investment in a portfolio of hedge funds, we show that the portfolio constructed using the StressVaR on average outperforms both the market and the portfolios constructed using common VaR measures. For the period from Feb. 2003 to June 2009, the StressVaR constructed portfolio outperforms the market by about 6% annually, and on average the competing VaR measures by around 3%. The performance numbers from Aug. 2007 to June 2009 are even more impressive. The SVaR portfolio outperforms the market by 20%, and the best competing measure by 4%.

q-fin.RM↗