1,720,975 research outputs found
Density estimates and short-time asymptotics for a hypoelliptic diffusion process
Full text linkWe study a system of n differential equations, each in dimension d. Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a local weak Hörmander condition, the noise propagates to the whole system. We prove upper bounds for the transition density (heat kernel) and its derivatives of any order. Then we give precise short-time asymptotics of the density at a suitable central limit time scale. Both these results account for the different non-diffusive scales of propagation in the various components. Finally, we provide a valuation formula for short-maturity at-the-money Asian basket options under correlated local volatility dynamics
Extreme At-The-Money Skew in a Local Volatility Model
No full textWe consider a local volatility model, with volatility taking two possible values, depending on the value of the underlying with respect to a fixed threshold. When the threshold is taken at the money, we establish exact pricing formulas for European call options and compute short-time asymptotics of the implied volatility surface. We derive an exact formula for the at-the-money implied volatility skew which explodes as , reproducing the empirical steep short end of the smile. This behaviour is a consequence of the singularity of the local volatility at the money. Finally, we look at continuous, non-differentiable versions of such a model. We still find, in simulations, exploding implied skews
Tube estimates for diffusion processes under a weak Hörmander condition
No full textWe consider a diffusion process under a local weak Hörmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains in a small tube around a deterministic trajectory (skeleton path). These bounds depend explicitly on the radius of the tube and on the energy of the skeleton path. We use a norm which reflects the non-isotropic structure of the problem, meaning that the diffusion propagates in R2R2 with different speeds in the directions σσ and [σ,b][σ,b]. We establish a connection between this norm and the standard control distance. On considère une diffusion dont les coefficients satisfont une condition d’Hörmander faible locale. On obtient des estimées gaussiennes de la densité en temps court et des bornes inférieures et supérieures exponentielles pour la probabilité que la diffusion reste dans un petit tube autour d’une trajectoire déterministe (« squelette »). Ces bornes dépendent explicitement du rayon du tube et de l’énergie du squelette. On utilise une norme qui prend en compte la structure non isotrope du problème, dans le sens où la diffusion se propage dans R2R2 avec des vitesses différentes dans la direction de σσ et [σ,b][σ,b]. On établit un lien entre cette norme et la distance de contrôle standard
Short-dated smile under rough volatility: asymptotics and numerics
No full textIn Friz et al. [Precise asymptotics for robust stochastic volatility models. Ann. Appl. Probab, 2021, 31(2), 896-940], we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small-noise formulae for option prices, using the framework [Bayer et al., A regularity structure for rough volatility. Math. Finance, 2020, 30(3), 782-832]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence
Precise asymptotics: Robust stochastic volatility models
No full textWe present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of Bayer et al. (Math. Finance 30 (2020) 782-832) In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, Inahama-Kawabi on rough path space. When applied to rough volatility models, for example, in the setting of Bayer, Friz and Gatheral (Quant. Finance 16 (2016) 887-904) and Forde-Zhang (SIAM J. Financial Math. 8 (2017) 114-145), one obtains precise asymptotics for European options which refine known large deviation asymptotics
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Prognostic factors affecting long term outcome after iver resection for hepatocellular carcinoma. Results in a series of 100 italian patients
No full textAppropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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