Zobrazeno 1 - 10
of 388
pro vyhledávání: '"Friz, Peter"'
The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates paths into high-dimensional feature vectors, capturing their intrinsic
Externí odkaz:
http://arxiv.org/abs/2408.05085
We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously viewed as t
Externí odkaz:
http://arxiv.org/abs/2407.11142
Autor:
Friz, Peter K., Gatheral, Jim
The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion
Externí odkaz:
http://arxiv.org/abs/2406.16131
The Euler-Maclaurin formula which relates a discrete sum with an integral, is generalised to the setting of Riemann-Stieltjes sums and integrals on stochastic processes whose paths are a.s. rectifiable, that is continuous and bounded variation. For t
Externí odkaz:
http://arxiv.org/abs/2403.09335
The combination of functional limit theorems with the pathwise analysis of deterministic and stochastic differential equations has proven to be a powerful approach to the analysis of fast-slow systems. In a multivariate setting, this requires rough p
Externí odkaz:
http://arxiv.org/abs/2402.13748
Autor:
Chiusole, Gideon, Friz, Peter K.
Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron-Martin), differential calculus (Malliavin), support description (Stroock-Varadhan), concentration
Externí odkaz:
http://arxiv.org/abs/2401.00169
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time
Externí odkaz:
http://arxiv.org/abs/2307.09216
The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients are definite iterated integrals of the path. The signature characterises the path up to a generalised form of reparametrisation. It is a classical result
Externí odkaz:
http://arxiv.org/abs/2305.19210
Autor:
Friz, Peter K., Wagenhofer, Thomas
In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all component
Externí odkaz:
http://arxiv.org/abs/2212.07817