1,151 research outputs found
Mathematical techniques for estimating operational readiness of complex systems
Development of methods for predicting operational readiness of complex systems based on probability theory is discussed. Operational readiness of systems is defined and mathematical relationships involved in determining readiness are presented. Example of reliability engineering and quality control is included
On the probability of hitting the boundary for Brownian motions on the SABR plane
Starting from the hyperbolic Brownian motion as a time-changed Brownian motion, we explore a set of probabilistic models–related to the SABR model in mathematical finance–which can be obtained by geometry-preserving transformations, and show how to translate the properties of the hyperbolic Brownian motion (density, probability mass, drift) to each particular model. Our main result is an explicit expression for the probability of any of these models hitting the boundary of their domains, the proof of which relies on the properties of the aforementioned transformations as well as time-change methods
Two examples of non strictly convex large deviations
We present two examples of a large deviations principle where the rate
function is not strictly convex. This is motivated by a model used in
mathematical finance (the Heston model), and adds a new item to the zoology of
non strictly convex large deviations. For one of these examples, we show that
the rate function of the Cramer-type of large deviations coincides with that of
the Freidlin-Wentzell when contraction principles are applied.Comment: 11 page
Large deviations for the extended Heston model: the large-time case
We study here the large-time behaviour of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals pathological behaviours of the asymptotic smile. In particular, we show that the condition assumed in Gatheral and Jacquier under which the Heston implied volatility converges to the SVI parameterisation is necessary and sufficient
Large and moderate deviations for stochastic Volterra systems
We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhijara, Dupuis and Ellis. We show in particular how this framework encompasses most rough volatility models used in mathematical finance and generalises many recent results in the literature
Arbitrage-free SVI volatility surfaces
In this article, we show how to calibrate the widely-used SVI
parameterization of the implied volatility surface in such a way as to
guarantee the absence of static arbitrage. In particular, we exhibit a large
class of arbitrage-free SVI volatility surfaces with a simple closed-form
representation. We demonstrate the high quality of typical SVI fits with a
numerical example using recent SPX options data.Comment: 25 pages, 6 figures Corrected some typos. Extended bibliography.
Paper restructured, Main theorem (Theorem 4.1) improved. Proof of Theorem 4.3
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