Related papers: Arbitrage-free SVI volatility surfaces
In this note, we introduce how to use Volatility Index (VIX) for postprocessing quantitative strategies so as to increase the Sharpe ratio and reduce trading risks. The signal from this procedure is an indicator of trading or not on a daily…
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
Stein variational inference (SVI) is a sample-based approximate Bayesian inference technique that generates a sample set by jointly optimizing the samples' locations to minimize an information-theoretic measure of discrepancy with the…
In this paper we give an algorithm for computing equations of Brauer-Severi varieties over perfect fields of characteristic 0. As an example we show the equations of all Brauer-Severi surfaces defined over $\mathbb{Q}$.
We study two complementary methodologies for calibrating implied volatility surfaces: analytical approximations and data-driven models based on rough path theory. On the analytical side, we revisit a second-order asymptotic expansion for…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options…
For the calibration of the parameters in static and dynamic SABR stochastic volatility models, we propose the application of the GPU technology to the Simulated Annealing global optimization algorithm and to the Monte Carlo simulation. This…
A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D\subseteq X$ and a morphism $\Lambda^{2}E\rightarrow\mathcal{O}_{X}$ satisfying some additional…
We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band…
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually…
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous…
We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the…
Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work (2004) the…
We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform…
Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and…
We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…
We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear…
In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of…
We consider the joint SPX-VIX calibration within a general class of Gaussian polynomial volatility models in which the volatility of the SPX is assumed to be a polynomial function of a Gaussian Volterra process defined as a stochastic…