Related papers: Generalised arbitrage-free SVI volatility surfaces
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean field formalism introduced by Saito for…
The purpose of this work is to explore the role that arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary…
In a rather general setting of multivariate stochastic volatility market models we derive global iterative probabilistic schemes for computing the free boundary and its Greeks for a generic class of American derivative models using…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices…
A volatility surface is an important tool for pricing and hedging derivatives. The surface shows the volatility that is implied by the market price of an option on an asset as a function of the option's strike price and maturity. Often,…
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its…
We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage…
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…
The significance of wettability between solid and liquid substances in different fields encourages scientists to develop accurate models to estimate the resultant apparent contact angles. Surface free energy (SFE), which is principally…
In this paper, we revisit the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab, for which the first complete proof was given…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
In financial terms, an implied volatility surface can be described by its term structure, its skewness and its overall volatility level. We use a PCA variational auto-encoder model to perfectly represent these descriptors into a latent…
This paper is concerned with the global solvability for the Navier-Stokes equations describing viscous free surface flows of infinite depth in three and higher dimensions. We first prove time weighted estimates of solutions to a linearized…
For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is…
Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of…
The null surface formalism of GR in three dimensions is presented, and the gauge freedom thereof, which is not just diffeomorphism, is discussed briefly.
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in all ``sufficiently volatile'' markets. In our formulation,…
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on…
Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the…