Related papers: Generalised 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…
The article describes a global and arbitrage-free parametrization of the eSSVI surfaces introduced by Hendriks and Martini in 2019. A robust calibration of such surfaces has already been proposed by the quantitative research team at Zeliade…
We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied…
The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We…
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…
We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently…
Following-up Fukasawa and Gatheral (Frontiers of Mathematical Finance, 2022), we prove that the BBF formula, the SABR formula, and the rough SABR formula provide asymptotically arbitrage-free approximations of the implied volatility under,…
We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characterization of the necessary condition for no arbitrage…
We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the…
In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus…
We describe a robust calibration algorithm of a set of SSVI slices (i.e. a set of 3 SSVI parameters $\theta, \rho, \varphi$ attached to each option maturity available on the market), which grants that these slices are free of Butterfly and…
The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful…
This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional…
We propose a two-step framework for predicting the implied volatility surface over time without static arbitrage. In the first step, we select features to represent the surface and predict them over time. In the second step, we use the…
In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such…
We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original…
We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as…
We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price…
The purpose of this work is to explore the role that random 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…
We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that when the underlying stock price martingale admits finite log-moments E[|log(S)|^q] for some positive q, the arbitrage-free growth in the left…