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## Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models

Mijatović, Aleksandar; Urusov, Mikhail
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.; Comment: 20 pages; most results in this paper were contained in the first version of submission 0905.3701; to appear in Finance & Stochastics

## Asymptotic arbitrage and num\'eraire portfolios in large financial markets

Rokhlin, Dmitry B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of the sequence of the num\'eraire portfolios, related to the small markets. The obtained criteria can be expressed in terms of contiguity, entire separation and Hellinger integrals, provided these notions are extended to sub-probability measures. As examples we consider market models on finite probability spaces, semimartingale and diffusion models. Also a discrete-time infinite horizon market model with one log-normal stock is examined.; Comment: 18 pages

## Generalised arbitrage-free SVI volatility surfaces

Guo, Gaoyue; Jacquier, Antoine; Martini, Claude; Neufcourt, Leo
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.14%
In this article we propose a generalisation of the recent work of Gatheral and Jacquier on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper. We further exhibit an arbitrage-free volatility surface different from Gatheral's SVI parameterisation.; Comment: 20 pages, 4 figures. Section 2 more precise. Added a section on non-smooth implied volatilities

## Arbitrage Opportunities in Misspecified Stochastic volatility Models

Jena, Rudra P.; Tankov, Peter
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.14%
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics is a classical Black-Scholes one, we give a new interpretation of the classical butterfly and risk reversal contracts in terms of their (near) optimality for arbitrage strategies. Our results are illustrated by a numerical example including transaction costs.; Comment: Several typos in section 5 have been corrected in this new version (with thanks to Amy Y. Zhou from MIT)

## Derivative pricing with virtual arbitrage

Ilinski, Kirill; Stepanenko, Alexander
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast market reaction, reduces to the Black-Scholes equation. Explicit formulas are obtained for European call and put vanilla options.; Comment: Latex, 10 pages

## A note on arbitrage, approximate arbitrage and the fundamental theorem of asset pricing

Fontana, Claudio
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
We provide a critical analysis of the proof of the fundamental theorem of asset pricing given in the paper "Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing" by B. Wong and C.C. Heyde (Stochastics, 2010) in the context of incomplete It\^o-process models. We show that their approach can only work in the known case of a complete financial market model and give an explicit counterexample.; Comment: 10 pages

## Credit Risk in a Geometric Arbitrage Perspective

Farinelli, Simone
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.14%
Geometric Arbitrage Theory, where a generic market is modelled with a principal fibre bundle and arbitrage corresponds to its curvature, is applied to credit markets to model default risk and recovery, leading to closed form no arbitrage characterizations for corporate bonds.; Comment: arXiv admin note: substantial text overlap with arXiv:0910.1671

## Static versus Dynamic Arbitrage Bounds on Multivariate Option Prices

d'Aspremont, Alexandre
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
We compare static arbitrage price bounds on basket calls, i.e. bounds that only involve buy-and-hold trading strategies, with the price range obtained within a multi-variate generalization of the Black-Scholes model. While there is no gap between these two sets of prices in the univariate case, we observe here that contrary to our intuition about model risk for at-the-money calls, there is a somewhat large gap between model prices and static arbitrage prices, hence a similarly large set of prices on which a multivariate Black-Scholes model cannot be calibrated but where no conclusion can be drawn on the presence or not of a static arbitrage opportunity.; Comment: Submitted to IMA series

## Non-Arbitrage up to Random Horizon for Semimartingale Models

Aksamit, Anna; Choulli, Tahir; Deng, Jun; Jeanblanc, Monique
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.14%
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the literature as the first kind of non-arbitrage. For this non-arbitrage notion, we obtain two principal results. The first result lies in describing the pairs of market model and random time for which the resulting stopped model fulfills NUPBR condition. The second main result characterises the random time models that preserve the NUPBR property after stopping for any market model. These results are elaborated in a very general market model, and we also pay attention to some particular and practical models. The analysis that drives these results is based on new stochastic developments in semimartingale theory with progressive enlargement. Furthermore, we construct explicit martingale densities (deflators) for some classes of local martingales when stopped at random time.; Comment: 40 pages. This version develops in details the ideas and the results of the previous version and fixes a glitch in the quasi-left-continuous case

## No-arbitrage conditions and absolutely continuous changes of measure

Fontana, Claudio
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.14%
We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of general semimartingale models, we show that an absolutely continuous change of measure does never introduce arbitrages of the first kind as long as the change of measure density process can reach zero only continuously.; Comment: 14 pages. Arbitrage, Credit and Informational Risks (C. Hillairet, M. Jeanblanc and Y. Jiao, eds.), Peking University Series in Mathematics, Vol. 6, World Scientific, 2014

## Arbitrage-free prediction of the implied volatility smile

Dellaportas, Petros; Mijatović, Aleksandar
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
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 time series of option prices corresponding to $n$ strikes (with $n$ large, e.g. $n\geq 40$) and the same maturity, is a difficult task due to the fact that option prices at any moment in time satisfy non-linear and non-explicit no-arbitrage restrictions. Hence any $n$-dimensional time series model also has to satisfy these implicit restrictions at each time step, a condition that is impossible to meet since the model innovations can take arbitrary values. We solve this problem for any $n\in\NN$ in the context of Foreign Exchange (FX) by first encoding the option prices at each time step in terms of the parameters of the corresponding risk-neutral measure and then performing the time series analysis in the parameter space. The option price predictions are obtained from the predicted risk-neutral measure by effectively integrating it against the corresponding option payoffs. The non-linear transformation between option prices and the risk-neutral parameters applied here is \textit{not} arbitrary: it is the standard mapping used by market makers in the FX option markets (the SABR parameterisation) and is given explicitly in closed form. Our method is not restricted to the FX asset class nor does it depend on the type of parameterisation used. Statistical analysis of FX market data illustrates that our arbitrage-free predictions outperform the naive random walk forecasts...

## Periodic Sequences of Arbitrage: A Tale of Four Currencies

Cross, Rod; Kozyakin, Victor; O'Callaghan, Brian; Pokrovskii, Alexei; Pokrovskiy, Alexey
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.14%
This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we find that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a "balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.; Comment: 35 pages, 48 bibliography references, submitted to Metroeconomica

## An Hilbert space approach for a class of arbitrage free implied volatilities models

Brace, A.; Fabbri, G.; Goldys, B.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.14%
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 $T$ an $K$, to be arbitrage free. The arbitrage free conditions give a system of stochastic PDEs for the evolution of the implied volatility surface ${\hat\sigma}_t(T,K)$. We will focus on the family obtained fixing a strike $K$ and varying $T$. In order to give conditions to prove an existence-and-uniqueness result for the solution of the system it is here expressed in terms of the square root of the forward implied volatility and rewritten in an Hilbert space setting. The existence and the uniqueness for the (arbitrage free) evolution of the forward implied volatility, and then of the the implied volatility, among a class of models, are proved. Specific examples are also given.; Comment: 21 pages

## Black-Scholes equation from Gauge Theory of Arbitrage

Ilinski, Kirill; Kalinin, Gleb