The Volatility Surface Arbitrage
         in Stress Testing Framework:
         Review and Current Practice

                  Suren Islyaev[0000−0002−6004−9995]

                       Riskcare, United Kingdom,
                       suren.islyaev@gmail.com



Abstract. This article reviews existing problems in the modelling of a
volatility surface. The review is the combination of theoretical and prac-
tical knowledge used in practice. Theoretical part discuss the evolution
of the volatility surface modelling approaches. We review different types
of volatility surfaces such as constant, local and stochastic volatility. We
give a brief overlook at existing models, their benefits and disadvantages.
We pinpoint the definition of volatility surface arbitrage and the condi-
tions that have to be satisfied in order to eliminate arbitrage. We study
different approaches to a volatility surface parametrisation and possible
risks arise with the parametrisation. Secondly, we discuss the impacts of
volatility surface models on the current market risk capital framework
(FRTB). The FRTB framework defines risk capital regulations and the
way how banks have to attribute their profits. The profit account attri-
bution requires them to produce stresses to the market data. We discuss
the volatility surface stresses, stress market data model validation and
the risks linked to this exercise.

Keywords: volatility modelling, volatility surface, stress market data
model validation