# De-Arbitraging with a Weak Smile: Application to Skew Risk

@article{MahdaviDamghani2013DeArbitragingWA, title={De-Arbitraging with a Weak Smile: Application to Skew Risk}, author={Babak Mahdavi-Damghani and Andrew Kos}, journal={ERN: Volatility (Topic)}, year={2013} }

The aim of this article is to address the methodology behind de-arbitraging a realistic volatility surface and stressing it without adding arbitrages. We derive from basic principles the constraints which the changes on the strike and the tenor axis must satisfy in order to make a volatility surface arbitrage-free. The two most influential parameterized versions of the volatility surface will then be discussed, along with their origin and their limitations. Furthermore, this review will address…

## 29 Citations

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## References

SHOWING 1-10 OF 20 REFERENCES

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

- Economics
- 1993

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and…

Pricing with a Smile

- Economics
- 1994

prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the…

A technique for calibrating derivative security pricing models: numerical solution of an inverse problem

- Mathematics, Economics
- 1997

A technique is presented for calibrating derivative security pricing models with respect to observed market prices. This technique can be applied in a very general multifactor setting where model…

The Misleading Value of Measured Correlation

- Psychology
- 2012

Within the framework of the financial industry, when representing relationships between assets, correlation is typically used. However, academics have long since questioned this method due to the…

The Volatility Surface: A Practitioner's Guide

- Economics
- 2006

List of Figures. List of Tables. Foreword. Preface. Acknowledgments. Chapter 1: Stochastic Volatility and Local Volatility. Stochastic Volatility. Derivation of the Valuation Equation, Local…

A market model for stochastic implied volatility

- Economics
- 1999

The model is able to capture the stochastic movements of a full term structure of implied volatilities and the conditions are derived that have to be satisfied to ensure absence of arbitrage in the model and its numerical implementation is discussed.

On Black‐Scholes Implied Volatility at Extreme Strikes

- Economics
- 2012

We survey recent results on the behavior of the Black-Scholes implied volatility at extreme strikes. There are simple and universal formulae that give quantitative links between tail behavior and…

Convergence of Heston to SVI

- Mathematics
- 2010

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…

On the theory of brownian motion

- Mathematics, Physics
- 1973

The spectrum of the Fokker-Planck operator for weakly coupled gases is considered. The operator is decomposed into operators acting on functions whose angular dependence is given by spherical…

THE IMPLIED VOLATILITY SURFACE DOES NOT MOVE BY PARALLEL SHIFTS

- Economics
- 2006

This note explores the analogy between the dynamics of the interest rate term structure and the implied volatility surface of a stock. In particular, we prove an impossibility theorem conjectured by…