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Arbitrage-free conditions for implied volatility surface by Delta

Author

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  • Wang, Ximei
  • Zhao, Yanlong
  • Bao, Ying

Abstract

Implied volatility surface provided by Deltas and maturities (IVS-DM) is widely used in financial fields, especially in foreign exchange options market, since it can effectively describe the characteristics of the volatilities. The main purpose of this paper is to develop arbitrage-free conditions for the IVS-DM. We propose sufficient conditions for the IVS-DM to be static arbitrage-free, which are proved to be necessary under a mild assumption. To test the arbitrage opportunities in the market data, we build a practical tool, which is more accurate than existing ones such as early warning indicator tests. For illustration, arbitrage tests are conducted on a simulated IVS-DM to show the effectiveness of the conditions. The results are consistent with the tests for the implied volatility surface provided by strikes and maturities. Furthermore, empirical examinations are implemented on EURUSD and USDJPY currency options to ensure the feasibility of the proposed conditions.

Suggested Citation

  • Wang, Ximei & Zhao, Yanlong & Bao, Ying, 2019. "Arbitrage-free conditions for implied volatility surface by Delta," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 819-834.
    • Handle: RePEc:eee:ecofin:v:48:y:2019:i:c:p:819-834
    DOI: 10.1016/j.najef.2018.08.011
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    References listed on IDEAS

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    More about this item

    Keywords

    Implied volatility surface; Foreign exchange market; Arbitrage-free condition; Deltas;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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