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Composite option pricing and the volatility surface construction

Author

Listed:
  • Kopaliani, R.

    (Bank Saint Petersburg, Saint Petersburg, Russia)

  • Denisov, N.

    (Bank Saint Petersburg, Saint Petersburg, Russia)

Abstract

This paper proposes a methodology for constructing a cross-asset volatility surface. This volatility surface makes it possible to evaluate the price and risk metrics of options for assets, which do not have a liquid options market and can be created through the composition of two liquid assets. A version of the derivation of an analytical formula for estimating the value of a European option on a cross-asset and expressions for calculating risk measures ("Greeks") are proposed. The key parameters for constructing a cross-asset surface are the correlation between the components of the cross-asset and the implied volatilities of the components of the cross-asset. Different approaches are presented for estimating the correlation coefficient: using historical correlation, dynamic conditional correlation model, and implied correlation. It is demonstrated that if the volatility "at the money" of a cross-asset is known, then the implied correlation is calculated explicitly, otherwise historical correlation or the DCC-GARCH (1,1) model can be used. It is shown that by fixing the implied volatility "at the money" of a less risky asset and varying the implied volatility of a riskier asset, the cross-asset volatility surface is obtained that is closest to the observed one. The article presents strict theoretical calculations and makes it possible to evaluate composite options price in practice.

Suggested Citation

  • Kopaliani, R. & Denisov, N., 2023. "Composite option pricing and the volatility surface construction," Journal of the New Economic Association, New Economic Association, vol. 60(3), pages 27-48.
    • Handle: RePEc:nea:journl:y:2023:i:60:p:27-48
    DOI: 10.31737/22212264_2023_3_27-48
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    cross-asset; exotic option; GARCH; implied volatility; option pricing; implied correlation;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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