Composite option pricing and the volatility surface construction

R. Kopaliani and N. Denisov
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R. Kopaliani: Bank Saint Petersburg, Saint Petersburg, Russia
N. Denisov: Bank Saint Petersburg, Saint Petersburg, Russia

Journal of the New Economic Association, 2023, vol. 60, issue 3, 27-48

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.

Keywords: cross-asset; exotic option; GARCH; implied volatility; option pricing; implied correlation (search for similar items in EconPapers)
JEL-codes: C00 G12 G13 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:nea:journl:y:2023:i:60:p:27-48

DOI: 10.31737/22212264_2023_3_27-48

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