Quanto Implied Volatility Smile

21 Pages Posted: 31 Jan 2014

See all articles by Alessandro Cesarini

Alessandro Cesarini

Banca Aletti - Gruppo Banco Popolare

Stefano Giovannitti

UniCredit S.p.A.

Date Written: January 30, 2014

Abstract

We propose a numerical procedure, addressed as copula integration method, to calculate quanto implied volatility adjustments. The method consists in a direct integration of the quanto vanilla payoff, using the bivariate terminal probability distribution of the asset and the relevant foreign exchange rate. The bivariate terminal distribution is obtained by coupling the marginal distributions of the two underlyings by means of a Gaussian copula. The asset and the foreign exchange rate marginal distributions are directly inferred from the corresponding Black-Scholes market volatility smiles. In order to obtain well defined marginal distributions, we propose an extrapolation method for the standard implied volatility outside the quoted region, which does not allow arbitrage opportunities. The validity of the copula integration method is established by comparing its predictions to exact results for quanto option prices, obtained by numerical computations in two realistic test cases, in which the dynamics of the assets is driven by a local volatility and a Heston stochastic volatility model.

Keywords: quanto options, quanto implied volatility adjustment, quanto effect, market implied probability distribution, implied volatility extrapolation, Gaussian copula

JEL Classification: G12, G13

Suggested Citation

Cesarini, Alessandro and Giovannitti, Stefano, Quanto Implied Volatility Smile (January 30, 2014). Available at SSRN: https://ssrn.com/abstract=2388093 or http://dx.doi.org/10.2139/ssrn.2388093

Alessandro Cesarini (Contact Author)

Banca Aletti - Gruppo Banco Popolare ( email )

Via Roncaglia, 12
Milan, 20146
Italy

Stefano Giovannitti

UniCredit S.p.A. ( email )

Piazza Gae Aulenti 3
Milan, 20154
Italy

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