Choosing and Calibrating a Copula for Quanto Option Pricing

Summary

The document outlines a proposed workflow for pricing a quanto option: estimate marginal distributions for the underlying asset and exchange rate, connect them with a copula, then calculate the expected payoff under the resulting joint distribution. Its main question is how to select and calibrate that dependence model. One suggested direction is to fit a bivariate Heston model to historical data and then use a nonparametric time-series copula estimation method.

The material frames this as an open modeling choice rather than presenting a recommended copula, calibration result, or option valuation. It recognizes that there is no universally correct family and mentions correlation and Kendall’s tau as possible calibration objectives for an Archimedean copula. However, it gives no comparison of candidate families, empirical evidence, parameter estimates, or treatment of market-implied versus historical dependence. Any implementation would need to assess whether the data and dependence assumptions are appropriate for the option’s pricing horizon.

Key ideas

• Quanto pricing requires modeling the joint behavior of the asset and exchange rate.
• A copula can link separately estimated marginal distributions into a bivariate distribution.
• The proposed workflow considers a bivariate Heston model and nonparametric copula estimation.
• Copula family selection and calibration remain unresolved modeling choices in the document.

Tags

# Suggestions to build a copula to price Quanto options


# Suggestions to build a copula to price Quanto options












I am willing to price a quanto option through the use of copulas. I will follow the following procedure:

1) Obtain the marginal distributions of the underlying asset and the exchange rate from market data.

2) Link both distributions through a copula.

3) Compute the quanto option price through definition (expected value of the payoff over the bi-dimensional distribution obtained from steps 1 and 2).

Steps 1 and 3 are simple. My question is about step 2:

which copula family should I choose? How should I calibrate it? I know there is no right answer for these questions, but I would like to have your opinion on a suitable way to do this task (e.g. calibrate a archimedian copula using correlation and kendals’s tau as calibration objective, ...).

My first idea is: 2.1) use a bivariate Heston model to be calibrated with historical data from the underlying asset and exchange rate 2.2) use the non-parametric copula calibration method proposed in this (1) paper

(1): NONPARAMETRIC ESTIMATION OF COPULAS FOR TIME SERIES, Jean-David FERMANIAN and, Olivier SCAILLET

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.