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