I want to build a bivariate risk-neutral distribution from two liquid assets (A and B) through the use of a copula. As A and B are liquid, I have the marginal distributions from the market. All I have to do is to build a copula in order to relate both assets. I want to do this with a non-parametric copula estimation method.
For this purpose I am willing to use the method given in this paper (1), which requires the time series (from A and B) as input. But there is an issue: the real world time series from A and B are under the real-world measure, while I want to estimate the bivariate distribution under the risk-neutral measure, thus I cannot use the real world time series from A and B as input. Would you have any idea on how to tackle this problem.
(1): Estimating copula densities through wavelets. Genest, C., Masiello, E., Tribouley, K. Elsevier, pp. 170-181, 2009.