Estimating a Risk-Neutral Copula from Real-World Asset Data

Summary

The document presents a modeling question about combining two liquid assets’ market-implied marginal distributions into a bivariate risk-neutral distribution. The proposed component is a non-parametric copula, with wavelet-based copula density estimation cited as a possible method. The challenge is that the cited method takes historical time series as input, and those observations reflect the real-world probability measure rather than the risk-neutral measure sought for pricing.

The text identifies this measure mismatch but does not provide a solution, empirical evidence, or an implementation procedure. It is therefore useful as a statement of a modeling problem rather than a complete method. Any approach would need to justify how dependence information is inferred or transformed under the risk-neutral measure; historical dependence cannot simply be assumed to match market-implied dependence.

Key ideas

• Market-implied marginal distributions for two assets do not alone specify their joint risk-neutral distribution.
• A copula can be used to represent dependence between the marginals.
• The referenced non-parametric wavelet method uses historical asset time series as input.
• Historical observations are under the real-world measure, creating a mismatch for risk-neutral estimation.
• The document raises this issue but does not offer a solution or supporting empirical results.

Tags

# Bivariate risk neutral distribution through copula


# Bivariate risk neutral distribution through copula












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.

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