Some Questions

[alecloudenback]

If some of the questions seem ill-informed please let me know. I'm exploring the territory as I experiment with EconomicScenarioGenerators.jl (specifically, working on integrating Copulas.jl in JuliaActuary/EconomicScenarioGenerators.jl#39

• when sampling from the copulas with rand do all the copulas return a value in [0,1] representing the cumulative probability to that point?
• Do you know of more convenient ways to construct a symmetric covariance matrix than to use the whole thing?

[lrnv]

Hey !

1° A random vector U_1,...,U_d following a copula has uniform margins by definition, which means that \mathbb P(U_i < u_i) = u_i for all u \in [0,1], i \in 1,...,d. Therefore yes, sampling directly from the copula gives values which, marginally, are also cumulative probabilities. But for the multivariate random vector, a sampled value is a point in R^d while a probability is a univariate quantity. I am not sure if this is clear enough..

However, to sample from a random vector with a given dependence structure, If you want to be sure you are doing it correctly, use the SklarDist type. In your case, if your question is about https://github.com/JuliaActuary/EconomicScenarioGenerators.jl/blob/e37c67a5ac1c34ea421f986383af4b386a5010f3/src/EconomicScenarioGenerators.jl#L145-L149 , then I think you did it right.

2° No i'm sorry, Maybe ask discourse you'll have more chance on this one.

3° Integrating copulas into an ESG is actually a very good Idea, I took a look at your package, and it seems very good ! However, If I may, maybe you could draw an example with a non-Gaussian dependence structure ? Perhaps a Clayton to have one extremal dependency (you may have to make it Survival if your random variables need to have the dependency in the other corner).