We are sourcing the discount factors for various currencies. What is the best interpolation method for dates between and out of the dates provided in the factors? Shall I go for flat forward or cubic spline? Please suggest if any other is better.
Be careful with various naive smooth interpolations of discount factors that are easy to screw up and may lead to unrealistic rates between the nodes.
But your choice depends on your planed usage.
If it's intended to calculate risk, and then hedges based on these risk calculations, then: definitely flat forwards to interpolate between nodes. Use the last observable forward to extrapolate past the last node. Whatever inaccuracies you introduce may not matter much because you intend to be flat IR risk.