Choosing Discount-Factor Interpolation for Curve Risk and Hedging

Summary

This discussion asks how to interpolate discount factors between quoted dates and extrapolate beyond the last available point. The response warns that naive smooth interpolation can create implausible rates between curve nodes, and recommends choosing a method based on how the curve will be used.

For interest-rate risk measurement and hedge construction, it recommends flat-forward interpolation between nodes and extending the final observable forward beyond the last node. The rationale is that the objective is to manage interest-rate exposure, so small curve inaccuracies may be less consequential when the portfolio is intended to be flat to that risk. This is a brief, use-case-specific recommendation rather than a general comparison of spline and forward methods. It does not specify implementation details, discuss alternative applications such as pricing, or quantify interpolation errors.

Key ideas

• Interpolation choices should reflect how the discount curve will be used.
• Naive smooth interpolation can imply unrealistic rates between curve nodes.
• For risk calculations and hedging, the response recommends flat-forward interpolation.
• It suggests extending the last observable forward beyond the final node.
• The recommendation does not assess every curve use case or quantify its errors.

Tags

# Interpolation and extrapolation of Discount factors


# Interpolation and extrapolation of Discount factors












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.

## Answer by Dimitri Vulis (score 4)

https://quant.stackexchange.com/a/69925

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.

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