Deriving Euribor 3M from Hull–White Discount Bonds

Summary

The document explains how a simulated short rate in the Hull–White model can be used to obtain Euribor 3M for projecting derivative cash flows. In the stated Euribor discounting framework, the forward rate over a three-month accrual period is derived from the ratio of discount bond prices for the period’s start and end dates, adjusted by the accrual fraction.

The proposed workflow is to simulate the short rate, evaluate the model’s analytic discount bond prices at the relevant dates, and substitute those prices into the forward-rate definition. This provides the link between a short-rate model and the three-month index. The response is concise and assumes the specified Euribor discounting framework; it does not discuss calibration, model limitations, or how to handle a multi-curve setup in which projection and discounting curves differ.

Key ideas

• Euribor 3M can be represented using discount bond prices at the accrual period’s start and end.
• The bond price ratio is converted into a rate by adjusting for the accrual fraction.
• Hull–White analytic bond price formulas connect the simulated short rate to the forward Euribor rate.
• The described construction assumes an Euribor discounting framework and does not address multi-curve projection.

Tags

# Euribor 3M simulation


# Euribor 3M simulation












I am required to simulate the trajectory of the Euribor3M rate as it is crucial for determining the future cash flows of my derivative instrument. I've received guidance to employ the Hull-White model. How can I transition from the short rate to Euribor? Is it accomplished through the forward zero-coupon bond?

I am following Brigo-Mercurio, but I don't understand what is the correct way to get it, so I really need advice so any help is appreciated.

## Answer by siou0107 (score 2)

https://quant.stackexchange.com/a/78074

If you are within a EURIBOR 3M discounting framework, just use the definition of EURIBOR 3M in terms of discount factors.

$$ L\left(t, T, T + \text{3M}\right) = \frac{1}{\delta\left(T, T + \text{3M}\right)} \left[\frac{P\left(t, T\right)}{P\left(t, T + \text{3M}\right)} - 1\right] $$

And use the analytic formulas available in the Hull-White model for discount bonds $P \left(t, \cdot\right)$ as a function of your (simulated) short rate $r_t$.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.