Modeling EURIBOR-Linked Products with €STR Discounting

Summary

The document asks how to price structured products that depend on three-month EURIBOR, including constant-maturity swap spreads, range accruals, and target redemption notes, when discounting uses €STR. It proposes modeling the €STR short rate with a multi-factor Hull–White framework, then representing EURIBOR as that rate plus a deterministic spread. Forward EURIBOR rates would be derived from hypothetical forward zero-coupon bonds built from the modeled rate.

The proposal is presented as a question, not as a validated pricing method. The author recognizes that a more complete approach may require jointly modeling discount and forwarding rates and their correlations, and asks whether a deterministic spread is adequate. No calibration, product valuation, market comparison, or answer is supplied, so the document identifies a modeling challenge and a simplified candidate framework without establishing its accuracy. The key limitation is that the spread’s deterministic assumption may not capture stochastic basis behavior relevant to these products.

Key ideas

• The products discussed reference three-month EURIBOR while discounting is performed using €STR.
• A candidate framework models the €STR short rate with a multi-factor Hull–White process.
• The proposed simplification represents EURIBOR as the modeled €STR rate plus a deterministic spread.
• Forward rates are constructed from hypothetical forward zero-coupon bonds rather than discount bonds.
• The document leaves open whether a deterministic basis spread is adequate and gives no validation or pricing results.

Tags

# EURIBOR dependent product pricing


# EURIBOR dependent product pricing












3M Euribor rates still exists (see https://www.ice.com/) and there still exist structured products depending on them : for instance a CMS spread whose udnerlying CMS rates depend on it. But also range accruals, TARNs etc.

My question is simple : which simple model to use today to price such products ?

I tried to think a bit :

- all discounts are done using ESTR so the model will have to diffuse the ESTR rate, probably in a short rate model way

- the model will have to either A) diffuse the forward 3M Euribor rates B) diffuse a short rate associated to theoretical zero-coupons (not discount zero-coupons) allowing to calculate the forward rates

- As 2.A is too much complicated for me I stick to 2.B : there should be correlations between the factors from the diffusion in 1 and the factors of the diffusion in 2.B : this is also to complicated : can I supposed a deterministic spread ?

Consider something like the following "model" :

$$r^{\textrm{ESTR}}_t = f_{0,t} + x_t$$

where $x_t$ is diffused such that $r^{\textrm{ESTR}}_t$ is a 2 or 3 factors Hull-White model and such that the discount zero-coupons are $P^{\textrm{disc}}_{0,T} = e^{-\int_0^T r^{\textrm{ESTR}}_s ds}$, and

$$r^{\textrm{EURIBOR}}_t = s(t) + r^{\textrm{ESTR}}_t$$

where $s(t)$ is a deterministic function, such that if one defines theoretical forward zero-coupon $P^{\textrm{fwd}}_{t,T} := e^{-\int_t^T r^{\textrm{EURIBOR}}_s ds}$ then the EURIBOR forward rates are $\frac{P^{\textrm{fwd}}_{t,T} - P^{\textrm{fwd}}_{t,T+3M}}{\delta P^{\textrm{fwd}}_{t,T}}$.

Would that be a reasonable model to price such products ? If not, what would some "similar" but reasonable ?

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