muRisQ-ir-models by Marc Henrard

muRisQ Advisory open source code for Interest Rate Models.

muRisQ stands for Management of Risk by Quantitative methods. The term risk management has to be understood in a large sense which includes risk strategies, ALM, quantitative impacts of regulation, and trading strategies.

You can find more details about our consulting and advisory services on our website muRisQ Advisory - Email:

muRisQ Advisory is managed by Marc Henrard. You can find more about his contribution to quantitative finance through his papers and his blog:

Repository content

This repository proposes code for pricing and risk management of interest rate derivatives.

The models implemented are based on proprietary research and academic literature as described in each implementation.

Comments and suggestions for improvements are welcome.


Some code proposed in this repository is based on OpenGamma Strata (version 2.6.0) library:


1. Compounded overnight futures

Description of the futures.

2. OIS futures

Description of an innovative futures design.


3. LIBOR Fallback analysis

LIBOR fallback options analysis. Value transfer, convexity adjustments and risk management. Compounding setting in arrears fixing computation.


4. CMS spread periods

Description of CMS spread fields and payoff. CMS spread coupons, caplets and floorlets. Generalized payoff: w1 * rate1 - w2 * rate2


1. Overnight-Overnight conventions and nodes

Swap conventions to deal with EFFR-SOFR and EONIA-ESTER transition. Associated template and nodes to calibrate curves.

2. Multiply curve

Curve description as the multiplication of two underlying curves. Used for intra-month seasonal adjustment in overnight-curves.

3. Collateral cheapest-to-deliver

Curve construction with intrinsic value of the cheapest-to-deliver. Option time value is not incorporated in this implementation. The construction provided the curve itself and the Jacobian to the underlying curves.

4. Cash flow equivalent

Extend the Strata calculator to cover overnight compounded in arrears payments.


1. Bachelier Formula


Explicit formula for implicit volatility.


2. Hull-White one-factor

3. G2++


4. Swaption with 2 collateral

Pricing of swaps and swaptions when two collateral rates are used: one for the swaption itself up to a given date before expiry and one other from that date on, including for the delivered swap. Swaption pricing with shifted SABR for physical delivery and par yield cash settlement.

5. LIBOR/Forward Market Model


LIBOR or Forward Market Model (also called BGM - Brace/Gatarek/Musiela) with displaced diffusion and deterministic LIBOR/OIS spread. The model dynamic is on the forward associated to pseudo-discount factors in a multi-curve and collateral discounting approach. Multi-factor model.



5. Rational Multi-curve Model


The model describes the evolution of the discount curve and the Libor process in an explicit way. The quantities are not presented through a SDE but directly as explicit quantities depending on simple random variables. This leads to explicit dynamic and in general (almost) explicit formulas for simple instruments and very easy Monte Carlo simulations.



Professional services

The models proposed here are only a small part of the code we have developed or have access to for research and advisory services purposes. Don’t hesitate to contact us if you are interested by other models, require advisory services or are looking for a training around similar models.

Trainings and workshops

We propose in-house training and workshops on subjects related to quantitative finance and risk management.

We offer extensive flexibility on the training organization.

A in-house tailor-made course with our experts presented to your full team often costs less than sending two people to a standard course organized by a large training firm.

Agenda tailored to your needs. Detailed lecture notes. Associated to open source code for practical implementation. Training in English or in French

Some of the popular courses are (course description and typical agendas available through the links):

Some recent public courses:


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