MVA Using Algorithmic Differentiation

At the end of 2018, the financial industry has still not yet established a consensus methodology for calculation of Margin Value Adjustment (MVA) on non- centrally cleared derivatives. MVA represents the expected funding cost of initial margin over the lifetime of a trade/portfolio, and is particularly relevant today due to BCBS-IOSCO 261 – more commonly referred to as the “Swaps Margin Rules”, it requires financial entities to exchange sufficient collateral to cover potential losses over a 10-day period with 99% confidence, and is complementary to the margin typically used to settle daily mark-to-market changes (variation margin), phasing-in to cover most derivatives market participants by September 2020. MVA is the most recent valuation adjustment (“xVA”), joining similar calculations for counterparty credit risk (CVA), the funding cost of variation margin (FVA), and the cost of capital (KVA), among others. MVA is particularly difficult to calculate due to the requirements for trade sensitivities along each Monte Carlo simulation path as inputs to ISDA’s Standard Initial Margin Model (SIMM). AD provides the most efficient and robust calculation of these in-simulation sensitivities.

Download the Whitepaper

Open Source Risk User Meeting 2018

Quaternion sponsors an Open Source Risk User Meeting in Frankfurt on Friday 23rd November 2018 at Fleming’s Hotel, Frankfurt City, Eschenheimer Tor 2.

“The Open Source Risk Project’s objective is to provide a free/open source platform for risk analytics and XVA. ORE is based on QuantLib and grew from work developed by market professionals and academics.” (

With this first meeting we want to provide a communication platform for the ORE users in the industry and ORE’s developers, contributors and creators, to help propagating ORE’s usage and its further development.

The agenda will cover short presentations of use cases and leave sufficient room for discussing the future of ORE’s usage.

Attending the conference will be free of charge, but the number of seats is limited. If you want to join, please register on the bottom of the agenda.

The following is an indicative agenda. If you would like to share your experience with ORE, please let us know with your registration. We would be happy to rearrange the agenda.

Agenda / Speakers

08:15-09:00 Registration
09:00-09:15 Welcome Roland Lichters (Quaternion)
09:15-09:45 XVA-Valuation Project with ORE Roland Kapl (OeBFA – Österreichische Bundesfinanzierungsagentur)
09:45-10:15 Understanding the Impact of Regulation on Systemic Risk with ORE Nikolai Nowaczyk (Quaternion)
10:15-10:45 ORE in Pricing of Bermudan Swaptions: Client Experience from Model Validation Dmitry Zaykovskiy (Deutsche Pfandbriefbank AG)
10:45-11:15 Tea/Coffee
11:15-11:45 XVA Model Validation Patrick Büchel (Commerzbank)
11:45-12:15 Structured Loan Pricing and Embedded Prepayment Options in Project Financing High Yield Markets Oleg Kulkov (Allianz Global Investors)
12:15-12:45 Alternative Use Case for ORE: An Interactive Application for Financial Planning and Controlling Andreas Kewenig (Aareal Bank AG)
13:00-14:00 Lunch
14:00-14:30 Sensitivity Analysis, ISDA SIMM Benchmarking and Backtesting with RESTORE Niall O’Sullivan (Quaternion)
14:30-15:00 ORE in Python and Java Roland Lichters (Quaternion)
15:00-15:30 A precursor to ORE in Excel: Calculating the VaR using Deriscope and QuantLib Ioannis Rigopoulos (Deriscope)
15:30-16:00 Tea/Coffee
16:00-17:00 Discussion All
17:00-17:15 Wrap up Roland Lichters (Quaternion)
17:15-19:00 Reception


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AcadiaSoft and Quaternion Form Risk Services Partnership

Norwell, MA, and Dublin, Ireland August [2], 2018 – AcadiaSoft Inc., the leading industry provider of margin automation solutions worldwide, and Quaternion Risk Management Ltd., a leading risk analytics firm, today announced the formation of a partnership to provide risk services for firms subject to initial margining requirements for non-centrally-cleared derivatives. The initiative couples AcadiaSoft’s proven capabilities in automation with Quaternion’s extensive quantitative expertise and will enable AcadiaSoft clients to access a range of services via the secure environment of the AcadiaSoft Hub.

“Combining AcadiaSoft’s existing infrastructure with our risk analytics tools presents opportunities to create new products that will greatly benefit both the smaller players in the non-centrally-cleared market facing near-term hurdles, as well as larger, established institutions looking to reduce spend on functions that have become ‘business-as-usual’ and could now be more efficiently outsourced and standardized,” said Donal Gallagher, chief executive officer at Quaternion.

Initially, the partnership will focus on helping firms with non-centrally cleared derivatives portfolios meet the operational and regulatory challenges associated with margin requirements. On September 1, 2016, the largest banks that trade non-centrally cleared derivatives were required to post and collect initial margin (IM) due to a new margin framework established by the Basel Committee on Banking Supervision (BCBS) and the International Organization of Securities Commissions (IOSCO), and each year since, and through 2020, those requirements touch a growing set of sell-side and buy-side firms.

“We expect to be able to significantly cut the burden placed on market participants by the non-cleared margin rules and make achieving compliance a straightforward process – even for relatively small firms,” said Fred Dassori, head of Risk Services and corporate development at AcadiaSoft. “After collaborating with the team at Quaternion on a range of projects over the past year, we’re excited to now be formalizing our partnership, and we’re looking forward to working together to greatly expand the set of tools we offer and give our clients a simple and efficient path forward.”

By offering these future services through the same platform as AcadiaSoft’s existing Initial Margin Exposure Manager and MarginManager products, which sit at the heart of the current IM calculation, reconciliation, and collateral messaging processes, AcadiaSoft and Quaternion aim to make their new risk services as seamlessly-integrated into existing industry workflows as possible.


About AcadiaSoft, Inc.

AcadiaSoft, Inc. is a financial industry collaborative that is uniquely focused on delivering margin automation and standards for counterparties engaged in collateral management. AcadiaSoft’s Advisory Groups, Best Practice Forums and Working Groups provide a unique framework for integrating the thought leadership and capabilities of over 650 market participants, market infrastructures and key service providers across the industry.

Owned and backed by the investment of 17 major industry participants and infrastructures, the AcadiaSoft community has grown to more than 650 client firms exchanging approximately $400B (billion) of collateral on daily basis. The Company’s growth has been driven by regulatory change in the derivatives industry that is increasing the demand for automated, transparent and verifiable collateral management.

AcadiaSoft is headquartered outside of Boston in Norwell, MA and has offices in London, Tokyo and New York.

For more information, see

About Quaternion Risk Management

Quaternion Risk Management Limited is a capital markets consulting practice advising on and implementing complex projects with a focus on the quantitative aspects of risk management, trading and finance. Quaternion has worked with some of the world’s leading financial institutions. The firm is headquartered in Dublin, Ireland with offices in London, Dusseldorf and New York. Quaternion partners with Columbia University on systemic risk projects and launched Columbia University’s Fintech Lab in late 2016. is Quaternion’s open source contribution to the risk community.
For more information on Quaternion, see

Press Contacts:

Eleis Brennan
+1 212-754-5610

Laura Craft
+44 20 3954 0196

Neil Ryan
Quaternion Risk Management
+353 1 678 7922

Big Data and Graph Theoretic Models: Simulating the Impact of Collateralization on a Financial System

In this paper we represent a financial system using a weighted directed graph model. We simulate and analyze the impact of financial regulations regarding the collateralization of derivative trades on systemic risk, employing a novel open source risk engine. The analysis finds that introducing collateralization does reduce the costs of resolving a financial system in crisis. It does not, however, change the distribution of risk in the system. The implications of the analysis highlight the importance of scenario based testing using hands on metrics to quantify the notion of system risk.

View Paper

Forecasting Initial Margin Requirements – A Model Evaluation

The introduction of mandatory margining for non-cleared portfolios has major implications for the pricing and risk measurement of OTC derivatives. In particular, a model for estimating future initial margin requirements is necessary to enable the calculation of pricing adjustments (MVA), net counterparty credit exposures and credit capital (RWA). Existing literature on the topic suggests a model which makes use of regression techniques, but little detail is available on the predictive quality of these models within a Monte Carlo simulation framework. We review these regression-based initial margin models in detail and compare their output against the actual margin requirements measured by the ISDA SIMM methodology. We observe that the models generally perform well for single trades but show some degradation for single option products and larger diversified portfolios. We investigate potential extensions and improvements to the model, along with examining some additional “conservatism” features that may have application in the context of credit exposure measurement. The Initial Margin modelling approaches discussed here are similarly applicable to centrally cleared or exchange-traded portfolios.

View Paper

ISDA Whitepaper – The Future of Derivatives Processing and Market Infrastructure

International Swaps and Derivatives Association highlights Open-Source as future of technology infrastructure.

Download the Whitepaper

Daisy Chains and Non-cleared OTC Derivatives

By Donal Gallagher, Roland Lichters, Sharyn O’Halloran, and Roland Stamm

The non-cleared over-the-counter (OTC) derivative market is estimated at $493 trillion notional [1]. One of the central triggers of the 2008 Financial Crisis was financial institutions’ excessive exposure to counterparty risk. These exposures peaked at over $4.5 trillion in 2008 [1]. The response of the global regulatory community to the financial crisis has been to introduce regulations and standards aimed at reducing the amount of counterparty credit risk in the financial system. These initiatives gave rise, for example, to the introduction of mandatory clearing for certain common classes of derivatives (cleared derivatives) and more recently the introduction of similar standards for non-cleared derivatives [2]. The primary means promoted to mitigate risk are mandatory variation margin (collateral against today’s value) and mandatory initial margin (collateral against the change in valuation in the event of default). The total amount of initial margin introduced as a result of these changes is estimated at $315 billion for US banks alone [3]. The regulatory expectation is that most derivatives classes will ultimately be subjected to mandatory clearing; however, the current volume and the slow rate of convergence toward mandatory clearing suggest that large volumes of derivative contracts will continue to be subject to the non-cleared OTC regime for the foreseeable future.

Download the Paper

SPS Spotlight – FinTech and Financial Regulation

Streamed live on 15 Nov 2016

Columbia University School of Professional Studies presents
A Panel Discussion with Professor Sharyn O’Halloran, Thomas Deely, and Guests

A key issue for regulators and the financial service industry is mitigating systemic large-scale counterparty risk. Currently, individual financial institutions and regulators conduct systemic risk exposure analysis using proprietary models and data protocols absent any agreed upon baseline, best practices or public scrutiny. Without industry standards, shared benchmarks, or means to validate results, the impact of alternative policy interventions on the overall risk in the financial system remains uncertain.

This initiative showcases new open source analytical tools that develop highly granular trade and cross-asset class risk simulation and aggregate at the counterparty level. Bringing large-scale open source risk models to the public domain will enable a standard-based approach that facilitates research and greater understanding of the impact that policy levers have on the financial system.

Questions? Please contact:


Quaternion Risk Management
tullett prebon information
Columbia School of Professional Studies
Columbia Business School
Columbia University Data Science Institute
Columbia Law school
Columbia School of International and Public Affairs

Ben McLannahan
US Banking Editor
Financial Times

Emanuel Derman
Director of the MS Program in Financial Engineering
Professor of Professional Practice
Industrial Engineering and Operations Research, Columbia University

Paul Glasserman, PhD
Jack R. Anderson Professor of Business
Decision, Risk, and Operations Research Director
Program for Financial Studies
Columbia Business School

Brian Ruane
CEO of Broker-Dealer Services & Head of Banks
Broker-Dealer and Investment Advisors Market and Alternative Asset Manager Segments
Bank New York Mellon

Mayur Thakur
Managing Director of Compliance Analytics
Goldman Sachs

Sharyn O’Halloran, PhD
George Blumenthal Professor of International and Public Affairs
Chief Academic Officer
Columbia University School of Professional Studies

A Multi Interest Rate Curve Model for Exposure Modelling


  • Andreas Boldin, Credit Suisse AG
  • Roland Lichters, Quaternion Risk Management
  • Andre Suess, Credit Suisse AG
  • Markus Trahe, Credit Suisse AG

November 16, 2016


The tenor basis phenomenon became significant with the 2007 financial crisis and has altered the traditional way of one-curve pricing and risk management to a multi-curve phenomenon. The stochastic nature of basis spreads between curves particularly poses a challenge for forward looking applications like XVA or real world measure exposure analytics. This paper presents a Two- factor Gaussian approach for modelling multiple fixing curves and basis spreads in the risk neutral and spot measure, shows the impact on basis swap exposure, investigates the correlation structure and discusses the pros and cons of interpreting as a spread or multi curve model respectively.

Download the paper here.

Quaternion Risk Management announces the launch of

Quaternion Risk Management announces the launch of – the first end-to-end open source risk application. will provide complex risk analytics for financial institutions through a series of releases.

Continue to follow our journey as, today, we launch our contribution to the development of next generation global risk standards. We welcome your contribution to our framework as its evolves.

Managing the alphabet soup of XVAs

Quaternion recently sponsored a September 14th webinar discussion on the evolution of XVAs. Participants included Scott Sobolewski (Principal Consultant at Quaternion), Yann Coatanlem (MD, Head of Multi-Asset Quantitative Analysis at Citigroup,
Massimo Morini (‎Head of Interest Rate and Credit Models, Banca IMI), and ‎Peter Zeitsch (Solution Architect at Calypso Technology).

The list of valuation adjustments banks must apply when pricing a derivative has grown exponentially and given rise to an alphabet soup of new valuation adjustments. The term XVAs has been coined to describe the entire family, namely funding valuation adjustment (FVA), capital valuation adjustment (KVA), and now, margin valuation adjustment (MVA). The sheer volume of these adjustments coupled with the impact on profitability has led banks to compute the capital required to support them through the life of the trade. This has considerably increased the computational complexity as well as placed demands for real time calculation of all of this information. Needless to say, dealers attempting to manage their XVAs are finding the process extremely challenging and a few have joined-up in an effort to curb their XVAs, under the banner of optimisation and trade compression.

Discussion topics included:

  • What is MVA and how does it interact with the other XVAs?
  • How complex is MVA, relative to other adjustments?
  • In practical terms, where is the industry on MVA at this point?
  • Do you expect MVA to follow the same evolutionary path that we’ve seen for other XVAs?
  • Interaction between MVA, KVA, CVA, DVA, FVA
  • Rank order of the different XVAs, once IM regime has been fully implemented
  • What are the key regulations that will determine the correct MVA/XVA treatment for a trade?
  • What are the practical / implementation challenges?
  • Given all of this, what timeline is likely for MVA to start showing up in pricing?
  • How much pricing dispersion is it likely to produce?
  • Can MVA already be seen for cleared trades with CCPs?
  • Accounting treatment for MVA (IFRS 9, 13)
  • What does the blending / blurring of XVAs mean for the way they are managed? What is the right organisational structure?

Listen to the webinar here.

How Do Dealer Banks Price Derivative Products?

Scott Sobolewski, a Principal Consultant in our Boston office, recently published an article in Treasury & Risk Magazine titled “How Do Dealer Banks Price Derivative Products?”. The article helps corporate treasurers, asset managers, and other end-users of over-the-counter (OTC) derivatives understand the various components of bank regulatory and capital charges currently built into dealer pricing. Most users have grown comfortable with concepts like CVA and FVA, though newer valuation adjustments for initial margin (MVA) and regulatory capital (KVA), as well as Basel’s new initial margin rule taking effect on September 1, 2016, make it more important than ever to keep pace with new regulation. The market environment necessitates that risk managers at large financial institutions and end-user treasury functions understand how bank pricing has evolved in the wake of Dodd Frank and Basel III, not only for regulatory compliance exercises like reporting or stress testing, but for proactive risk management. By facilitating increased understanding on both sides of a derivatives trade, Quaternion hopes to increase liquidity within the shrinking uncleared OTC derivative market and reduce overall systemic risk across the financial system.

The full Treasury & Risk Magazine article can be found here, and the manuscript is also available here.

QuantLib User Meeting, London, 12 July 2016

Quaternion sponsored a QuantLib User Meeting at the Chartered Accountants’ Hall, One Moorgate Place, London EC2R 6EA on Tuesday 12th July 2016.

“The QuantLib project is aimed at providing a comprehensive software framework for quantitative finance. QuantLib is a free/open-source library for modeling, trading, and risk management in real-life. […] Appreciated by quantitative analysts and developers, it is intended for academics and practitioners alike, eventually promoting a stronger interaction between them.” (

With this meeting we want to provide a communication platform for both QuantLib users in the industry and QuantLib’s developers, contributors and creators, to help propagating QuantLib’s usage. This meeting continues a tradition of annual user forums and brings this event back to London where the first event of this type was held on January 18th, 2011.

Final Agenda / Speakers

08:15-09:00 User registration
09:00-09:15 Welcome Roland Lichters (Quaternion)
09:15-10:15 The abcd of Interest Rate Basis Spreads Luigi Ballabio (StatPro) and Ferdinando Ametrano (Banca IMI)
10:15-11:00 Open Risk Engine Peter Caspers, Niall O’Sullivan and Roland Lichters (Quaternion)
11:00-11:30 Tea/Coffee
11:30-12:15 Reposit 1.8 and the Future of Spreadsheet Addins Eric Ehlers (Reposit)
12:15-12:45 A simple application of the QuantLib observer pattern – Multi-Curve-Sensitivities Michael von den Driesch (IKB)
12:45-13:30 Lunch
13:30-14:15 QuantLibAdjoint News Alexander Sokol (CompatibL)
14:15-15:00 A sound modelling and backtesting framework for forecasting initial margin requirements Daniel Aziz (Credit Suisse)
15:00-15:30 Tea/Coffee
15:30-16:15 Calibration using Neural Networks Andres Hernandez (IBM)
16:15-16:45 Multi-Curve Convexity Sebastian Schlenkrich (d-fine)
16:45-17:00 Wrap up Roland Lichters (Quaternion)
17:15-20:00 Reception


The conference was held in the Auditorium and Atrium of the prestigious Chartered Accountants’ Hall at the Institute of Chartered Accountants, One Moorgate Place, London EC2R 6EA, details of which can be found here.

The location is easily accessible from Moorgate and Bank tube stations as can be seen here.


The presentations can be downloaded shortly from the QuantLib web site here.

The Future of Quantitative Models in Risk Management

A top-class panel of risk experts from banks, universities and audit companies discussed the current state and the future of standard approaches, risk factor models, simulation and regulation on May 3rd 2016 in Frankfurt.
While a South Korean delegation was getting into the mood for the annual meeting of the Asian Development Bank at the Grandhotel Hessischer Hof, many risk managers from banks and other companies arrived in the room next door. The setting was perfect for the eclectic mix of experts, who maintained an interesting discussion for more than an hour. Roland Stamm, Partner at Quaternion Risk Management, was responsible for the organization of the evening and moderated the panel. The discussion was very dynamic and marked by both unanimously agreed and opposed analyses of various aspects of the status quo in risk modeling.

Roland Stamm’s welcome address

Roland Stamm’s welcome address

Continue Reading…

Modern Derivatives Pricing and Credit
Exposure Analysis


Roland Lichters, Roland Stamm, Donal Gallagher

Modern Derivatives Pricing and Credit Exposure Analysis: Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtesting

The past 10 years have see an incredible change in pricing financial products, driven by the credit crisis which started in 2007 with the near bankruptcy of Bear Sterns, reaching a first climax with the implosion of the US housing market and the banking world’s downfall, and then turning into a sovereign debt crisis in Europe. A major change to have affected the landscape has been the increasing complexity in the valuation of derivatives – multi-curve pricing , various value adjustments (XVAs) using Monte Carlo simulation of markets through time , credit risk measurement and capital allocation – all based on increasingly complex mathematical and IT machinery.

Published in November 2015, Modern Derivatives Pricing and Credit Exposure Analysis is a comprehensive, practical guidebook for modern derivatives pricing and credit analysis, written with the practitioner in mind. Theoretically rigorous but focused on market practice, it provides a detailed and consistent toolkit of pricing and risk methods to cope with the increasing complexities of today’s derivatives management. The presented risk factor evolution models for six different asset classes allow efficient computation of various value adjustments (XVAs) and risk measures in a competitive and increasingly regulated environment. The text bridges the gap between the risk-neuraland real-world measure for backtesting purposes and explains different methods for speeding up XVA computation in order to allow fast calculations of margin adjustment or XVA greeks.

Written to provide sound theoretical detail with practical implementation, this book provides readers with both an overview and deep dive into valuation and risk methods applied in the industry today.

See the book at the Palgrave Macmillan website.

Part I – Discounting

  • Discounting Before the Crisis
  • What Changed With the Crisis
  • Clearing House Pricing
  • Global Discounting
  • CSA Discounting
  • Fair Value Hedge Accounting

Part II – Credit and Debit Value Adjustment

  • Fundamentals: Unilateral and Bilateral CVA
  • Single Trade CVA: Interest Rate Swaps, FX Forwards, Cross Currency Swap Flavours

Part III – Risk factor Evolution

  • Monte Carlo Framework
  • Interest Rates: Linear Gauss Markov Model, Stochastic Basis, CSA Discounting Revisited
  • Foreign Exchange: Multi-Currency LGM, Cross Currency Basis
  • Inflation: Jarrow-Yildirim and Dodgson-Kainth Models
  • Equity and Commodity: One and Two-Factor Models
  • Credit: Gaussian, Extended Cox-Ingersoll-Ross, Black-Karasinski and Peng-Kou Models

Part IV – XVA

  • Cross Asset Scenario Generation
  • Netting and Collateral
  • Early Exercise and American Monte Carlo
  • CVA Risk and Algorithmic Differentiation
  • Funding Value Adjustment: FVA Debate, Expectation and Semi-Replication Approach, MVA
  • Capital and Tax Value Adjustment: KVA by Semi-Replication, TVA

Part V – Credit Risk

  • Fundamentals, Portfolio Credit Models
  • Pricing Portfolio Credit Products: Synthetic CDOs, Cashflow Structures
  • Credit Risk for Derivatives: Real-World Measure, SA-CCR, Internal Model Approach, CVA Capital Charge
  • Backtesting: Framework, Risk-Factor Backtesting, Portfolio Backtesting

Part VI – Appendix

  • The Change of Measure Toolkit
  • The Feynman-Kac Connection
  • The Black76 Formula
  • Hull-White Model
  • Linear Gauss Markov Model
  • Dodgson Kainth Model
  • Cox-Ingersoll Ross Model with Jumps
  • Filtration Switching and the Peng-Kou Model

A Sound Modelling and Backtesting Framework for Forecasting Initial Margin Requirements


  • Fabrizio Anfuso, Credit Suisse Securities (Europe) Limited
  • Daniel Aziz, Credit Suisse Securities (Europe) Limited
  • Paul Giltinan, Quaternion Risk Management
  • Klearchos Loukopoulos, Credit Suisse Securities (Europe) Limited

January 15, 2016


The introduction by regulators of mandatory margining for bilateral OTCs is going to have a major impact on the derivatives market, particularly in light of the additional funding costs and liquidity requirements that large financial institutions will face. Fabrizio Anfuso, Daniel Aziz, Paul Giltinan and Klearchos Loukopoulos propose in the following a simple and consistent framework, equally applicable to non-cleared and cleared portfolios, to develop and backtest forecasting models for Initial Margin.

Download the paper here.

Efficient Simulation of the Multi Asset
Heston Model


  • Marco de Innocentis, Credit Suisse Securities (Europe) Limited
  • Roland Lichters , Quaternion Risk Management
  • Markus Trahe, Quaternion Risk Management

February 8, 2016


This paper describes a procedure for efficiently simulating a multi asset Heston model with an arbitrary correlation structure. Very little literature can be found on the topic (e.g. Wadman (2010) and Dimitroff et al. (2011)), the latter being very restrictive on correlation assumptions. The scheme proposed in this text is based on Andersen’s Quadratic Exponential (QE) scheme (2008) and operates with an arbitrary input correlation structure, which is partially decorrelated via a Gaussian copula approach to fit the single asset QE prerequisites. Given a long term horizon, it is shown numerically that, in the multi asset QE (MQE) scheme, all combinations of terminal correlations converge quickly to the true terminal correlations for decreasing Monte Carlo time step size, if the input correlation matrix is interpreted as the system’s instantaneous correlation matrix. Convergence of vanilla and spread option prices is investigated, in order to verify the appropriate behaviour for higher moments of the marginal and the joint distribution under MQE. Finally, the superiority of MQE vs. Taylor based schemes is shown by comparing convergence of the empirical PDF, calculated with Monte Carlo, to the “exact” function calculated via Fourier inversion.

Download the paper here.

Valuation of a Cashflow CDO Without Monte Carlo Simulation


  • Donal Gallagher, Quaternion Risk Management
  • James P. Gleeson, University of Limerick, Ireland
  • Chris Kenyon, Lloyds Banking Group
  • Roland Lichters, Quaternion Risk Management

September 15, 2009


Unlike tranches of synthetic CDOs, that depend only on the defaults of the underlying securities, tranches of cashflow CDOs also depend on the interest cash flows from the coupons of the securities. Whilst fast, accurate, (semi-)analytic methods exist for pricing synthetic CDO tranches (Hull and White 2004), no equivalent methods exist for pricing cashflow CDO tranches because of their dependence on both principal and interest waterfalls. We introduce an analytical approximation that renders cashflow CDOs amenable to (semi-)analytic pricing. The complication of needing the joint distribution of interest and outstanding notional is reduced to needing only their marginal distributions. We show that our analytic approximation is globally valid with bounded errors that are small in most cases. Furthermore, our approach can be extended to more detailed structural features such as interest coverage tests and over-collateralization tests. We present results from realistic cashflow CDO examples.

Download the paper here.

Wall Street Meets FinTech

Wall Street Meets FinTech: Interactive Visualization of Simulations of Systemic Financial Market Risk Conditional on Policy Interventions was the subject of a recent demo at Columbia University’s Data Science Day where Quaternion Risk Management (QRM) announced a new research partnership with the faculty of Columbia University in New York. The event was designed to foster collaboration between innovators in academia and industry through demos and lightning talks by Columbia University researchers presenting their latest work in data science. “This partnership launches the inaugural collaboration within the ‘Financial Risk Analytics and Regulation Innovation Lab’ at Columbia’s School of Professional Studies,” says Sharyn O’Halloran (George Blumenthal Professor of Political Economics and Professor of International and Public Affairs).
Continue Reading…

The Future of Models in Risk Capital

The authors of “Modern Derivatives Pricing and Credit Exposure Analysis” – Roland Lichters, Roland Stamm and Donal Gallagher, all Partners of Quaternion Risk Management, launched their book at a well attended event run by QRM at The Marriott in Canary Wharf on Monday 29th February 2016.
The event was kicked off with a Panel discussion by a selection of well known industry figures, moderated by Ms. Laura Noonan, Investment Banking Correspondent of the Financial Times. The Panel included:

  • Dr. Fabrizio Anfuso – Head of Collateralized Exposure Modelling at Credit Suisse
  • Dr. Ronnie Barnes – Principal at Cornerstone Research
  • Dr. Paul Burnett – Global Head of Traded Risk Analytics at HSBC
  • Dr. Giovanni Cesari – XVA Analytics Ltd.
  • Dr. Andrew Green – Head of CVA/FVA Quantitative Research at Lloyds Banking Group
  • Mr. Stéphane Boivin – Senior Policy Expert, European Banking Authority

Continue Reading…

State-of-the-art credit exposure simulation: new approaches to credit risk

Quaternion Risk Management (Quaternion), the Quant consultancy risk and pricing specialists, are delighted to present an afternoon workshop in Frankfurt on Tuesday 9th June 2015 at 16.00 at Grandhotel Hessischer Hof, Friedrich-Ebert-Anlage 40, 60325 Frankfurt am Main, followed by drinks. Continue Reading…

Quaternion Risk Management powers the InCol Analytics Platform InCol Intelligence launched today

LONDON, 26 March 2015—Quaternion Risk Management Limited (“Quaternion”), provider of specialised risk analytics consultancy, services and software, is now powering InCol.   InCol structures and sources cost efficient senior secured term debt for rated and non-rated financial institutions.

Quaternion’s risk engine performs complex analytics and is the lynchpin of the InCol Intelligence platform. The platform allows issuers of, and investors in, senior secured term debt to optimise their positions and to assess where and when opportunities arise. It facilitates the unlocking of quality collateral pools from new issuers which can be matched with secured term debt investors’ requirements.Continue Reading…

Quaternion Risk Management collaborates with UBS Delta to deliver CVA Service launched today

LONDON, 17 October 2014—Quaternion Risk Management Limited (Quaternion), provider of specialized risk analytic consultancy, services and software are now working together with UBS Delta, the award-winning provider of risk and performance analytics to provide counterparty exposure, CVA/DVA analytics and reporting services to the financial and corporate community.

Quaternion’s risk engine and complex analytics have been integrated into UBS Delta to provide the CVA Service.

Continue Reading…