IBOR Transition

Unsecured short-term interbank funding in the IBOR market (“InterBank Offered Rates”) has declined dramatically following the 2012 rate-fixing scandals and its integrity has been openly called into question. In July 2017, the UK’s Financial Conduct Authority declared that it would no longer persuade or compel banks to submit their interbank borrowing rates after 2021. While central bank-led working groups have been convening since 2014 to establish appropriate Alternative Reference Rates (“ARRs”) for each IBOR currency, the FCA’s triggering event has solidified the need for financial market participants to prepare for the impending cessation of IBORs. Given outstanding uncertainties in the working groups’ determination of ARRs per currency, calculating IBOR exposures and establishing a transition plan is critical in advance of 2021 while there still remains sufficient time to proactively manage the market, accounting, and legal risks. This White Paper describes Quaternion’s IBOR-related services aimed at helping financial market participants prepare for 2021:

  1. Evaluation of existing IBOR exposures and hedge effectiveness, including stress testing
  2. Portfolio compression of IBORswhile maintaining the same duration-adjusted exposure
  3. Quantitative support during legal renegotiations of derivative and loan documentation
  4. Calculation of go-forward spread and tenor adjustments to equalize ARRs and LIBORs

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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.

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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.

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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.

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ISDA Whitepaper – The Future of Derivatives Processing and Market Infrastructure

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

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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.

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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.

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.

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.