Vivien BRUNEL's home page


Choosing modelling options and transfer criteria for IFRS 9: from theory to practice, RiskMinds conference, Amsterdam, Dec. 2015

Sizing the Stage 2 portfolios for IFRS 9 provisions
Submited to Risk (Nov. 2015)
IFRS 9 norms require classifying non-defaulted loans into two stages depending on their credit quality evolution since initial recognition by the bank. In this paper, we propose an optimal way to perform this classification. Target values of some key performance indicators of the provisioning model emerge from the implementation of this process. In particular we compute the target value of the stage 2 "Hit Rate" and the size of the stage 2 portfolio.


Operational risk modeled analytically II: the consequences of classification invariance
Submited to Risk (Apr. 2015)
Most of the banks’ operational risk internal models are based on loss pooling in risk and business line categories. The parameters and outputs of operational risk models are sensitive to the pooling of the data and the choice of the risk classification. In a simple model, we establish the link between the number of risk cells and the model parameters by requiring invariance of the bank’s loss distribution upon a change in classification. We provide details on the impact of this requirement on the domain of attraction of the loss distribution, on diversification effects and on cell risk correlations.

Operational risk modelled analytically
Risk (July 2014)
I obtain new results on operational risk correlations. With the use of analytical models for operational risk, I show that the uniform correlation assumption is a robust assumption for measuring the bank's capital charge.

New results on the correlation problem for operational risk
Journal of Financial Perspective (July 2014)
I describe new results on operational risk correlations. Based on analytical models for operational risk, I show that the uniform correlation assumption is a robust assumption for measuring the bank's capital charge.

Dealing with seller's risk
Risk (October 2006)
The risk of trade receivables securitisations comes from both the pool of assets and the seller of the assets. I develop a model for securitisation exposures that deals with both risks, and analyse in detail the interplay between debtors’ risk and seller’s risk.

Pricing credit derivatives with uncertain default probabilities
Wilmott magazine (January 2006)
When transition probabilities are uncertain parameters, we show that the price of a credit spread option is solution of an integro-differential PDE systems. More interestingly, we provide with an intuitive understanding of what uncertain transition probabilities means.

Super-replication problem in a jumping financial market
Finance 2002 - Hors - Série, n°46 (January 2003).
We solve the super-replication problem when asset returns and/or volatilities follow a Wiener process with jumps. Option prices in this framework are solution of integro-differential PDE

On the optimal growth rate strategy : long term opportunities and short term risk
Banque & Marchés n°57 (March 2002), with Jérôme Legras.
Price of the best paper 2002 in Banque & Marchés
On the long run, the financial theory shows that there is an optimal investment strategy independant of the agents' preferences. We show that this strategy remains optimal when investment horizons are finite.

Using credit derivatives, (French version)
Quants, HSBC-CCF (2001), with Pierre de la Noue.
Taxonomy of credit derivatives and the role of quantitative approaches.


Model-independant approximation formulas for ABS duration (2008) (with Faïçal JRIBI)
The price and sensitivities of an amortizing asset are linked to the cash-flows distribution. We show that including prepayment risk in a pricing model is obtained by changing the cash-flow distribution. This formalism leads to simple calculations and to accurate approximation formulas for ABS duration that takes into account both discounting and dispersion of the cash-flows.

Universal measure for pricing credit portfolios (2006) (with Benoît ROGER)
We propose a way for pricing credit portfolios based on the market price of credit risk. This approach allows to reconcile the mark to loss and the mark to market approaches for computing economic capital and leads to a correct evaluation of the cost of capital.

Minimal models for credit risk : an information theory approach (2004)
We consider maximum entropy loss distributions applied to credit portfolios and ABS as a reference starting point in order to compare models or sets of parameters between themselves.

Pricing of equities with embedded optional clausis: study of PPR's proposal on Gucci (2003) (with François SOUPE)
We consider the case of a stock option embedded in the stock itself. We show how the price of the stock is shifted and how its dynamics is modified.

Le risque opérationnel (2001, in French)
We apply ruin theory to operational risk and show that it leads naturally to a computation of economic capital.


Credit VaR
Incidents of defaults
Monte Carlo Simulations for risk management
Should we buy a bond under or above par ? (in French)
Cost of adding a guarantee to a fund


Modelling challenges linked to IFRS 9 norms, RiskMinds conference, Amsterdam, Dec. 2014
A recent history of credit risk (in French), ESILV, Paris, Nov. 2014
Operational risk modelled analytically, Cass Business School, London, Oct. 2014