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  • Journal article
    Cont R, Minca A, 2015,

    Credit default swaps and systemic risk

    , Annals of Operations Research, Vol: 247, Pages: 523-547, ISSN: 0254-5330

    We present a network model for investigating the impact on systemic risk of central clearing of over the counter (OTC) credit default swaps (CDS). We model contingent cash flows resulting from CDS and other OTC derivatives by a multi-layered network with a core-periphery structure, which is flexible enough to reproduce the gross and net exposures as well as the heterogeneity of market shares of participating institutions. We analyze illiquidity cascades resulting from liquidity shocks and show that the contagion of illiquidity takes place along a sub-network constituted by links identified as ’critical receivables’. A key role is played by the long intermediation chains inherent to the structure of the OTC network, which may turn into chains of critical receivables. We calibrate our model to data representing net and gross OTC exposures of large dealer banks and use this model to investigate the impact of central clearing on network stability. We find that, when interest rate swaps are cleared, central clearing of credit default swaps through a well-capitalized CCP can reduce the probability and the magnitude of a systemic illiquidity spiral by reducing the length of the chains of critical receivables within the financial network. These benefits are reduced, however, if some large intermediaries are not included as clearing members.
  • Journal article
    Cass T, Lyons T, 2015,

    Evolving communities with individual preferences

    , Proceedings of the London Mathematical Society, Vol: 110, Pages: 83-107, ISSN: 0024-6115

    The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space (๐›บ,๎ˆฒ,๐œˆ) where ๐œˆ determines the abundance of individual preferences. The preferences of an individual ๐œ”∈๐›บ are described by a measurable choice ๐‘‹(๐œ”)of a rough path.We aim to identify, for each individual, a choice for the forward evolution ๐‘Œ๐‘ก(๐œ”)for an individual in the community. These choices ๐‘Œ๐‘ก(๐œ”) must be consistent so that ๐‘Œ๐‘ก(๐œ”)correctly accounts for the individual's preference and correctly models their interaction with the aggregate behaviour of the community.In general, solutions are continuum of interacting threads analogous to the huge number of individual atomic trajectories that together make up the motion of a fluid. The evolution of the population need not be governed by any overโ€arching partial differential equation (PDE). Although one can match the standard nonโ€linear parabolic PDEs of McKean–Vlasov type with specific examples of communities in this case. The bulk behaviour of the evolving population provides a solution to the PDE.We focus on the case of weakly interacting systems, where we are able to exhibit the existence and uniqueness of consistent solutions.An important technical result is continuity of the behaviour of the system with respect to changes in the measure ๐œˆassigning weight to individuals. Replacing the deterministic ๐œˆ with the empirical distribution of an independent and identically distributed sample from ๐œˆleads to many standard models, and applying the continuity result allows easy proofs for propagation of chaos.The rigorous underpinning presented here leads to uncomplicated models which have wide applicability in both the physical and social sciences. We make no presumption that the macroscopic dynamics are modelled by a PDE.This work builds on the fine probability literature considering the limit behaviour for systems where
  • Journal article
    Bender C, Pakkanen MS, Sayit H, 2015,

    Sticky continuous processes have consistent price systems

    , Journal of Applied Probability, Vol: 52, Pages: 586-594, ISSN: 1475-6072

    Under proportional transaction costs, a price process is said to have aconsistent price system, if there is a semimartingale with an equivalentmartingale measure that evolves within the bid-ask spread. We show that acontinuous, multi-asset price process has a consistent price system, underarbitrarily small proportional transaction costs, if it satisfies a naturalmulti-dimensional generalization of the stickiness condition introduced byGuasoni [Math. Finance 16(3), 569-582 (2006)].
  • Journal article
    Cont R, Wagalath L, 2014,

    Fire sales forensics: Measuring endogenous risk

    , Mathematical Finance, Vol: 26, Pages: 835-866, ISSN: 0960-1627

    We propose a tractable framework for quantifying the impact of loss-triggered fire sales on portfolio risk, in a multi-asset setting. We derive analytical expressions for the impact of fire sales on the realized volatility and correlations of asset returns in a fire sales scenario and show that our results provide a quantitative explanation for the spikes in volatility and correlations observed during such deleveraging episodes. These results are then used to develop an econometric framework for the forensic analysis of fire sales episodes, using observations of market prices. We give conditions for the identifiability of model parameters from time series of asset prices, propose a statistical test for the presence of fire sales, and an estimator for the magnitude of fire sales in each asset class. Pathwise consistency and large sample properties of the estimator are studied in the high-frequency asymptotic regime. We illustrate our methodology by applying it to the forensic analysis of two recent deleveraging episodes: the Quant Crash of August 2007 and the Great Deleveraging following the default of Lehman Brothers in Fall 2008. © 2014 Wiley Periodicals, Inc.
  • Journal article
    Jacquier A, Mijatovic A, 2014,

    Large deviations for the extended Heston model: the large-time case

    , Asia-Pacific Financial Markets, Vol: 21, Pages: 263-280, ISSN: 1573-6946

    We study here the large-time behaviour of all continuous affine stochasticvolatility models (in the sense of Keller-Ressel) and deduce a closed-formformula for the large-maturity implied volatility smile. Based on refinementsof the Gartner-Ellis theorem on the real line, our proof reveals pathologicalbehaviours of the asymptotic smile. In particular, we show that the conditionassumed in Gatheral and Jacquier under which the Heston implied volatilityconverges to the SVI parameterisation is necessary and sufficient.
  • Journal article
    Cont R, 2014,

    Central clearing of OTC derivatives: Bilateral vs multilateral netting

    , Statistics & Risk Modeling, Vol: 31, Pages: 3-22, ISSN: 2193-1402

    We study the impact of central clearing of over-the-counter (OTC) transactions on counterparty exposures in a market with OTC transactions across several asset classes with heterogeneous characteristics. The impact of introducing a central counterparty (CCP) on expected interdealer exposure is determined by the tradeoff between multilateral netting across dealers on one hand and bilateral netting across asset classes on the other hand. We find this tradeoff to be sensitive to assumptions on heterogeneity of asset classes in terms of `riskyness' of the asset class as well as correlation of exposures across asset classes. In particular, while an analysis assuming independent, homogeneous exposures suggests that central clearing is efficient only if one has an unrealistically high number of participants, the opposite conclusion is reached if differences in riskyness and correlation across asset classes are realistically taken into account. We argue that empirically plausible specifications of model parameters lead to the conclusion that central clearing does reduce interdealer exposures: the gain from multilateral netting in a CCP overweighs the loss of netting across asset classes in bilateral netting agreements. When a CCP exists for interest rate derivatives, adding a CCP for credit derivatives is shown to decrease overall exposures. These findings are shown to be robust to the statistical assumptions of the model as well as the choice of risk measure used to quantify exposures.
  • Journal article
    Cass T, Clark M, Crisan D, 2014,

    The filtering equations revisited

    , Springer Proceedings in Mathematics and Statistics, Vol: 100, Pages: 129-162, ISSN: 2194-1009

    The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the changeof– probability-measure method introduced by Kallianpur and Striebel to derive the filtering equations and the Bayes-like formula that bears their names. More recent work, however, has generally preferred other methods. In this paper, we reconsider the change-of-measure approach to the derivation of the filtering equations and show that many of the technical conditions present in previous work can be relaxed. The filtering equations are established for general Markov signal processes that can be described by amartingale-problem formulation.Two specific applications are treated.
  • Journal article
    Brigo D, Capponi A, Pallavicini A, 2013,

    ARBITRAGE-FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS

    , Mathematical Finance, Vol: 24, Pages: 1252146-1252146, ISSN: 0960-1627

    We develop an arbitrage-free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on-default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation-induced contagion is illustrated with numerical examples.
  • Journal article
    Deuschel JD, Friz PK, Jaquier A, Violante Set al., 2013,

    Marginal density expansions for diffusions and stochastic volatility, Part II: Applications

    , Communications on Pure and Applied Mathematics, Vol: n/a, ISSN: 0010-3640

    Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics; cf. G. Ben Arous (1988). Our small noise expansion allows for a "second order" exponential factor. Applications include tail and implied volatility asymptotics in some correlated stochastic volatility models; in particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).
  • Conference paper
    Brigo D, Armstrong J, 2013,

    Stochastic filtering by projection: the example of the cubic sensor

    , Geometric Science of Information: First International Conference, Pages: 685-692

    The “projection method” is an approach to finding numerical approximations to the optimal filter for non linear stochastic filtering problems. One uses a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic differential equation given by the filtering problem onto a finite dimensional manifold inside the space of densities. This reduces the problem to finite dimensional stochastic differential equation.Previously, the projection method has only been considered for the Hilbert space structure associated with the Hellinger metric. We show through the numerical example of the quadratic sensor that the approach also works well when one projects using the direct L 2 metric.Previous implementations of projection methods have been limited to solving a single problem. We indicate how one can build a computational framework for applying the projection method more generally.
  • Journal article
    Cass T, Litterer C, Lyons T, 2013,

    Integrability and tail estimates for Gaussian rough differential equations

    , Annals of Probability, Vol: 41, Pages: 3026-3050
  • Journal article
    Cont R, Deguest R, 2013,

    EQUITY CORRELATIONS IMPLIED BY INDEX OPTIONS: ESTIMATION AND MODEL UNCERTAINTY ANALYSIS

    , Mathematical Finance, Vol: 23, Pages: 496-530, ISSN: 0960-1627

    We propose a method for constructing an arbitrage-free multiasset pricing model which is consistent with a set of observed single- and multiasset derivative prices. The pricing model is constructed as a random mixture of N reference models, where the distribution of mixture weights is obtained by solving a well-posed convex optimization problem. Application of this method to equity and index options shows that, whereas multivariate diffusion models with constant correlation fail to match the prices of index and component options simultaneously, a jump-diffusion model with a common jump component affecting all stocks enables to do so. Furthermore, we show that even within a parametric model class, there is a wide range of correlation patterns compatible with observed prices of index options. Our method allows, as a by product, to quantify this model uncertainty with no further computational effort and propose static hedging strategies for reducing the exposure of multiasset derivatives to model uncertainty.
  • Journal article
    Jacquier A, Roome P, 2013,

    The Small-Maturity Heston Forward Smile

    , SIAM Journal on Financial Mathematics

    In this paper we investigate the asymptotics of forward-start options and theforward implied volatility smile in the Heston model as the maturity approacheszero. We prove that the forward smile for out-of-the-money options explodes andcompute a closed-form high-order expansion detailing the rate of the explosion.Furthermore the result shows that the square-root behaviour of the varianceprocess induces a singularity such that for certain parameter configurationsone cannot obtain high-order out-of-the-money forward smile asymptotics. In theat-the-money case a separate model-independent analysis shows that thesmall-maturity limit is well defined for any Ito diffusion. The proofs rely onthe theory of sharp large deviations (and refinements) and incidentally weprovide an example of degenerate large deviations behaviour.
  • Book
    Brigo D, Morini M, Pallavicini A, 2013,

    Counterparty Credit Risk, Collateral and Funding: with Pricing Cases for all Asset Classes

    , Publisher: Wiley, ISBN: 978-0-470-74846-6

    The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular ‘concrete’ financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a ‘feel’ for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.
  • Journal article
    BRIGO D, CAPPONI A, PALLAVICINI A, PAPATHEODOROU Vet al., 2013,

    PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK

    , International Journal of Theoretical and Applied Finance, Vol: 16, Pages: 1350007-1350007, ISSN: 0219-0249

    <jats:p> This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies. </jats:p>
  • Journal article
    Cont R, Fournie D-A, 2013,

    Functional Ito calculus and stochastic integral representation of martingales

    , Annals of Probability, Vol: 41, Pages: 109-133, ISSN: 0091-1798

    We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependentfunctionals which possess certain directional derivatives. The construction isbased on a pathwise derivative, introduced by B Dupire, for functionals on thespace of right-continuous functions with left limits. We show that this functional derivative admits a suitable extension to the space ofsquare-integrable martingales. This extension defines a weak derivative whichis shown to be the inverse of the Ito integral and which may be viewed as a non-anticipative "lifting" of the Malliavin derivative. These results lead to a constructive martingale representation formula for Ito processes. By contrast with the Clark-Haussmann-Ocone formula, this representation only involves non-anticipative quantities which may be computed pathwise.
  • Journal article
    Bernard C, Cui Z, Forde M, Jacquier A, McLeish D, Mijatovic Aet al., 2013,

    The large-maturity smile for the Heston model (vol 15, pg 755, 2011)

    , FINANCE AND STOCHASTICS, Vol: 17, Pages: 223-224, ISSN: 0949-2984
  • Journal article
    Cont R, Minca A, 2013,

    RECOVERING PORTFOLIO DEFAULT INTENSITIES IMPLIED BY CDO QUOTES

    , Mathematical Finance, Vol: 23, Pages: 94-121

    We propose a stable nonparametric algorithm for the calibration of “top-down” pricing models for portfolio credit derivatives: given a set of observations of market spreads for collateralized debt obligation (CDO) tranches, we construct a risk-neutral default intensity process for the portfolio underlying the CDO which matches these observations, by looking for the risk-neutral loss process “closest” to a prior loss process, verifying the calibration constraints. We formalize the problem in terms of minimization of relative entropy with respect to the prior under calibration constraints and use convex duality methods to solve the problem: the dual problem is shown to be an intensity control problem, characterized in terms of a Hamilton–Jacobi system of differential equations, for which we present an analytical solution. Given a set of observed CDO tranche spreads, our method allows to construct a default intensity process which leads to tranche spreads consistent with the observations. We illustrate our method on ITRAXX index data: our results reveal strong evidence for the dependence of loss transitions rates on the previous number of defaults, and offer quantitative evidence for contagion effects in the (risk-neutral) loss process.
  • Journal article
    Cont R, Kukanov A, Stoikov S, 2013,

    The Price Impact of Order Book Events

    , Journal of Financial Econometrics, Vol: 12, Pages: 47-88

    We study the price impact of order book events - limit orders, market ordersand cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that,over short time intervals, price changes are mainly driven by the order flowimbalance, defined as the imbalance between supply and demand at the best bidand ask prices. Our study reveals a linear relation between order flowimbalance and price changes, with a slope inversely proportional to the marketdepth. These results are shown to be robust to seasonality effects, and stableacross time scales and across stocks. We argue that this linear price impactmodel, together with a scaling argument, implies the empirically observed"square-root" relation between price changes and trading volume. However, therelation between price changes and trade volume is found to be noisy and lessrobust than the one based on order flow imbalance.
  • Journal article
    Cont R, Deguest R, He X, 2013,

    Loss-Based Risk Measures

    , Statistics and Risk Modeling, Vol: 30, Pages: 133-167

    Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of estimators of loss-based risk measures: we provide a general criterion for qualitative robustness of risk estimators and compare thiscriterion with sensitivity analysis of estimators based on influence functions. Finally, we provide examples of statistically robust estimators for loss-based risk measures.
  • Journal article
    Cont R, Wagalath L, 2013,

    RUNNING FOR THE EXIT: DISTRESSED SELLING AND ENDOGENOUS CORRELATION IN FINANCIAL MARKETS

    , Mathematical Finance, Vol: 23, Pages: 718-741

    We propose a simple multiperiod model of price impact from trading in a market with multiple assets, which illustrates how feedback effects due to distressed selling and short selling lead to endogenous correlations between asset classes. We show that distressed selling by investors exiting a fund and short selling of the fund’s positions by traders may have nonnegligible impact on the realized correlations between returns of assets held by the fund. These feedback effects may lead to positive realized correlations between fundamentally uncorrelated assets, as well as an increase in correlations across all asset classes and in the fund’s volatility which is exacerbated in scenarios in which the fund undergoes large losses. By studying the diffusion limit of our discrete time model, we obtain analytical expressions for the realized covariance and show that the realized covariance may be decomposed as the sum of a fundamental covariance and a liquidity-dependent “excess” covariance. Finally, we examine the impact of these feedback effects on the volatility of other funds. Our results provide insight into the nature of spikes in correlation associated with the failure or liquidation of large funds.
  • Book chapter
    Cont R, Moussa A, Santos EB, 2013,

    Network structure and systemic risk in banking systems.

    , Handbook of Systemic Risk, Editors: Fouque, Langsam, Publisher: Cambridge University Press, Pages: 327-367, ISBN: 9781107023437

    We present a quantitative methodology for analyzing the potential for contagion and systemic risk in a network of interlinked financial institutions, using a metric for the systemic importance of institutions: the Contagion Index. We apply this methodology to a data set of mutual exposures and capital levels of financial institutions in Brazil in 2007 and 2008, and analyze the role of balance sheet size and network structure in each institution's contribution to systemic risk. Our results emphasize the contribution of heterogeneity in network structure and concentration of counterparty exposures to a given institution in explaining its systemic importance. These observations plead for capital requirements which depend on exposures, rather than aggregate balance sheet size, and which target systemically important institutions.
  • Journal article
    Cont R, Kokholm T, 2013,

    A CONSISTENT PRICING MODEL FOR INDEX OPTIONS AND VOLATILITY DERIVATIVES

    , Mathematical Finance, Vol: 23, Pages: 248-274, ISSN: 0960-1627

    We propose a flexible framework for modeling the joint dynamics of an index and a set of forward variance swap rates written on this index. Our model reproduces various empirically observed properties of variance swap dynamics and enables volatility derivatives and options on the underlying index to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index.
  • Journal article
    Deuschel JD, Friz PK, Jacquier A, Violante Set al., 2013,

    Marginal density expansions for diffusions and stochastic volatility, Part I: Theoretical foundations

    , Communications on Pure and Applied Mathematics, Vol: n/a, ISSN: 0010-3640

    Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited.In particular, we are interested in density expansions of the projection$(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions arefound which replace the well-known "not-in-cutlocus" condition known fromheat-kernel asymptotics; cf. G. Ben Arous (1988). Our small noise expansionallows for a "second order" exponential factor. Applications include tail andimplied volatility asymptotics in some correlated stochastic volatility models;in particular, we solve a problem left open by A. Gulisashvili and E.M. Stein(2009).
  • Journal article
    Jacquier A, Roome P, 2012,

    Asymptotics of forward implied volatility

    , SIAM Journal on Financial Mathematics, Vol: 6(1), ISSN: 1945-497X

    We prove here a general closed-form expansion formula for forward-startoptions and the forward implied volatility smile in a large class of models,including the Heston stochastic volatility and time-changed exponential L\'evymodels. This expansion applies to both small and large maturities and is basedsolely on the properties of the forward characteristic function of theunderlying process. The method is based on sharp large deviations techniques,and allows us to recover (in particular) many results for the spot impliedvolatility smile. In passing we (i) show that the forward-start date has to berescaled in order to obtain non-trivial small-maturity asymptotics, (ii) provethat the forward-start date may influence the large-maturity behaviour of theforward smile, and (iii) provide some examples of models with finite quadraticvariation where the small-maturity forward smile does not explode.
  • Book chapter
    Amini H, Cont R, Minca A, 2012,

    Stress Testing the Resilience of Financial Networks

    , Finance at Fields, Editors: Grasselli, Hughston, Publisher: World Scientific Publishing Company, Pages: 17-36, ISBN: 9789814407885

    We propose a simulation-free framework for stress testing the resilience of a financial network to external shocks affecting balance sheets. Whereas previous studies of contagion effects in financial networks have relied on large scale simulations, our approach uses a simple analytical criterion for resilience to contagion, based on an asymptotic analysis of default cascades in heterogeneous networks. In particular, our methodology does not require to observe the whole network but focuses on the characteristics of the network which contribute to its resilience. Applying this framework to a sample network, we observe that the size of the default cascade generated by a macroeconomic shock across balance sheets may exhibit a sharp transition when the magnitude of the shock reaches a certain threshold: Beyond this threshold, contagion spreads to a large fraction of the financial system. An upper bound is given for the threshold in terms of the characteristics of the network.
  • Journal article
    BRIGO D, BUESCU C, MORINI M, 2012,

    COUNTERPARTY RISK PRICING: IMPACT OF CLOSEOUT AND FIRST-TO-DEFAULT TIMES

    , International Journal of Theoretical and Applied Finance, Vol: 15, Pages: 1250039-1250039, ISSN: 0219-0249

    <jats:p> In the absence of a universally accepted procedure for the credit valuation adjustment (CVA) calculation, we compare a number of different bilateral counterparty valuation adjustment (BVA) formulas. First we investigate the impact of the choice of the closeout convention used in the formulas. Important consequences on default contagion manifest themselves in a rather different way depending on which closeout formulation is used (risk-free or replacement), and on default dependence between the two entities in the deal. Second we compare the full bilateral formula with an approximation that is based on subtracting two unilateral credit valuation adjustment (UCVA) formulas. Although the latter might be attractive for its instantaneous implementation once one has a unilateral CVA system, it ignores the impact of the first-to-default time, when closeout procedures are ignited. We illustrate in a number of realistic cases both the contagion effect due to the closeout convention, and the CVA pricing error due to ignoring the first-to-default time. </jats:p>
  • Journal article
    Cont R, Jessen R, 2012,

    Constant Proportion Debt Obligations (CPDOs): Modeling and Risk Analysis

    , Quantitative Finance, Vol: 12, Pages: 1199-1218

    Constant Proportion Debt Obligations (CPDOs) are structured credit derivatives that generate high coupon payments by dynamically leveraging a position in an underlying portfolio of investment-grade index default swaps. CPDO coupons and principal notes received high initial credit ratings from the major rating agencies, based on complex models for the joint transition of ratings and spreads for all names in the underlying portfolio. We propose a parsimonious model for analysing the performance of CPDO strategies using a top-down approach that captures the essential risk factors of the CPDO. Our approach allows us to compute default probabilities, loss distributions and other tail risk measures for the CPDO strategy and analyse the dependence of these risk measures on various parameters describing the risk factors. We find that the probability of the CPDO defaulting on its coupon payments can be made arbitrarily small—and thus the credit rating arbitrarily high—by increasing leverage, but the ratings obtained strongly depend on assumptions on the credit environment (high spread or low spread). More importantly, CPDO loss distributions are found to exhibit a wide range of tail risk measures inside a given rating category, suggesting that credit ratings are insufficient performance indicators for such complex leveraged strategies. A worst-case scenario analysis indicates that CPDO strategies have a high exposure to persistent spread-widening scenarios and that CPDO ratings are shown to be quite unstable during the lifetime of the strategy.
  • Book chapter
    Brigo D, Capproni A, 2012,

    Bilateral Credit Valuation Adjustment with Application to Credit Default Swaps

    , Managing and Measuring Capital: For Banks and Financial Institutions, Editors: Ong, Publisher: Risk Books
  • Journal article
    Cass T, Hairer M, Litterer C, Tindel Set al., 2012,

    Smoothness of the density for solutions to Gaussian Rough Differential Equations

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