Publications
98 results found
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.
Cont R, Schaanning E, 2014, Fire sales, indirect contagion and systemic stress-testing, Publisher: SSRN
We present a framework for modeling the phenomenon of fire sales in a network of financial institutions with common asset holdings, subject to leverage or capital constraints. Asset losses triggered by macro-shocks may interact with portfolio constraints, resulting in liquidation of assets, which in turn affects market prices, leading to contagion of losses when portfolios are marked to market. If mark-to-market losses are large, this may in turn lead to a new round of fire sales.In contrast to balance sheet contagion mechanisms based on direct linkages, this price-mediated contagion is transmitted through common asset holdings, which we quantify through liquidity-weighted overlaps across portfolios. Exposure to price-mediated contagion leads to the concept of indirect exposure to an asset class, as a consequence of which the risk of a portfolio depends on the matrix of asset holdings of other large and leveraged portfolios with similar assets. Our model provides an operational systemic stress testing method for quantifying the exposure of the financial system to these effects.Using data from the European Banking Authority, we apply this method to the examine the exposure of the EU banking system to price-mediated contagion.Our results indicate that, even with optimistic estimates of market depth, moderately large macro-shocks may trigger fire sales which then lead to substantial losses across bank portfolios, modifying the outcome of bank stress tests.Moreover, we show that price-mediated contagion leads to a heterogeneous cross-sectional loss distribution across banks, which cannot be replicated simply by applying a macro-shock to bank portfolios in absence of fire sales. We propose a bank-level indicator, based on the analysis of liquidity-weighted overlaps across bank portfolios, which is shown to be strongly correlated with bank losses due to fire sales and may be used to quantify the contribution of a financial institution to price-mediated contagion. Unlike m
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.
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.
Arulkumaran N, Rhodes A, 2013, Critical illness in obstetrics. Preface.
Arulkumaran N, Rhodes A, 2013, Critical Illness in Obstetrics Preface, Publisher: ELSEVIER SCI LTD, Pages: 789-789
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Amini H, Cont R, Minca A, 2012, Stress testing the resilience of financial networks, International Journal of theoretical and Applied Finance, Vol: 15, Pages: 1250006-1250026
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.
, 2012, Preface, Frontiers in Quantitative Finance: Volatility and Credit Risk Modeling, Pages: 1-299
The Petit D'euner de la Finance-which author Rama Cont has been co-organizing in Paris since 1998-is a well-known quantitative finance seminar that has progressively become a platform for the exchange of ideas between the academic and practitioner communities in quantitative finance. Frontiers in Quantitative Finance is a selection of recent presentations in the Petit D'euner de la Finance. In this book, leading quants and academic researchers cover the most important emerging issues in quantitative finance and focus on portfolio credit risk and volatility modeling. © 2009 John Wiley & Sons, Inc. All rights reserved.
Pollak I, Avellaneda M, Bacry E, et al., 2011, Improving the Visibility of Financial Applications Among Signal Processing Researchers, IEEE SIGNAL PROCESSING MAGAZINE, Vol: 28, Pages: 14-15, ISSN: 1053-5888
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- Citations: 1
Cont R, 2011, Statistical Modeling of High Frequency Financial Data: Facts, Models and Challenges, IEEE Signal Processing Magazine, Vol: 28, Pages: 16-25
The availability of high-frequency data on transactions, quotes and order flow in electronic order-driven markets has revolutionized data processing and statistical modeling techniques in finance and brought up new theoretical and computational challenges. Market dynamics at the transaction level cannot be characterized solely in terms the dynamics of a single price and one must also take into account the interaction between buy and sell orders of different types by modeling the order flow at the bid price, ask price and possibly other levels of the limit order book.We outline the empirical characteristics of high-frequency financial time series and provide an overview of stochastic models for the continuous-time dynamics of a limit order book, focusing in particular on models which describe the limit order book as a queuing system. We describe some applications of such models and point to some open problems.
Cont R, Mancini C, 2011, Nonparametric tests for pathwise properties of semimartingales, BERNOULLI, Vol: 17, Pages: 781-813, ISSN: 1350-7265
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- Citations: 50
Cont R, Larrard AD, 2011, Price dynamics in a Markovian limit order market, SIAM Journal on Financial Mathematics, Vol: 4, Pages: 1-25, ISSN: 1945-497X
We propose and study a simple stochastic model for the dynamics of a limitorder book, in which arrivals of market order, limit orders and ordercancellations are described in terms of a Markovian queueing system. Throughits analytical tractability, the model allows to obtain analytical expressionsfor various quantities of interest such as the distribution of the durationbetween price changes, the distribution and autocorrelation of price changes,and the probability of an upward move in the price, {\it conditional} on thestate of the order book. We study the diffusion limit of the price process andexpress the volatility of price changes in terms of parameters describing thearrival rates of buy and sell orders and cancelations. These analytical resultsprovide some insight into the relation between order flow and price dynamics inorder-driven markets.
Cont R, Kan YH, 2011, Dynamic Hedging of Portfolio Credit Derivatives, SIAM JOURNAL ON FINANCIAL MATHEMATICS, Vol: 2, Pages: 112-140, ISSN: 1945-497X
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- Citations: 19
Cont R, Lantos N, Pironneau O, 2011, A Reduced Basis for Option Pricing, SIAM JOURNAL ON FINANCIAL MATHEMATICS, Vol: 2, Pages: 287-316, ISSN: 1945-497X
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- Citations: 21
Cont R, Deguest R, Scandolo G, 2010, Robustness and Sensitivity Analysis of Risk Measurement Procedures, Quantitative Finance, Vol: 10, Pages: 593-606
Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ‘risk measure’ that summarizesthe risk of the portfolio. We define the notion of ‘risk measurement procedure’, which includesboth of these steps, and introduce a rigorous framework for studying the robustness of riskmeasurement procedures and their sensitivity to changes in the data set. Our results point to aconflict between the subadditivity and robustness of risk measurement procedures and showthat the same risk measure may exhibit quite different sensitivities depending on theestimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurementprocedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property.
Cont R, Fournie D-A, 2010, Change of variable formulas for non-anticipative functionals on path space, Journal of Functional Analysis, Vol: 259, Pages: 1043-1072
We derive a functional change of variable formula for non-anticipativefunctionals defined on the space of right continuous paths with left limits.The functional is only required to possess certain directional derivatives,which may be computed pathwise. Our results lead to functional extensions ofthe Ito formula for a large class of stochastic processes, includingsemimartingales and Dirichlet processes. In particular, we show the stabilityof the class of semimartingales under certain functional transformations.
Cont R, 2010, Model Calibration
<jats:title>Abstract</jats:title><jats:p>A derivative pricing model is said to be calibrated to a set of benchmark instruments if the value of these instruments, computed in the model, correspond to their market prices.<jats:italic>Model calibration</jats:italic>is the procedure of selecting model parameters in order to verify the calibration condition. Model calibration can be viewed as the<jats:italic>inverse problem</jats:italic>associated with the pricing of derivatives. In the theoretical situation where prices of call options are available for all strikes and maturities, the calibration problem can be explicitly solved using an inversion formula. In real situations, given a finite (and often sparse) set of derivative prices, model calibration is an ill‐posed problem whose solution often requires a<jats:italic>regularization</jats:italic>method. We discuss various—deterministic and stochastic—algorithms for solving them.</jats:p>
Cont R, 2010, Mandelbrot, Benoit
<jats:title>Abstract</jats:title> <jats:p>Benoit Mandelbrot, the founder of fractal geometry, has been, among numerous other contributions to fields ranging from mathematics to hydrology, an early contributor to the then‐nascent field of stochastic modeling in finance. Obsessed with the wild variability of financial market prices, he was the first to advocate the use of heavy‐tailed distributions and power laws, Lévy processes, and long‐range dependence for modeling market fluctuations.</jats:p>
CONT R, Stoikov S, Talreja R, 2010, A stochastic model for order book dynamics, Operations Research, Vol: 58, Pages: 549-563
We propose a continuous-time stochastic model for the dynamics of a limit order book. The model strikes a balance between three desirable features: it can be estimated easily from data, it captures key empirical properties of order book dynamics, and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on high-frequency observations of the order book and illustrate the results on data from the Tokyo Stock Exchange. Using simple matrix computations and Laplace transform methods, we are able to efficiently compute probabilities of various events, conditional on the state of the order book: an increase in the midprice, execution of an order at the bid before the ask quote moves, and execution of both a buy and a sell order at the best quotes before the price moves. Using high-frequency data, we show that our model can effectively capture the short-term dynamics of a limit order book. We also evaluate the performance of a simple trading strategy based on our results.
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