## Publications

75 results found

Blacque-Florentin PM, Cont R, Functional Itô calculus and martingale representation formula for integer-valued measures

We develop a calculus for functionals of integer-valued measures, whichextends the Functional It\^o calculus to functionals of Poisson random measuresin a pathwise sense. We show that smooth functionals in the sense of thispathwise calculus are dense in the space of square-integrable (compensated)integrals with respect to a large class of integer-valued random measures. As aconsequence, we obtain an explicit martingale representation formula for allsquare-integrable martingales with respect to the filtration generated by suchinteger-valued random measures. Our representation formula extends beyond thePoisson framework and allows for random and time-dependent compensators.

Cont R, Heidari M, Optimal rounding under integer constraints

Given real numbers whose sum is an integer, we study the problem of findingintegers which match these real numbers as closely as possible, in the sense ofL^p norm, while preserving the sum. We describe the structure of solutions forthis integer optimization problem and propose an algorithm with complexity O(Nlog N) for solving it. In contrast to fractional rounding and randomizedrounding, which yield biased estimators of the solution when applied to thisproblem, our method yields an exact solution which minimizes the relativerounding error across the set of all solutions for any value of p greater than1, while avoiding the complexity of exhaustive search. The proposed algorithmalso solves a class of integer optimization problems with integer constraintsand may be used as the rounding step of relaxed integer programming problems,for rounding real-valued solutions. We give several examples of applicationsfor the proposed algorithm.

Ananova A, Cont R, 2017, Pathwise integration with respect to paths of finite quadratic variation, *Journal de Mathématiques Pures et Appliquées*, Vol: 107, Pages: 737-757, ISSN: 0021-7824

Amini H, Cont R, Minca A, 2016, RESILIENCE TO CONTAGION IN FINANCIAL NETWORKS, *MATHEMATICAL FINANCE*, Vol: 26, Pages: 329-365, ISSN: 0960-1627

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- Citations: 16

CONT RAMA, WAGALATH LAKSHITHE, 2016, INSTITUTIONAL INVESTORS AND THE DEPENDENCE STRUCTURE OF ASSET RETURNS, *International Journal of Theoretical and Applied Finance*, Vol: 19, Pages: 1650010-1650010, ISSN: 0219-0249

Cont R, Bally V, Caramellino L, 2016, Stochastic Integration by Parts and Functional Itô Calculus, Publisher: Birkhäuser, ISBN: 978-3-319-27128-6

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012).The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes.Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations.This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to practitioners in mathematical finance.

Cont R, Kukanov A, 2016, Optimal order placement in limit order markets, *Quantitative Finance*, Vol: 17, Pages: 21-39, ISSN: 1469-7696

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the structure oftransaction fees and rebates across exchanges. We propose a quantitativeframework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows to study how the interplay between the state of order books, the fee structure, order flow properties and preferences of a trader determine the optimal placement decision. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general problem of order placement across multiple exchanges, we propose a stochastic algorithm for computing the optimal policy and study the sensitivity of the solution to various parameters using a numerical implementation of the algorithm.

Cont R, Lu Y, 2016, Weak approximation of martingale representations, *STOCHASTIC PROCESSES AND THEIR APPLICATIONS*, Vol: 126, Pages: 857-882, ISSN: 0304-4149

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- Citations: 2

Cont R, Minca A, 2016, Credit default swaps and systemic risk, *Annals of Operations Research*, Vol: 247, Pages: 523-547, ISSN: 0254-5330

Cont R, Wagalath L, 2016, Risk management for whales, *Risk -London- Risk Magazine Limited-*, ISSN: 0952-8776

We propose framework for modeling portfolio risk which integrates market risk with liquidation costs which may arise in stress scenarios. Our model provides a systematic method for computing liquidation-adjusted risk measures for a portfolio. Calculation of Liquidation-adjusted VaR (LVaR) for sample portfolios reveals a substantial impact of liquidation costs on portfolio risk for portfolios with large concentrated positions.

Cont R, 2015, The end of the waterfall: Default resources of central counterparties, *Journal of Risk Management in Financial Institutions*, Vol: 8, Pages: 365-389, ISSN: 1752-8887

Central counterparties (CCPs) have become pillars of the new global financial architecture following the financial crisis of 2008. The key role of CCPs in mitigating counterparty risk and contagion has in turn cast them as systemically important financial institutions whoseeventual failure may lead to potentially serious consequences for financial stability, andprompted discussions on CCP risk management standards and safeguards for recovery andresolutions of CCPs in case of failure. We contribute to the debate on CCP default resourcesby focusing on the incentives generated by the CCP loss allocation rules for the CCP and itsmembers and discussing how the design of loss allocation rules may be used to align theseincentives in favor of outcomes which benefit financial stability. After reviewing theingredients of the CCP loss waterfall and various proposals for loss recovery provisions forCCPs, we examine the risk management incentives created by different ingredients in theloss waterfall and discuss possible approaches for validating the design of the waterfall.We emphasize the importance of CCP stress tests and argue that such stress tests need toaccount for the interconnectedness of CCPs through common members and cross-marginagreements. A key proposal is that capital charges on assets held against CCP Default Fundsshould depend on the quality of the risk management of the CCP, as assessed throughindependent stress tests.

Cont R, Bentata A, 2015, Forward equations for option prices in semimartingale models, *Finance and Stochastics*, Pages: 617-651, ISSN: 1432-1122

We derive a forward partial integro-differential equation for prices of calloptions in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. A uniquenesstheorem is given for the solutions of this equation. This result generalizesDupire's forward equation to a large class of non-Markovian models with jumps.

Cont R, Kokholm T, 2014, Central clearing of OTC derivatives: Bilateral vs multilateral netting, *Statistics & Risk Modeling*, Vol: 31, ISSN: 2193-1402

Cont R, Kukanov A, Stoikov S, 2014, The Price Impact of Order Book Events, *JOURNAL OF FINANCIAL ECONOMETRICS*, Vol: 12, Pages: 47-88, ISSN: 1479-8409

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- Citations: 32

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, Deguest R, 2013, EQUITY CORRELATIONS IMPLIED BY INDEX OPTIONS: ESTIMATION AND MODEL UNCERTAINTY ANALYSIS, *MATHEMATICAL FINANCE*, Vol: 23, Pages: 496-530, ISSN: 0960-1627

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- Citations: 5

Cont R, Deguest R, He XD, 2013, Loss-based risk measures, *Statistics & Risk Modeling*, Vol: 30, ISSN: 2193-1402

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

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- Citations: 39

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

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- Citations: 17

Cont R, Minca A, 2013, RECOVERING PORTFOLIO DEFAULT INTENSITIES IMPLIED BY CDO QUOTES, *MATHEMATICAL FINANCE*, Vol: 23, Pages: 94-121, ISSN: 0960-1627

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- Citations: 12

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, Wagalath L, 2013, RUNNING FOR THE EXIT: DISTRESSED SELLING AND ENDOGENOUS CORRELATION IN FINANCIAL MARKETS, *MATHEMATICAL FINANCE*, Vol: 23, Pages: 718-741, ISSN: 0960-1627

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- Citations: 15

Cont R, de Larrard A, 2013, Price Dynamics in a Markovian Limit Order Market, *SIAM JOURNAL ON FINANCIAL MATHEMATICS*, Vol: 4, Pages: 1-25, ISSN: 1945-497X

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- Citations: 30

Amini H, Cont R, Minca A, 2012, Stress testing the resilience of financial networks, *International Journal of Theoretical and Applied Finance*, Vol: 15, ISSN: 0219-0249

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 World Scientific Publishing Company.

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.

Bentata A, Cont R, 2012, Short-time asymptotics for marginal distributions of semimartingales

We study the short-time asymptotics of conditional expectations of smooth andnon-smooth functions of a (discontinuous) Ito semimartingale; we compute theleading term in the asymptotics in terms of the local characteristics of thesemimartingale. We derive in particular the asymptotic behavior of call optionswith short maturity in a semimartingale model: whereas the behavior of\textit{out-of-the-money} options is found to be linear in time, the short timeasymptotics of \textit{at-the-money} options is shown to depend on the finestructure of the semimartingale.

Cont R, 2012, Preface, *Frontiers in Quantitative Finance: Volatility and Credit Risk Modeling*

Cont R, Jessen C, 2012, Constant Proportion Debt Obligations (CPDOs): modeling and risk analysis, *QUANTITATIVE FINANCE*, Vol: 12, Pages: 1199-1218, ISSN: 1469-7688

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- Citations: 3

Cont R, Larrard AD, 2012, Order book dynamics in liquid markets: limit theorems and diffusion approximations

We propose a model for the dynamics of a limit order book in a liquid marketwhere buy and sell orders are submitted at high frequency. We derive afunctional central limit theorem for the joint dynamics of the bid and askqueues and show that, when the frequency of order arrivals is large, theintraday dynamics of the limit order book may be approximated by a Markovianjump-diffusion process in the positive orthant, whose characteristics areexplicitly described in terms of the statistical properties of the underlyingorder flow. This result allows to obtain tractable analytical approximationsfor various quantities of interest, such as the probability of a price increaseor the distribution of the duration until the next price move, conditional onthe state of the order book. Our results allow for a wide range ofdistributional assumptions and temporal dependence in the order flow and applyto a wide class of stochastic models proposed for order book dynamics,including models based on Poisson point processes, self-exciting pointprocesses and models of the ACD-GARCH family.

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