Imperial College London

ProfessorRamaCont

Faculty of Natural SciencesDepartment of Mathematics

Chair in Mathematical Finance
 
 
 
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Contact

 

+44 (0)20 7594 0802r.cont Website

 
 
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Location

 

806Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

88 results found

Cont R, Sirignano J, 2018, Universal features of price formation in financial markets: perspectives from Deep Learning, Publisher: SSRN

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a stock, as revealed through the order book, to subsequent variations in its market price. We assess the model by testing its out-of-sample predictions for the direction of price moves given the history of price and order flow, across a wide range of stocks and time periods. The universal price formation model is shown to exhibit a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific.

WORKING PAPER

Sirignano J, Cont R, 2018, Universal features of price formation in financial markets: perspectives from Deep Learning

Using a large-scale Deep Learning approach applied to a high-frequencydatabase containing billions of electronic market quotes and transactions forUS equities, we uncover nonparametric evidence for the existence of a universaland stationary price formation mechanism relating the dynamics of supply anddemand for a stock, as revealed through the order book, to subsequentvariations in its market price. We assess the model by testing itsout-of-sample predictions for the direction of price moves given the history ofprice and order flow, across a wide range of stocks and time periods. Theuniversal price formation model is shown to exhibit a remarkably stableout-of-sample prediction accuracy across time, for a wide range of stocks fromdifferent sectors. Interestingly, these results also hold for stocks which arenot part of the training sample, showing that the relations captured by themodel are universal and not asset-specific. The universal model --- trained on data from all stocks --- outperforms, interms of out-of-sample prediction accuracy, asset-specific linear and nonlinearmodels trained on time series of any given stock, showing that the universalnature of price formation weighs in favour of pooling together financial datafrom various stocks, rather than designing asset- or sector-specific models ascommonly done. Standard data normalizations based on volatility, price level oraverage spread, or partitioning the training data into sectors or categoriessuch as large/small tick stocks, do not improve training results. On the otherhand, inclusion of price and order flow history over many past observations isshown to improve forecasting performance, showing evidence of path-dependencein price dynamics.

WORKING PAPER

Teniente E, Weidlich M, 2018, Preface, Pages: V-VI, ISBN: 9783319740294

BOOK CHAPTER

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

© 2016 The Author(s) We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise ‘signal plus noise’ decomposition for regular functionals of an irregular path with non-vanishing quadratic variation, as a unique sum of a pathwise integral and a component with zero quadratic variation.

JOURNAL ARTICLE

Cont R, Gordy M, 2017, Special Issue: Monitoring Systemic Risk: Data, Models and Metrics, Statistics and Risk Modeling, Vol: 34, ISSN: 2193-1402

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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.

BOOK

Cont R, Duffie D, Glasserman P, Rogers C, Vega-Redondo Fet al., 2016, Preface to the special issue on systemic risk: Models and mechanisms, Operations Research, Vol: 64, Pages: 1053-1055, ISSN: 0030-364X

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

© 2015, Springer Science+Business Media New York. 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

Cont R, Wagalath L, 2016, Institutional investors and the dependence structure of asset returns, International Journal of Theoretical and Applied Finance, Vol: 19, ISSN: 0219-0249

© 2016 World Scientific Publishing Company. We propose a model of a financial market with multiple assets that takes into account the impact of a large institutional investor rebalancing its positions so as to maintain a fixed allocation in each asset. We show that feedback effects can lead to significant excess realized correlation between asset returns and modify the principal component structure of the (realized) correlation matrix of returns. Our study naturally links, in a quantitative manner, the properties of the realized correlation matrix - correlation between assets, eigenvectors and eigenvalues - to the sizes and trading volumes of large institutional investors. In particular, we show that even starting with uncorrelated "fundamentals", fund rebalancing endogenously generates a correlation matrix of returns with a first eigenvector with positive components, which can be associated to the market, as observed empirically. Finally, we show that feedback effects flatten the differences between the expected returns of assets and tend to align them with the returns of the institutional investor's portfolio, making this benchmark fund more difficult to beat, not because of its strategy but precisely because of its size and market impact.

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

REPORT

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

Arulkumaran N, Rhodes A, 2013, Critical illness in obstetrics. Preface.

BOOK CHAPTER

Arulkumaran N, Rhodes A, 2013, Critical illness in obstetrics. Preface.

BOOK CHAPTER

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

JOURNAL ARTICLE

Cont R, Deguest R, He XD, 2013, Loss-based risk measures, Statistics and Risk Modeling, Vol: 30, Pages: 133-167, ISSN: 2193-1402

Starting from the requirement that risk of financial portfolios should be measured in terms of 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 convex loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of the risk estimators associated with the family of loss-based risk measures: we provide a general criterion for the qualitative robustness of the risk estimators and compare this criterion with a sensitivity analysis of estimators based on influence functions. We find that the risk estimators associated with convex loss-based risk measures are not robust. © 2013, by Oldenbourg Wissenschaftsverlag, München, Germany, All rights reserved.

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

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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.

BOOK CHAPTER

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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