07 Oct

Paolo Guasoni, “Stochastics and market frictions: An overview”

Wednesday October 19 2016
15:00
Scuola Normale Superiore
Aula Mancini

Paolo Guasoni
Dublin City University

Abstract

In the last decades Finance theory has benefited from its affinity with the theory of Stochastic Processes, in particular martingales and stochastic control. These theories have subtly influenced the development of Finance along the path in which they were most successful, thereby disregarding market frictions such as trading costs, incomplete information, and incentives. This talk outlines recent developments in stochastic methods for models with frictions, how they undermine several tenets of portfolio theory, and how they stimulate new approaches to stochastic control. The talk concludes with a mention of frictions arising from mortality and operational risk.

07 Oct

Franco Flandoli, “From Clinical Oncology to scaling limits”

Thursday October 13 2016
16:30
Scuola Normale Superiore
Aula Bianchi

Franco Flandoli
University of Pisa

Abstract

A problem of Clinical Oncology will be shortly introduced and its modelling based on differential equations and statistical elements will be illustrated. The above modelling is the simplest possible, for a first investigation. In order to make it more realistic, two natural mathematical elements are particle systems and Partial Differential Equations. It is here that scaling limit questions arise. As an example, two problems will be described: a first, partially solved one, connecting proliferating particles with the so called Fisher-KPP equations; and a second one, widely open, about the features, potentially of KPZ type, of the proliferating boundary.

07 Oct

Damiano Brigo, “Intrinsic stochastic differential equations as jets: theory and applications”

Monday October 10 2016
16:00
Scuola Normale Superiore
Aula Mancini

Damiano Brigo
Imperial College, London

Abstract

We quickly introduce Stochastic Differential Equations (SDEs) and their two main calculi: Ito and Stratonovich. Briefly recalling the definition of jets, we show how Ito SDEs on manifolds may be defined intuitively as 2-jets of curves driven by Brownian motion and show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can lead to intuitive and intrinsic representations of Ito SDEs, presenting several plots and numerical examples. We give a new geometric interpretation of the Ito-Stratonovich transformation in terms of the 2-jets of curves induced by consecutive vector flows. We interpret classic quantities and operators in stochastic analysis geometrically. We hint at applications of the jet representation to i) dimensionality reduction by projection of infinite dimensional stochastic partial differential equations (SPDEs) onto finite dimensional submanifolds for the filtering problem in signal processing, and ii) consistency between dynamics of interest rate factors and parametric form of term structures in mathematical finance. We explain that the mainstream choice of Stratonovich calculus for stochastic differential geometry is not optimal when combining geometry and probability, using the mean square optimality of projection on submanifolds as a fundamental
application.

05 Sep

Gabriele La Spada, “Competition, reach for yield, and money market funds”

Tuesday September 13 2016
11:00
Scuola Normale Superiore
Aula Bianchi

Gabriele La Spada
Federal Reserve Bank of New York

Abstract

Do asset managers reach for yield because of competitive pressures in a low-rate environment? I propose a tournament model of money market funds (MMFs) to study this issue. When funds care about relative performance, an increase in the risk premium leads funds with lower default costs to increase risk-taking, while funds with higher default costs decrease risk-taking. Without changes in the premium, lower risk-free rates reduce the risk-taking of all funds. I show that these predictions are consistent with MMF risk-taking during the 2002-08 period and that rank-based performance is indeed a key determinant of money flows to MMFs.

05 Jul

Anirban Chakraborti, “Sectoral co-movements and volatilities of Indian stock market: An analysis of daily returns data”

Wednesday July 6 2016
11:30
Scuola Normale Superiore
Aula Fermi

Anirban Chakraborti
Jawaharlal Nehru University, New Delhi, India

Abstract

First, we review the techniques of decomposing aggregate correlation matrices to study co-movements in financial data. We apply the techniques to daily return time series from the Indian stock market. Secondly, we use the multi-dimensional scaling methods to visualise the dynamic evolution of the stock market. This method helps to differentiate sectors in the market in the form of clusters. The other objective is to detect periods of instability in the market. Finally, our aim is to decompose the aggregate volatility into sectoral components. Such a mapping allows us to study impact of different sectors on the market behaviour and vice versa.

27 Jun

Marc Mezard, “Boole, Shannon, and the challenge of data science: A statistical physics perspective”

Wednesday June 29 2016
15:00
Scuola Normale Superiore
Aula Azzurra

Marc Mezard
École Normale Supérieure, Paris

Abstract

In 1854, in his treatise on the Laws of Nature, George Boole had stated a clear goal : « to investigate the fundamental laws of those operations of the mind by which reasoning is performed ». This led him to study the foundations of logic and of probabilities. A century later, Claude Shannon opened the way to a mathematical understanding of information and of its communication. The fields of research initiated by these two giants play a major role in contemporary science, and in particular in the handling of large amounts of data, and in the extraction of information out of these data. However, in large-size problems, collective phenomena of the type studied in statistical physics, like phase transitions, start to play a major role. This talk will study the importance of phase transitions in some core problems of Boolean logics and of information theory, with a special focus on the importance of glassy phases.

10 Mar

Jiro Akahori, “Ito atlas and around”

Thursday March 17 2016
13:00
Scuola Normale Superiore
Aula Mancini

Jiro Akahori
Ritsumeikan University, Shiga, Japan

Abstract

I will discuss Malliavin’s canonic diffusion on the circle and related topics including a link to the Fourier method.

01 Mar

Christian Brownlees, “Community Detection in Partial Correlation Networks”

Friday March 11 2016
10:30
Scuola Normale Superiore
Aula Bianchi

Christian Brownlees
Universitat Pompeu Fabra, Barcelona

Abstract

In this work we propose a community detection algorithm for partial correlation networks. We assume that the variables in the network are partitioned into communities. The presence of nonzero partial correlation between two variables is determined by a Bernoulli trial whose probability depends on whether the variables belong to the same community or not. The community partition is assumed to be unobserved and the goal is to recover it from a sample of observations. To tackle this problem we introduce a community detection algorithm called Blockbuster. The algorithm detects communities by applying k-means clustering to the eigenvectors corresponding to the largest eigenvalues of the sample covariance matrix. We study the properties of the procedure and show that Blockbuster consistently detects communities when the network dimension and the sample size are large. The methodology is used to study real activity clustering in the United States.

22 Jan

Maria Rita Iacò, “Copulas in uniform distribution, optimal transport and finance”

Tuesday January 26 2016
13:00
Scuola Normale Superiore
Aula Bianchi

Maria Rita Iacò
Technische Universität Graz

Abstract

The aim of this talk is to give an overview of some results obtained in the framework of copulas. The last ones got considerable attention in the last years, especially in finance where they are used to perform stress-tests and robustness checks in situations of extreme downside events. However, soon after the global financial crisis of 2007–2008, several people argued that copulas, together with other mathematical instruments, have been one of the main causes of the market crashes.
During this talk I will describe some problems in uniform distribution and finance which were described by using a copula approach. Since we will deal with an optimisation problem, we will finally show how this problem can be perfectly embedded in the general theory of optimal transport.

16 Dec

Nicola Fusari, “Pricing Short-Term Market Risk: Evidence from Weekly Options”

Thursday December 17 2015
13:00
Scuola Normale Superiore
Aula Bianchi

Nicola Fusari
Johns Hopkins Carey Business School

Abstract
We study short-term market risks implied by weekly S&P 500 index options. The introduction of weekly options has dramatically shifted the maturity profile of traded options over the last five years, with a substantial proportion now having expiry within one week. Economically, this reflects a desire among investors for actively managing their exposure to very short-term risks. Such short-dated options provide an easy and direct way to study market volatility and jump risks. Unlike longer-dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment, i.e., changes in the investment opportunity set. Adopting a novel general semi-nonparametric approach, we uncover variation in the shape of the negative market jump tail risk which is not spanned by market volatility. Incidents of such tail shape shifts co- incide with serious mispricing of standard parametric models for longer-dated options. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events on the market that are not always “signaled” by the level of market volatility and elude standard asset pricing models.

Joint work with Torben G. Andersen AND Viktor Todorov.

04 Nov

Domenico Di Gangi, “Assessing Systemic Risk Due to Fire Sales Spillover Through Maximum Entropy Network Reconstruction”

Wednesday November 11 2015
13:00
Scuola Normale Superiore
Aula Bianchi

Domenico Di Gangi
Department of Physics, University of Pisa,

Abstract
Assessing systemic risk in financial markets is of great importance but it often requires data that are unavailable or available at a very low frequency. For this reason, systemic risk assessment with partial information is potentially very useful for regulators and other stakeholders. In this paper we consider systemic risk due to fire sales spillover and portfolio rebalancing by using the risk metrics defined by Greenwood et al. (2015). By using the Maximum Entropy principle we propose a method to assess aggregated and single bank’s systemicness and vulnerability and to statistically test for a change in these variables when only the information on the size of each bank and the capitalization of the investment assets are available. We prove the effectiveness of our method on 2001-2013 quarterly data of US banks for which portfolio composition is available.

Please find the preprint at the url:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2639178

01 Sep

Frederic Abergel, “Limit order books driven by Hawkes processes”

Tuesday September 8 2015
11:30
Scuola Normale Superiore
Aula Bianchi

Frederic Abergel
CMAP, Ecole Centrale-Supelec, Paris

Abstract
Hawkes processes offer an interesting toolbox to model the interplay between different agents on financial markets. This talk will present some recent results on Hawkes process-driven limit order books, focusing on questions of ergodicity and asymptotic behaviour. Some numerical simulations will also be commented.

02 Jul

Roberto Casarin, “Bayesian Nonparametric Calibration and Combination of Predictive Distributions”

Thursday July 2 2015
13:00
Scuola Normale Superiore
Aula Bianchi

Roberto Casarin
Department of Economics – Università Ca’ Foscari di Venezia

Abstract
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights. Building on the work of Ranjan and Gneiting (2010) and Gneiting and Ranjan (2013), we use infinite beta mixtures for the calibration. The proposed Bayesian nonparametric approach takes advantage of the flexibility of Dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions. The inference procedure is based on Gibbs sampling and allows accounting for uncertainty in the number of mixture components, mixture weights, and calibration parameters. The weak posterior consistency of the Bayesian nonparametric calibration is provided under suitable conditions for unknown true density. We study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of daily S&P returns and daily maximum wind speed at the Frankfurt airport. Joint work with Federico Bassetti and Francesco Ravazzolo.

06 May

Massimiliano Caporin, “The impact of network connectivity on factor exposures, asset pricing and portfolio diversification”

Wednesday May 6 2015
13:00
Scuola Normale Superiore
Aula Bianchi

Massimiliano Caporin
Department of Economics and Management “Marco Fanno” – Università di Padova

Abstract
The need for understanding the propagation mechanisms behind the recent financial crises lead the increased interest for works associated with asset interconnections. In this framework, network-based methods have been used to infer from data the linkages between institutions. In this paper, we elaborate on this and make a step forward by introducing network linkages into linear factor models. Networks are used to infer the exogenous and contemporaneous links across assets, and impacts on several dimensions: network exposures act as in inflating factor for systematic exposure to common factors with implications for pricing; the power of diversication is reduced by the presence of network connections; in the presence of network links a misspecied traditional linear factor model provides residuals that are correlated and heteroskedastic. We support our claims with an extensive simulation experiment. Joint work with Monica Billio, Roberto Panzica, and Loriana Pelizzon.

14 Apr

Vladimir Filimonov, “Exogenous versus endogenous dynamics in the price discovery process”

Thursday April 14  2015
13.00
Scuola Normale Superiore
Aula Russo

Vladimir Filimonov
ETH Zurich, Switzerland

Abstract
The talk discusses feedback mechanisms in the price discovery process: from high-frequency market-making and algorithmic trading to long-term behavioral mechanisms. In order to quantify short-term endogeneity we propose an index derived by calibrating the self-excited Hawkes model on empirical time series of trades. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact and the the feedback look by which past trading activity may influence future trading activity. Technically known in the mathematical literature on branching processes as the branching ratio, the reflexivity index is defined as an average ratio of the number of price moves that are due to endogenous interactions to the total number of all price changes, which also include exogenous events. This index quantifies at the same time both “criticality” of the system (stability and susceptibility to large shocks) and its “efficiency” (in sense of the Efficient Market Hypothesis). We calibrate our measure on several financial and commodity futures markets and documented presence of “micro” regime shifts that coincided with “macro” changes in trading methods or sentiments of investors. Finally we relate our analysis to recent evidences of an intrinsic “criticality” of price discovery and make a bridge between short- and long-memory models.

10 Apr

Joao da Gama Batista, “Sudden trust collapse in networked societies”

Friday April 10  2015
13.00
Scuola Normale Superiore
Aula Bianchi

Joao da Gama Batista
Laboratoire de mathématiques appliquées aux systèmes – École Centrale de Paris

Abstract
Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The basic assumption of our model is that whereas trustworthiness begets trustworthiness, panic also begets panic, in the sense that a small decrease in trustworthiness may be amplified and ultimately lead to a sudden and catastrophic drop of collective trust. We show, using both numerical simulations and mean-field analytic arguments, that there are extended regions of the parameter space where two equilibrium states coexist: a well-connected network where global confidence is high, and a poorly connected network where global confidence is low. In these coexistence regions, spontaneous jumps from the well-connected state to the poorly connected state can occur, corresponding to a sudden collapse of trust that is not caused by any major external catastrophe. In large systems, spontaneous crises are replaced by history dependence: whether the system is found in one state or in the other essentially depends on initial conditions.

01 Apr

Tommaso Colozza, “Supply of public debt and demand for risk premia: a Minskian approach to credit risk”

Wednesday April 1  2015
13.00
Scuola Normale Superiore
Aula Mancini

Tommaso Colozza
Dipartimento di Statistica e Matematica Applicata all’Economia – Università di Pisa

Abstract
Financial stability of EMU countries is managed by policy makers through several key macroeconomic indicators; the market instead monitors creditworthiness with credit risk premia embedded in sovereign yields. A demand-supply approach solves this duality: in a Minskian framework, positive inelastic shifts in debt-to-GDP ratio due to widespread macro-financial distress may lower risk appetites of lenders and increase risk premia, up to default. Time-variating risk appetites justify statistical relevance of debt-to-gdp variation on yields levels; if conveniently decomposed, debt velocity allows also to imply a default probability measure comparable to standard CDS-implied measures.

20 Mar

Roberto Renò, “Multi-jumps”

Friday March 20  2015
13.00
Scuola Normale Superiore
Aula Bianchi

Roberto Renò
Dipartimento di Economia Politica e Statistica – Università di Siena

Abstract
The simultaneous occurrence of jumps in several stocks (multi-jumps) can be associated to major nancial news, is correlated with sudden spikes of the variance risk premium, and determines an increase in the stock variances and correlations which signicantly deteriorates the diversication potential of asset allocation. The latter evidence implies a reduction in the demand of stocks by an aware risk-averse investor. These facts can be easily overlooked by the usage of standard univariate jump statistics, which just lack sucient power. They are instead revealed in a clearly cut way by using a novel test based on smoothed estimators of the integrated variance ofindividual stocks.

Joint work with Massimiliano Caporin and Aleksey Kolokolov.

19 Feb

Roberto Baviera, “A thermometer for financial instability in the euro area economy and the role of carry trade”

Thursday February 19  2015
13.00
Scuola Normale Superiore
Aula Bianchi

Roberto Baviera
Financial Engineering, Dipartimento di Matematica -Politecnico di Milano

Abstract

This study suggests a simple financial instability indicator for the euro area economy.
It works as a discrete thermometer with three possible outcomes depending on the severity of the crisis. This indicator is based on the specific shape of the credit term structure for the two main peripheral countries in the area. The paper discusses how some key features of term structure are linked to government debt carry trade.
In order to assess the performance of the proposed market-based indicator, the paper shows how the identified episodes of financial turmoil are related with the timing and the intensity of unconventional measures in the euro area.

04 Nov

Fabio Caccioli, “Instabilities in portfolio optimization and regularization”

Tuesday November 4  2014
13.00
Scuola Normale Superiore
Aula Bianchi

Fabio Caccioli
University College London

Abstract

We consider the problem of portfolio selection in presence of market impact, and we show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show that the impact function determines which regularizer is to be used, and we characterize the typical behavior of the optimal portfolio in the limit of large portfolio sizes for the case of Expected Shortfall.

10 Sep

Xuezhong He, “Optimality of momentum and reversal”

Wednesday September 10  2014
13.00
Scuola Normale Superiore
Aula Bianchi

Xuezhong He
University of Technology – Sydney (Australia)

Abstract

We develop a continuous-time asset price model to capture short-run momentum and long-run reversal. By studying a dynamic asset allocation problem, we derive the optimal investment strategy in closed form and show that the combined momentum and reversal strategies are optimal. We then estimate the model to the S&P 500 and demonstrate that, by taking the timing opportunity with respect to trend in return and market volatility, the optimal strategies outperform not only pure momentum and pure mean reversion strategies, but also the market index and time series momentum strategy. Furthermore we show that the optimality also holds to the out-of-sample tests and short-sale constraints and the out performance is immune to market states, investor sentiment and market volatility.

07 Apr

Paolo Porcedda, “Asimmetrie informative e selezione avversa nella gestione del portafoglio creditizio nell’esperienza di un primario istituto creditizio italiano”

Monday April 7  2014
13.00
Scuola Normale Superiore
Aula Bianchi

Paolo Porcedda
UniCredit Bank

Abstract

Alimentata dalle pressioni esercitate dalle autorità di vigilanza bancaria a seguito dell’introduzione della nuova normativa regolamentare (cd Basilea 2), nei primi anni 2000 i principali istituti di credito delle economie avanzate cercarono di dotarsi di sistemi centralizzati di misurazione della probabilità di default delle controparti affidate fondati su modelli statistici, in alcuni casi anche molto complessi. Il salto “culturale” comportato da tale riassetto organizzativo, con le implicazioni che ne sono derivate in termini di pratiche decisionali e sistemi di misurazione delle performance aziendali e relativa incentivazione, potrebbe essere tra le cause dei problemi di esigibilità dei prestiti riscontrati negli anni più recenti.
Secondo la nostra tesi, infatti, i profondi cambiamenti causati da tali ristrutturazioni nei processi di valutazione ed erogazione del credito non hanno, da un lato, tenuto in piena considerazione gli effetti dell’asimmetria informativa venutasi a creare con il nuovo modello organizzativo (risk management accentrato, che “cala” le proprie valutazioni sulla rete distributiva che eroga i prestiti) e ciò ha portato ad un tipico paradosso di “principal-agent” non facilmente risolvibile con le sole soluzioni già proposte nella
letteratura esistente sull’argomento. Dall’altro, sono stati sottovalutati i problemi di selezione avversa che i modelli quantitativi di misurazione del merito di credito implicano se applicati senza gli adeguati correttivi.

27 Feb

Emmanuel Bacry, “Hawkes process and applications”

Thursday February 27  2014
13.00
Scuola Normale Superiore
Aula Bianchi

Emmanuel Bacry
CMAP, UMR 7641 CNRS, Ecole Polytechnique, France

Abstract

Hawkes processes are point self-exciting point processes particularly well suited for applications. Introduced in the 70s, that have been used in very various domaines such as high-frequency financial time-series modeling or viral diffusion in social networks.
After describing how they are defined and their main properties, we shall discuss some problems linked to parametric estimations (in high dimensions) as well as non parametric estimations. We will present several applications.

09 Jan

Youngna Choi, “Financial Instability Contagion: a Dynamical Systems Approach”

Thursday January 9  2014
13.00
Scuola Normale Superiore
Aula Bianchi

Youngna Choi
Montclair State University

Abstract

We build a multi-agent dynamical system for the global economy to investigate and analyze financial crises. The agents are large aggregates of a subeconomy, and the global economy is a collection of subeconomies. We use well-known theories of dynamical systems to represent a financial crisis as propagation of a negative shock on wealth due the breakage of a financial equilibrium. We first extend the framework of the market instability indicator, an early warning signal defined for a single economy as the spectral radius of the Jacobian matrix of the wealth dynamical system. Then, we formulate a quantitative definition of instability contagion in terms thereof. Finally, we analyze the mechanism of instability contagion for both single and multiple economies. Our contribution is to provide a methodology to quantify and monitor the level of instability in sectors and stages of a structured global economic model and how it may propagate between its components.

07 Oct

Emilio Barucci, “Does a countercyclical buffer affect bank management?”

Monday October 7  2013
13.00
Scuola Normale Superiore
Aula Bianchi

Emilio Barucci
Politecnico di Milano

Abstract

We analyze the effect of the countercyclical capital buffer, as provided by the Basel III regulation, on bank management.
The goal of the regualtion is to reduce bank leverage and excess risk taking.
We show that the countercyclical buffer increases the incentive for equity holders to take excess risk investing in assets with high drift rate independently of their volatility. Therefore, the buffer induces risk-shifting incentives, however it is effective in reducing the bank size and its leverage but the magnitudo is rather small.

Joint work with Luca Del Viva, ESADE Business School

04 Jun

Ying Chen, “Filtering Asynchronous High Frequency Data”

Tuesday June 4  2013
13.00
Scuola Normale Superiore
Aula Bianchi

Ying Chen
Department of Statistics & Applied Probability – National University of Singapore

Abstract

We develop a synchronizing technique for irregularly spaced and asynchronous high frequency data. The technique learns from the dependence structure of raw data and iteratively recovers the unobserved values of the synchronous series at high sampling frequency.
The numerical results illustrate the performance of the proposed technique and compared to the conventional techniques — Previous Tick technique and Refresh Time technique. The proposed technique provides good performance in terms of accuracy and feature.
Moreover, a realized covariance estimator is constructed by incorporating the synchronized technique. We compare the feature of the estimator with several alternative estimators.

22 May

Matthieu Cristelli, “A New Metrics for Country Fitness and Product Complexity”

Wednesday May 22  2013
13.00
Scuola Normale Superiore
Aula Bianchi

Matthieu Cristelli
ISC-CNR, Institute for Complex Systems –
Department of Physics, “Sapienza” University

Abstract

Classical economic theories prescribe specialization of countries industrial production. Inspection of the country databases of exported products shows that this is not the case: successful countries are extremely diversified, in analogy with biosystems evolving in a competitive dynamic environment. The challenge is assessing quantitatively the non-monetary and non-income based competitive advantage of diversification which represents the hidden potential for development and growth. In a series of recent works [1,2] we develop a new statistical approach based on coupled non-linear maps, whose fixed point defines a new metrics for the country Fitness and product Com-plexity. The idea underlying such an approach is that the intangible features determining the competitiveness of a country can be quantified by properly measuring what a country exports. We show that a non-linear iteration is necessary to bound the complexity of products by the fitness of the less competitive countries exporting them. Given the paradigm of economic complexity, the correct and simplest approach to measure the competitiveness of countries is the one presented in this work.The two metrics allow to define a new kind of fundamental analysis of the hidden growth potential of countries. It is possible to compare non-monetary factors of fitness and complexity with measures of economic intensity such as the countries GDP per capita. We argue that this comparison is informative on the growth potential of countries. As an example, countries that show both a high fitness and a high complexity, but a low GDP per capita, are very likely to strongly boost their income in the next years. From preliminary analysis with growth data from 1995 to 2010, it is possible to see that results well reflect what occurred in the real world over that period.

06 Mar

Fulvio Corsi, “When Micro Prudence increases Macro Risk: The Destabilizing Effects of Financial Innovation, Leverage, and Diversification”

Wednesday March 6 2013
13:00
Scuola Normale Superiore
Aula Mancini

Fulvio Corsi
Scuola Normale Superiore

Abstract
By exploiting basic common practice accounting and risk management rules, we propose a simple analytical dynamical framework to investigate the effects of micro- prudential changes on macro-prudential outcomes. Specifically, we study the consequence of the introduction of a financial innovation that allow reducing the cost of portfolio diversification in a financial system populated by financial institutions having capital requirements in the form of VaR constraint and following standard mark-to- market and risk management rules. We provide a full analytical quantification of the multivariate feedback effects between investment prices and bank behavior induced by portfolio rebalancing in presence of asset illiquidity and show how changes in the constraints of the bank portfolio optimization endogenously drive the dynamics of the balance sheet aggregate of financial institutions and, thereby, the availability of bank liquidity to the economic system and systemic risk. The model shows that when financial innovation reduces the cost of diversification below a given threshold, the strength (due to higher leverage) and coordination (due to similarity of bank portfolios) of feed- back effects increase, triggering a transition from a stationary dynamics of price returns to a non stationary one characterized by steep growths (bubbles) and plunges (bursts) of market prices.

05 Mar

Federico Poloni and Giacomo Sbrana, “Estimating Econometric Models through Matrix Equations”

Tuesday March 5  2013
13.00
Scuola Normale Superiore
Aula Bianchi

Federico Poloni
Dipartimento di Informatica – Università di Pisa
Giacomo Sbrana
Rouen Business School

Abstract

We present an algorithm to estimate the parameters of multivariate ARMA, GARCH and stochastic volatility models. The approach is based on a moment estimator; a similar approach has already been suggested in literature for univariate GARCH but its generalization to multivariate models requires some more linear algebra machinery, especially in the field of matrix equations.
The resulting estimator is extremely fast to compute, in comparison to maximum-likelihood approaches. We also discuss methods to regularize and improve this estimate.

29 Jan

Marco Bianchetti, “Consistent No-Arbitrage Derivatives’ Pricing Including Funding And Collateral”

Tuesday January 29 2013
13:00
Scuola Normale Superiore
Aula Bianchi

Marco Bianchetti
Intesa Sanpaolo

Abstract
We revisit the problem of general no-arbitrage pricing of derivatives including the funding component. We show that, by adopting the no-arbitrage approach based on replication, PDE, and Feynman-Kac theorem, an appropriate treatment of the self-financing conditions allows straightforward and consistent proofs of the relevant pricing formulas covering a broad range of cases. In particular, we firstly recover the basic results for single currency funding of derivatives including, step by step, perfect or partial collateral, repo, and dividends. Next, we generalize the analysis to the case of multiple currency funding, and we examine the special case of interest rate derivatives. These results are useful to provide a simple and consistent framework of modern pricing formulas, fostering a broader understanding of the current market practice of CSA discounting, and to set solid theoretical grounds supporting further generalizations to include other risk factors, counterparty risk (CVA and DVA) in particular.
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06 Nov

Marko Weber, “Dynamic Trading Volume”

Tuesday November 6 2012
13:00
Scuola Normale Superiore
Aula Bianchi

Marko Weber
Dublin City University and Scuola Normale Superiore Pisa

Abstract
We derive the process followed by trading volume, in a market with finite depth and constant investment opportunities, where a representative investor, with a long horizon and constant relative risk aversion, trades a safe and a risky asset. Trading volume approximately follows a Gaussian, mean-reverting diffusion, and increases with depth, volatility, and risk aversion. The model generates an endogenous ban on leverage and short-selling. Joint work with Paolo Guasoni.
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24 Jul

Bence Toth, “Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets”

Tuesday July 24 2012
12:00
Scuola Normale Superiore
Aula Bianchi

Bence Toth
Capital Fund Management, Paris, France

Abstract
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and vanishes around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the “square-root” impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.

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18 Jul

James G. M. Gatheral, “Arbitrage-free SVI volatility surfaces”

Wednesday July 18 2012
13:00
Scuola Normale Superiore
Aula 2

James G. M. Gatheral
Baruch College, The City University of New York

Abstract
In this talk we motivate the widely-used SVI (“stochastic volatility inspired”) parameterization of the implied volatility surface and show how to calibrate it in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data. We conclude by suggesting that SVI might one day replace SABR as the implied volatility parameterization of choice.
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13 Jul

James G. M. Gatheral, “Optimal Order Execution”

Friday July 13 2012
11:30
Scuola Normale Superiore
Aula Bianchi

James G. M. Gatheral
Baruch College, The City University of New York

Abstract
We review various models of market impact. We use variational calculus to derive optimal execution strategies, noting that in many conventional models, static strategies are dynamically optimal. We then present a model in which the optimal strategy does depend on the stock price and derive an explicit closed-form solution for this strategy by solving the HJB equation. We discuss price manipulation, indicating modeling choices for which this is unlikely to be a problem. We present empirical evidence and some heuristic arguments justifying the well-known square-root formula for market impact. Assuming price dynamics that are consistent with the square-root formula, we suggest likely properties of optimal execution strategies.
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19 Jun

Enrico Scalas, “Intraday Option Pricing”

Tuesday June 19 2012
11:00
Scuola Normale Superiore
Aula Bianchi

Enrico Scalas
DISIT, Università del Piemonte Orientale and Basque Center for Applied Mathematics, Bilbao

Abstract
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools.
Reference: Scalas E. and Politi M. (2012). A parsimonious model for intraday European option pricing. Economics Discussion Papers, No 2012-14, Kiel Institute for the World Economy.

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13 Apr

Robert Almgren, “Quantitative Problems in Optimal Execution”

Friday April 13 2012
13:00
Scuola Normale Superiore
Aula Bianchi

Robert Almgren
New York University and Quantitative Brokers

Abstract
Execution of large transactions so as to minimize market impact and trading costs is a very important aspect of modern financial markets. We will give an overview of the quantitative tools that are used to approach this problem and how they are implemented in practice. These include balance of risk and reward, design of optimal trajectories, and the mathematical issues that arise in optimal response to time-varying liquidity and volatility.

15 Feb

Roberto Renò, “Price and Volatility Co-Jumps”

Wednesday February 15 2012
13:00
Scuola Normale Superiore
Aula Bianchi

Roberto Renò
Università degli Studi di Siena

Abstract
A sizeable proportion of large, discontinuous, changes in asset prices are found to be associated with contemporaneous large, discontinuous, changes in volatility (i.e., co-jumps), negative price jumps usually occurring along with positive volatility jumps. We document that the co-jumps yield an economically-meaningful portion of leverage, return skewness, and the implied volatility smirk. These, and other, effects are uncovered in the context of a flexible modeling approach (allowing, among other features, for independent as well as common jumps, volatility-dependent jump arrivals, and time-varying leverage) and a novel identification strategy relying on infinitesimal cross-moments and high-frequency price data.
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14 Dec

Emmanuel Bacry, “Modelling Microstructure using Multivariate Hawkes Processes”

Wednesday December 14 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Emmanuel Bacry
Ecole Polytechnique

Abstract
Hawkes processes are used for modelling tick-by-tick variations of a single or of a pair of asset prices. For each asset, two counting processes (with stochastic intensities) are associated respectively to the positive and negative jumps of the price. We show that, by coupling these intensities using a kernel function, one can reproduce high-frequency mean reversion structure as well as Epps effect which are both characteristic of the microstructure. We define a numerical method that provides a non-parametric estimation of the kernel shape, it is find to be slowly decaying (power-law) suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics. The consequences for market impact are discussed using a model very simple model for exogeneous trades.
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23 Nov

Umberto Cherubini, “CDS and the City”

Wednesday  November 23 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Umberto Cherubini
Università di Bologna

Abstract

We discuss the peculiarity of the CDS tool in the realm of credit derivatives. We show how to use such products for the hedging of credit risk and for synthetic creation of it. We show how to use CDS quotes to bootstrap the term structure of the implied probability of default of an obligor. We finally discuss the relevance of the market in which CDS are traded, which is Over-The-Counter. As an illustration we provide a case of CDS used in the funding of a municipal entity.

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20 Sep

Aldo Nassigh, “Default and Credit Migration Risk in Trading Portfolios”

Tuesday September 20 2011
16:00
Scuola Normale Superiore
Aula Bianchi

Monica Billio
Unicredit, Milano

Abstract
Default and credit migration risk was treated as negligible for a long time in banks’ trading portfolios, characterized by an investment horizon of few days. This was consistent with the ‘Constant Level of Risk’ assumption according to which, in case of deterioration of the creditworthiness of the obligor, exposures with high credit quality would have been replaced with the goal of moving the asset allocation back to the original risk profile. If perfect market liquidity and continuous Brownian motion for asset prices are granted, losses induced by the frequent rebalancing of the portfolio can indeed be neglected. The rise and blow up of the Credit Trading bubble (also named Sub-Prime, Lehman and Sovereign crises) showed the shortcomings of such approach. In 2004, the Basel Committee on Banking Supervision asked banks to set aside capital for credit risk in trading portfolios, in response to the rising credit exposures and the improvements in risk management best practice observed in the banking system. Such capital add-on (named ‘Incremental Risk Charge’) will enter into force in December 2011. The proper evaluation of default and credit migration risk under the constant level of risk assumption translates into the call for modeling portfolio credit risk in the framework of short-term, multi-step simulations. Aim of the seminar is to give an update on recent developments regarding modeling the Incremental Risk Charge and to raise some critical and unresolved issues as: the difficulty in adapting to this problem the mainstream treatment of portfolio credit risk by continuous-time Markov Chains applied to the rating migration process; the lack of an unambiguous approach to the estimation of asset correlations, leading to large discrepancies in the capital level required by the various models developed so far.

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10 May

Daniel Nehren and Lorenzo Balducci, “Un incontro con JP Morgan”

Tuesday May 10 2011

15:00
Scuola Normale Superiore
Aula Mancini

Daniel Nehren
Head of Linear Quantitative Research, JP Morgan New York

Introduction to Algorithmic Trading

Lorenzo Balducci
Quantitative Research, JP Morgan London

Quantitative Research at JP Morgan

Following this link you can download the slides of the talk by Lorenzo Balducci: Slides_Balducci.

19 Apr

Franco Nardini, “Innovation, specialization and growth in a model of structural change”

Tuesday April. 19 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Franco Nardini
Università di Bologna

Abstract
The aim of this talk is to investigate the nexus between demand patterns and innovation as it stems from research efforts and the extent of specialization. In the proposed model an innovation race conducted by entrants investing in research and development against established incumbents raises productivity at the industry level and leads to a shift in the aggregate demand pattern and consequently to a redistribution of the profit fund among industries and a restructuring of the production process in each industry. The talk argues that the degree of development as reflected in a demand share distribution is characterized by a corresponding distribution of specialized sectors that becomes more even across industries as the development process proceeds and investigates the consequences in terms of economic growth.
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05 Apr

Marko Hans Weber, “On portfolio optimization in markets with frictions”

Tuesday April 5 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Marko Hans Weber
Scuola Normale Superiore

Abstract
The classic portfolio optimization problem was solved by Robert Merton in 1969 in his paper “Lifetime portfolio selection under uncertainty: the continuous time case”. In an economy formed by two assets, a risk-free bond and a stock, which has standard Black-Scholes dynamics, he finds explicitly the optimal trading strategy for an agent with constant relative risk aversion. The mainstream literature assumes a frictionless market, but ignoring transaction costs and liquidity may seriously affect the reliability of a financial model. The objective of the talk is to give a review on the effects of introducing proportional transaction costs. Indeed, the results by Merton are no longer valid in this framework. We also want to approach the issue of liquidity, which has been studied just marginally in the literature, and then compare the impact that both kind of frictions have.
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29 Mar

Monica Billio, “Econometric measures of systemic risk in the finance and insurance sectors”

Tuesday March 29 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Monica Billio
Department of Economics – Università Ca’ Foscari di Venezia

Abstract
We propose several econometric measures of systemic risk to capture the interconnectedness among the monthly returns of hedge funds, banks, brokers, and insurance companies based on principal components analysis and Granger-causality tests. We find that all four sectors have become highly interrelated over the past decade, increasing the level of systemic risk in the finance and insurance industries. These measures can also identify and quantify financial crisis periods, and seem to contain predictive power for the current financial crisis. Our results suggest that hedge funds can provide early indications of market dislocation, and systemic risk arises from a complex and dynamic network of relationships among hedge funds, banks, insurance companies, and brokers.
Joint work with Mila Getmansky, Andrew W. Lo, and Loriana Pellizzon.

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15 Mar

Salvatore Federico, “Rappresentazione a dimensione infinita per problemi di controllo con ritardo”

Tuesday March 15 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Salvatore Federico
Università di Bologna

Abstract
I problemi di controllo con ritardo nella variabile di stato e/o di controllo emergono in maniera naturale in molti contesti applicativi (Fisica, Biologia, Economia, ecc.). La prima parte del seminario sarà dedicata all’illustrazione di una serie di esempi di interesse in ambito economico-finanziario. La seconda parte del seminario sarà dedicata alla descrizione delle difficoltà matematiche a cui bisogna far fronte nell’affrontare tali problemi ed alla descrizione dell’approccio di rappresentazione a dimensione infinita agli stessi. Infine l’ultima parte sarà dedicata allo studio di alcuni problemi specifici e all’illustrazione di alcuni risultati di regolarità per le equazioni di Hamilton-Jacobi-Bellman associate.
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08 Mar

Maurizio Pratelli, “Calcolo delle greche e integrazione per parti secondo Malliavin”

Tuesday March 8 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Maurizio Pratelli
Università degli Studi di Pisa

Abstract
Si usano chiamare greche le derivate dei prezzi (ad esempio di opzioni) rispetto ad opportuni parametri: quando non sono disponibili formule esplicite per i prezzi questi vengono usualmente calcolati con metodi Montecarlo. Tuttavia il calcolo (o almeno l’approssimazione) delle derivate pone forti problemi di instabilità numerica. Per ovviare a questa difficoltà P.L.Lions e collaboratori hanno adattato il metodo di integrazione per parti, originariamente introdotto da P.Mallavin per affrontare con tecniche probabilistiche il teorema di Hormander sulla caratterizzazione degli operatori ipoellittici: il lavoro di Lions ha aperto la strada a numerose applicazioni. In questo seminario intendo esporre sinteticamente le idee essenziali del “calcolo di Malliavin” ed esporne alcune applicazioni a problemi posti dalla Finanza Matematica.
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03 Mar

Andrea Pallavicini, “Surviving the Credit Crunch: new features for post-crisis pricing models”

Tuesday May 3 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Andrea Pallavicini
Mediobanca, Milano

Abstract
Starting from the beginning of the credit crunch many pricing models fail to incorporate market movements since they are designed to discard features now crucial in such turmoil situation. In particular, credit risk cannot be neglected any longer while modelling other asset classes: single counterparties can default, and extreme events may happen too, such as the default of sectors of the economy, or even the break-down of the whole system. A new generation of pricing models able to naturally include counterparty and systemic risk along with more exotic features, such as funding and liquidity effects, is still under construction, but it is now possible to discern the first steps. In this presentation we focus on credit and the interest-rate asset classes. In particular, we describe some old approaches which survived the crisis (loss models with default clustering or self-excitement), and some new proposals driven by recent market trends or by modifications in regulation framework (CVA evaluation framework, credit contagion models, multiple yield-curve models).
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15 Feb

Giacomo Bormetti, “Minimal model of financial stylized facts”

Tuesday February 15 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Giacomo Bormetti
Scuola Normale Superiore – Pisa

Abstract
In this seminar I will present joint work with D. Delpini from the University of Pavia. We afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatilitiy of financial returns. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails, and of the relevant correlation functions. We also propose a systematic methodology for estimating the model parameters, and we describe the empirical analysis of the Standard & Poor 500 index daily returns, confirming the ability of the model to capture many of the established stylized fact as well as the scaling properties of empirical distributions over different time horizons.

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02 Feb

Lucio M. Calcagnile, “Misurare l’efficienza informativa dei mercati finanziari”

Wednesday February 2 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Lucio M. Calcagnile
Scuola Normale Superiore

Abstract
Un mercato finanziario è detto “efficiente” se è efficiente nel processare l’informazione disponibile, se – cioè – gli agenti che lo compongono assimilano e incorporano immediatamente nei prezzi tutte le informazioni rilevanti. È possibile stabilire se un mercato è efficiente in senso assoluto ovvero quantificare il grado di efficienza relativa di un mercato rispetto a un altro? Esporrò alcuni lavori recenti in letteratura che con metodi diversi tentano di misurare l’efficienza relativa. Presenterò esperimenti e analisi condotti su serie temporali finanziarie ad alta frequenza usando il contesto della teoria dell’informazione e l’entropia di Shannon quale strumento per misurare l’efficienza. Illustrerò infine alcuni vantaggi e svantaggi che si presentano nell’analisi di serie ad alta frequenza.

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