29 May

Andrea Pallavicini, “Arbitrage-Free Pricing with Funding Costs and Collateralization”

Friday May 29  2015
9.30 – 13.00
Scuola Normale Superiore
Aula Fermi

Andrea Pallavicini
Banca IMI, Milano and Imperial College, London

Arbitrage-Free Pricing with Funding Costs and Collateralization

The financial crisis started in 2007 has shown that any pricing framework must include from the very beginning the possibility of default of any market player. As a consequence derivative valuation and risk analysis have moved from exotic derivatives managed on simple single-asset classes to simple derivatives embedding credit risk and new, or previously neglected, types of complex and interconnected non-linear effects. Derivative valuation is adjusted to include counterparty credit risk and contagion effects along with funding costs due to collateral posting, treasury policies, and regulatory constraints. A second level of complexity is produced by moving from a single trade to the whole bank portfolio. Aggregation-dependent valuation processes, and theirs operational challenges, arising from non-linearities are discussed both from a mathematical and practical point of view.

Download slides here.

All interested people are kindly invited.

19 Jun

Luca Capriotti, “Real Time Risk Management with Adjoint Algorithmic Differentiaton”

Friday June 20  2014
11.00 – 12.30, 14.30 – 16.00
Scuola Normale Superiore
Aula Bianchi

Luca Capriotti
Credit Suisse London

Real Time Risk Management with Adjoint Algorithmic Differentiaton

Adjoint Algorithmic Differentiation (AAD) is one of the principal innovations in risk management of the recent times. In this minicourse I will introduce AAD and show how it can be used to implement the calculation of price sensitivities in complete generality and with minimal analytical effort. The focus will be the application to Monte Carlo methods – generally the most challenging from the computational point of view. With several examples I will illustrate the workings of AAD and demonstrate how it can be straightforwardly implemented to reduce the computation time of the risk of any portfolio by order of magnitudes. 

Download flyer here and slides here.

All interested people are kindly invited.

13 May

Paolo Guasoni, “Frictions and Fees in Portfolio Choice”

Monday May 13  2013, 16.00 – 18.00 Aula 2
Tuesday May 14  2013, 11.00 – 13.00 Aula 2
Wednesday May 15  2013, 14.00 – 16.00 Aula Bianchi
Thursday May 16  2013, 11.00 – 13.00 Aula 2
Scuola Normale Superiore

Paolo Guasoni
Boston University and Dublin College University

Frictions and Fees in Portfolio Choice

All interested people are kindly invited.

09 May

Jean-Philippe Bouchaud, “Instabilities in Financial Markets”

Thursday May 9  2013, 16.00 – 18.00 Aula Mancini
Friday May 10  2013, 14.00 – 16.00 Aula Mancini
Monday May 13  2013, 9.00 – 11.00 Aula Bianchi
Scuola Normale Superiore

Jean-Philippe Bouchaud
Capital Fund Management and Ecole Polytechnique

Instabilities in Financial Markets

May 9 “Stylized facts: old pieces and new results”
May 10 “Price formation, market impact and HFT”
May 13 “Instabilities: some (dangerous) feedback loops”

All interested people are kindly invited.

08 Apr

Rama Cont, “Functional Ito calculus and Functional Kolmogorov equations”

Monday April 8 2013, 10.00 – 13.00 Aula Tonelli
Monday April 15 2013, 10.00 – 13.00 Aula Tonelli
Monday April 22 2013, 10.00 – 13.00 Aula Tonelli
Tuesday April 23 2013, 9.00 – 12.00 Aula 2
Wednesday April 24 2013, 9.00 – 12.00 Aula Dini
Monday May 27 2013, 10.00 – 13.00 Aula Tonelli
Scuola Normale Superiore

Rama Cont
Imperial College London and CNRS
Laboratoire de Probabilités et Modeles Aléatoires, Université Paris VI-VII

Functional Ito calculus and Functional Kolmogorov equations

All interested people are kindly invited.

04 Oct

Rosario Nunzio Mantegna, “Econophysics Investigation of Financial Markets: Correlation, Heterogeneity and Agent Based Models”

Tuesday October 4 2011  15.00 – 17.00 Aula Bianchi
Wednesday October 5 2011 11.00 – 13.00 Aula Bianchi
Thursday October 6 2011 11.00 – 13.00 Aula Mancini
Scuola Normale Superiore

Rosario Nunzio Mantegna
Università di Palermo

Lecture 1. Correlation, hierarchical clustering and correlation based networks in financial markets
Download slides here.

Lecture 2. Heterogeneity and specialization of investors in financial markets
Download slides here.

Lecture 3. Agent based modeling of financial markets
Download slides here.

13 Apr

Jean-Philippe Bouchaud, “An introduction to Statistical Phy-nance”

Wednesday April 13 2011, 14.00 – 16.00 Aula Dini
Thursday April 14 2011, 14.00 – 16.00 Aula Dini
Friday April 15 2011, 11.00 – 13.00 Aula Fermi
Scuola Normale Superiore

Jean-Philippe Bouchaud
Science & Finance, Capital Fund Management, Paris

Lecture 1. (Wednesday April 13) The dynamics of price in financial markets

  • Fat tails and intermittent dynamics: empirical facts and models
  • High frequency and seasonality effects
  • Cross sectional and multivariate effects
  • Correlations and copulas

Lecture 2. (Thursday April 14) Price formation and microstructure

  • Order book dynamics
  • Order flow dynamics
  • Impact and liquidity
  • Is price dynamics exogenous or endogenous?

Lecture 3. (Friday April 15) The world of financial derivatives

  • The worrying ways of financial engineering
  • Option pricing: welcome to a non Black-Scholes world
  • Volatility modelling: GARCH and multiscale/multifractal frameworks
  • The hedge Monte-Carlo method
  • The need for “second generation” models 
14 Feb

Sylvain Arlot, “Advanced Course on Statistics”

Monday February 14 2011, 14.00 – 16.00 Aula Bianchi

Tuesday February 15 2011, 9.00 – 11.00 Aula Fermi

Thursday February 17 2011, 14.00 – 16.00 Aula Fermi

Tuesday February 22 2011, 14.00 – 16.00 Aula Dini

Wednesday February 23 2011, 9.00 – 11.00 Aula Bianchi

Scuola Normale Superiore


Advanced Course on Statistics

Lecture 1. (Monday February 14) Statistical learning

  • the statistical learning learning problem
  • examples: prediction, regression, classification, density estimation
  • estimators: definition, consistency, examples
  • universal learning rates and No Free Lunch Theorems [1]
  • the estimator selection paradigm, bias-variance decomposition of the risk
  • data-driven selection procedures and the unbiased risk estimation principle

Lecture 2. (Tuesday February 15) Model selection for least-squares regression

  • ideal penalty, Mallows’ Cp
  • oracle inequality for Cp (i.e., non-asymptotic optimality of the corresponding model selection procedure), corresponding learning rates [2]
  • the variance estimation problem
  • minimal penalties and data-driven calibration of penalties: the slope heuristics [3,4]
  • algorithmic and other practical issues [5]

Lecture 3. (Thursday February 17) Linear estimator selection for least-squares regression [6]

  • linear estimators: (kernel) ridge regression, smoothing splines, k-nearest neighbours, Nadaraya-Watson estimators
  • bias-variance decomposition of the risk
  • the linear estimator selection problem: CL penalty
  • oracle inequality for CL
  • data-driven calibration of penalties: a new light on the slope heuristics

Lecture 4. (Tuesday February 22) Resampling and model selection

  • regressograms in heteroscedastic regression: the penalty cannot be a function of the dimensionality of the models [7] 
  • resampling in statistics: general heuristics, the bootstrap, exchangeable weighted bootstrap [8]  
  • study of a case example: estimating the variance by resampling  
  • resampling penalties: why do they work for heteroscedastic regression? oracle-inequality. comparison of the resampling weights [9]

Lecture 5. (Wendsday February 23) Cross-validation and model/estimator selection [10]  

  • cross-validation: principle, main examples 
  • cross-validation for estimating of the prediction risk: bias, variance  
  • cross-validation for selecting among a family of estimators: main properties, how should the splits be chosen?  
  • illustration of the robustness of cross-validation: detecting changes in the mean of a signal with unknown and non-constant variance [11]  
  • correcting the bias of cross-validation: V-fold penalization. Oracle-inequality. [12] Read More