Euclide. Validation of Financial Models. Presentation of Research Project

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1 Euclide Validation of Financial Models Presentation of Research Project September 9, 2009

2 Table of Contents Résumé (Français)...4 Problématique...4 Les modèles financiers et leurs fonctions...4 Le projet de recherche...5 Contenu théorique...6 Une plateforme logicielle...6 Un cadre pour la communication et la collaboration...6 Étapes du projet...7 Preuve de principe étendue...7 Recherche et developpement à moyen terme...7 Réflexion méthodologique sur la métrique de validation...8 Modélisation du domaine financier...8 Connexions à des bases de données externes...8 Développement informatiques de la plateforme PRAXIS...8 Problem Statement...9 Financial models...9 Why do we need models?...10 The nature of Model Risk...10 Similar Scientific Problems and Their Solutions...11 The Genesis of E-Science...11 Validation of algorithms in BioInformatics...12 The need for Massive Computing Ressources in Physics...12 A Short Survey of Existing E-Science Platforms...13 Focus of this Research Project...15 The scientific focus...16 A computational environment...16 A framework for communication and collaboration...17 Why PRAXIS? (www.bioside.org/www.diviz.org)...17 Project Milestones...18 Extended Proof of Principle...18 Medium-term Research Plan...18

3 Model Validation Framework...18 Model of the Financial Domain...19 Connectivity to Historical Databases...19 Developpement of the PRAXIS Framework...19 Bibliography...20 Appendix A: Survey of Workflow Engines...21 Appendix B: Proof of Principle Using PRAXIS...26 Appendix C: The Misspecification Risk: A Simple Example...29 Résumé L'objectif général du projet est de concevoir une méthodologie et de développer un environnement informatique de validation de modèles financiers, avec comme objectif de rassembler une communauté scientifique sur ce thème. L'innovation principale de ce projet est de structurer la démarche autour d'une plateforme informatique qui permet de formaliser et de partager des protocoles complets de validation. Télécom-Bretagne et l'université de Bretagne Sud (UBS) mènent conjointement ce projet au sein de l'équipe de recherche Lab-STICC, qui regroupe des statisticiens, des spécialistes des modèles stochastiques, et des informaticiens. Dans un premier temps, on proposera le libre usage de cette plate-forme aux chercheurs en finance, en les invitant à y incorporer leurs modèles pour des tests empiriques. De plus, nous rendrons la plateforme accessible aux industriels du domaine, voire même aux agences de notation et aux autorités de tutelle. A notre connaissance, il s agira là de la première plate-forme de test de modèles financiers, collaborative, ouverte et librement disponible. Problématique Le projet de recherche est motivé par trois observations. En observant la production scientifique dans le domaine de la finance quantitative, on est frappé par l'abondance de modèles proposés, mais aussi par la rareté des études empiriques de validation de ces mêmes modèles. La crise financière de 2008 a cruellement mis en lumière de lourdes déficiences dans la validation des modèles de valorisation et d'appréciation des risques. Ceci conduit à observer que la notion de robustesse d'un modèle financier n'est pas clairement définie. Les autorités de tutelle définissent des normes de risque, mais il est

4 clair que la situation n'est pas comparable au degré de normalisation et certification atteint dans d'autres industries. Les modèles financiers et leurs fonctions La valorisation et la gestion du risque des produits financiers est fondée sur l'utilisation de «modèles» pris au sens large. Ces modèles ont deux composantes: Ils postulent un processus de diffusion pour les facteurs de risque sous-jacents Ils offrent une méthode de calcul de la valeur présente (espérance actualisée de valeur future). Dans les marchés liquides, l'utilité d'un modèle est limitée car le marché procure des prix fiables en continu. Un modèle devient indispensable dans les marchés illiquides: on calibre un modèle à l'aide d'instruments liquides, et on utilise ce modèle pour valoriser des instruments illiquides sujets aux mêmes facteurs de risque. C'est dans cette procédure que se glisse le risque spécifique de modélisation. En effet, plusieurs modèles concurrents peuvent être également bien calibrés aux données des marchés liquides, mais peuvent produire des résultats très disparates sur des produits exotiques (un exemple simple est présenté en annexe C.) Utiliser un modèle mal spécifié expose à un double risque: On valorise trop agressivement certains produits exotiques, gagnant ainsi des mandats précisément sur les produits mal valorisés, Le modèle mal spécifié donne de mauvais indicateurs de risque, et la stratégie de couverture se révèle déficiente. De fait, valider un modèle demande de valider chaque composante séparément, et aussi de valider l'ensemble, c'est à dire valider l'interaction des composantes entre elles dans une perspective dynamique. Pour mener à bien cette tâche, la recherche en finance de marché, et la pratique de la finance quantitative doit faire face à un double défi: Valider les modèles sur une base scientifique indiscutable Pour ce faire, utiliser une infrastructure comprenant: un accès à des bases de données historiques une capacité de calcul la capacité à exprimer et publier des protocoles de validation, et non plus simplement des résultats de calcul. Ces défis ont également été rencontrés dans d'autres disciplines, spécifiquement en biologie

5 et physique. Des réponses originales ont été apportées, donnant lieu à un nouveau type de démarche scientifique nommée «escience». Cette approche n'a pas encore, à notre connaissance, été exploité dans le domaine de la finance quantitative. Le projet de recherche Ce projet de recherche s'articule en trois volets: Préciser la notion de «robustesse» d'un modèle en définissant une métrique qui prennent en compte l'aspect multi-critères de toute mesure de risque. Développer un outil de validation s'appuyant sur une plateforme logicielle ouverte et distribuée, qui encouragera les contributions de chercheurs issus de différents horizons (statisticiens, mathématiciens financiers, informaticiens, etc). Expérimenter un nouveau type de production scientifique, fondé sur la publication des protocoles expérimentaux, la collaboration et l'enrichissement progressif du produit de recherche, et ultimement la création d'un réseau social autour du domaine de recherche. Contenu théorique Le projet se concentre sur le risque de mis-spécification, sur les moyens de détecter ce risque, de le mesurer et de développer des modèles robustes. Ce choix est motivé par des raisons à la fois méthodologiques et pratiques. D'un point de vue théorique, le risque de mis-spécification doit être précisément défini. Il y a une littérature abondante sur l'estimation robuste de modèles. Malgré cela, on constate un déficit de recherche théorique et encore plus, empirique, sur la validation des modèles financiers. Ce projet de recherche contribuera à combler cette lacune en finance quantitative. D'un point de vue pratique, le risque de mis-spécification est le soucis constant du gérant de risque. Une avancée, même modeste, en ce domaine pourra avoir un impact immédiat sur la qualité de la gestion du risque financiers des banques et gérants de fonds. Une plateforme logicielle Tirant notre inspiration des plateformes de bio-informatique et de physique des particules, le but de ce projet est de construire un environnement logiciel pour supporter l'effort de recherche. Notre volonté de créer une plateforme de «escience» pour la finance quantitative est motivée par plusieurs considérations:

6 Le premier but est de lever les obstacles qui limitent aujourd'hui la recherche empirique sur la validation des modèles. Observant les succès enregistrés dans les autres disciplines, nous somme convaincus qu'une plateforme de «escience» est une étape essentielle qui permettra de: mettre en commun les puissances de calcul nécessaires simplifier l'accès aux données créer un «langage commun» qui facilitera les études comparatives de modèles et les simulations. L'annexe B résume la preuve de principe réalisée avec la plateforme «PRAXIS» pour illustrer ce que peut représenter une plateforme de «escience» pour la finance quantitative. Un cadre pour la communication et la collaboration Une plateforme de «escience» devrait de plus créer des nouveaux modes de communication entre les acteurs du domaine. C'est peut-être là que réside l'intérêt principal du projet, et son caractère le plus innovant. Nous pouvons déjà imaginer quelques scénarios: Dans le monde universitaire, notre objectif est de créer un langage commun entre les chercheurs en finance quantitative, encourageant ainsi les projets collaboratifs au même titre que le logiciel statistique «R» a fédéré la communauté des statisticiens autour d'une plateforme logicielle et des formats de données [R-software]. En se tournant maintenant vers les industriels, (la plateforme sera dotée d'une licence permettant son utilisation par des organismes privés, sachant que les certains aspects concrets restent à définir), on peut imaginer les scénarios suivant: L'équipe de validation de modèle d'une banque d'investissement pourrait utiliser cette plateforme, non seulement pour effectuer ses tests, mais aussi pour documenter et garder la trace de tout ses protocoles expérimentaux. Un éditeur de logiciel pourrait exposer sa bibliothèque de calcul sous forme de service web, et un client pourrait utiliser la plateforme pour comparer ses modèles internes à la librairie de l'éditeur, sans avoir à procéder à une installation de la librairie tierce. Une banque d'investissement pourrait publier ses modèles internes sous forme de service web, et accorder un accès contrôlé à une agence de notation ou une autorité de tutelle, de façons à soumettre les modèles à un «stress test» sans avoir à

7 délocaliser sa logistique ni révéler les détails de mise en œuvre des algorithmes. Étapes du projet Le projet s'articulera en deux chantiers, qui se chevauchent partiellement: Preuve de principe étendue Une première preuve de principe est déjà réalisée. Elle intègre les librairies de calcul financier PREMIA (INRIA/ENPC) [Premia] et R-Metrics (ETH Zurich) [Rmetrics]. Il s'agit de poursuivre ce développement et obtenir rapidement, à l'horizon fin 2009, un prototype suffisamment abouti pour traiter un problème réel de validation, en utilisant la plateforme PRAXIS. L'objectif étant de créer un exemple réaliste d'une plateforme d' «escience» pour la finance quantitative, et d'identifier les développements à apporter à la plateforme logicielle PRAXIS. Le problème sera défini conjointement avec un industriel (banque ou société de conseil). Recherche et développement à moyen terme Le second chantier est à plus long terme, et comprend des développements informatiques importants, ainsi que plusieurs thèmes de recherche. Réflexion méthodologique sur la métrique de validation La définition d'une méthodologie de validation est le cœur de ce projet de recherche. On peut approcher la question sous deux angles complémentaires. Selon une première approche, que l'on nommera «statique», on s'intéresse à la validation de chaque composante des modèles de valorisation et d'estimation du risque. Dans la seconde approche, on s'intéresse à la qualité de la gestion dynamique de couverture, mesurée par l'erreur de réplication, réalisée grâce à un modèle. Cette mesure est pertinente à un double titre puisque, d'une part, elle reflète le souci concret du praticien (gérer le risque de marché), et que d'autre part l'existence d'une stratégie de réplication est une des hypothèse de base de la valorisation des produits dérivés. Néanmoins, il n'y pas de critères universellement reconnus de mesure de cette erreur. Ce recherche devrait être menée avec un partenaire industriel. Modélisation du domaine financier L'objectif de cette étape est d'identifier les composants d'une plateforme de validation de modèles financiers, et de définir des protocoles de communication entre les composants du système logiciel: entrepôts de données ou simulateurs modules de calculs financiers

8 modules de simulation de stratégies de gestion modules d'évaluation et de visualisation des performances L'aspect le plus complexe de cette modélisation concerne la représentation générique des instruments financiers, représentation qui doit rester indépendante des librairies de calculs. Cet aspect de la recherche pourrait être mené avec un partenaire industriel (éditeur de logiciel). Connexions à des bases de données externes Les bases de données historiques sont des composantes essentielles d'une plateforme de validation. Elles sont indispensables pour toutes simulations historiques, et sont notoirement difficiles à constituer par les chercheurs eux-mêmes. L'objectif est de procurer une connexion native à la base de données historique en cours de constitution par EuroFidai et le pôle de compétitivité Finance Innovation. Développement informatiques de la plateforme PRAXIS Dans le but de rendre la plateforme utilisable par le plus grand nombre, nous prévoyons de développer PRAXIS pour améliorer l'ergonomie, la documentation, et aussi pour ajouter certaines fonctions qui rendront plus aisée la modélisation de systèmes dynamiques. L'effort de développement est estimé à 6 années-homme.

9 The Euclide Project Problem Statement This research project is motivated by three observations: The scientific production in the domain of quantitative finance has an abundance of papers presenting models for the dynamic of asset prices, but very few empirical studies on the validity of such models, or on the calibration to actual data. Reasons for such discrepancies are numerous: market data is notoriously hard to obtain, and empirical studies require a significant investment of time and resources. The financial crisis of 2008 has highlighted serious deficiencies in the validation of financial models used to price complex derivatives. It is worth noting that the financial crisis does not originate from an extreme event, but from a modest downturn in the U.S. real estate market, which became enormously amplified by highly leveraged derivative products. The notion of robustness of a financial model is not clearly defined. Various regulatory bodies have defined risk measures, capital adequacy requirements, etc. but it is clear that these norms do not provide the level of security that standardization and normalization has provided in other industries. One often uses the expression Financial Engineering, but this industry has not yet developed the type of norms and safety standards that can be found, say, in civil or mechanical engineering. To further investigate these questions, it is necessary to carefully define the notion of Financial Model, its nature and its usage. Financial models The valuation and risk management of financial instruments, and specifically complex derivatives, require the use of models. Broadly defined, these models have three components: The specification of a diffusion process for the underlying risk factors The definition of a calibration procedure for determining the parameters of the diffusion processes, using historical and/or current market information A calculation method for the expected present value of a payoff, under the risk-neutral measure. Note that all three aspects are linked, in the sense that the nature of the diffusion process

10 often determines the calibration method, as well as the numerical schemes that are available for computing the expected present value. Why do we need models? When pricing and hedging vanilla instruments, for which there exists a liquid market, the need for a model is minimal, and the standard practice is as follows: Using the Black-Scholes model, compute the implied volatility for each listed option Compute a smooth volatility surface by interpolation Use this volatility surface to price any Vanilla option Recalibrate the model as needed. A model becomes indispensable in the absence of a liquid market for the instruments of interest. Note that the instrument does not need to be exotic. For example, a model is needed to price deep out of the money European options, because there is no liquid market for such claims. In this case, a model is calibrated on a set of liquid instruments, then used to price and manage the risk of illiquid derivatives subject to the same risk factors. It in this process that model risk appears. There are in fact several aspects to model risk, and they are now briefly reviewed. The nature of Model Risk The nature of model risk has been extensively discussed, and two types of risk are commonly identified. In this research project, we will focus on one type of model risk. For the sake of completeness, however, both types of risk are next briefly described. The first type of risk, the one that we consider in this research project, is model misspecification, i.e. the risk associated with the use of a model that is not an accurate representation of the dynamic of the risk factors. The second type of risk is market dislocation, where the market value of illiquid instrument depart markedly from fair value. Market Dislocation Market dislocation refers to the occurrence of discrepancies between market value and fair value (or model value), that are caused not by a flaw in the model, but by such factors as a flight to liquidity or a change in risk premium. These conditions have been observed during the various recent credit crisis, the collapse of LTCM, and of course the financial crisis of

11 2008. Under normal conditions, the Efficient Market Hypothesis (EMH) tells us that arbitrageurs would immediately step in, take advantage of the discrepancy, and the market impact of their trades would promptly close the arbitrage. In times of financial crisis, risk aversion and preference for liquidity prevent arbitrageurs from stepping in, and the discrepancy can endure. Unfortunately, this type of risk is hard to quantify, and even harder to mitigate. Rebonato's recommendations (Rebonato, 2001) for dealing with this risk are mostly organizational: know your competition, price the exotic deals with several models, calibrate the models with various algorithms, etc. As such, it is a topic for research in management science rather than in mathematical finance. Model Misspecification Several models can be equally well fitted to the same set of vanilla market data. Yet, these models will yield different results when used to price exotic derivatives. If one accepts the assumption that there is one true model, that accurately captures the dynamic of the risk factors, the risk here amounts to using the wrong model. Using the wrong model will not only yield the wrong price, but will also define an inadequate hedging strategy. An exotic derivative is priced according to the model, and hedged with vanilla instruments, such that the exposure to risk factors is canceled by the hedge portfolio. At expiry, the true value of the exotic derivative will be revealed, without need for a model. Therefore, the practical issue is to verify that the model generates a hedging strategy that correctly replicates the payoff at expiry. This question has in fact many aspects: What is the stability of the estimated parameters? Are risk indicators stable? Are they accurate (i.e. do they correctly predict VaR consumption)? In summary, by using a misspecified model, the risk of a trading desk is compounded: The desk quotes some exotic products too aggressively, and ends up winning many mandates precisely on the products that are mis-priced The model provides incorrect estimates of the risk, and the dynamic hedging strategy proves ineffective on these same products. Similar Scientific Problems and Their Solutions The scientific and practical challenges related to model validation are not unique to

12 mathematical finance. In fact, we find similar issues in other scientific domains, specifically in bio-informatics and computational physics. Both fields have developed original solutions to cope with these issues, and we next briefly survey these developments. The Genesis of E-Science The term e-science is used to describe scientific research that is computationally intensive, or require data sets that are so large that a distributed network environment and grid computing resources become a necessity. As a side effect, which will be crucial in our case, the same technology enables distributed collaboration. The term e-science was reportedly [E-Science] coined by John Taylor, the Director General of the United Kingdom's Office of Science and Technology in 1999 and was used to describe a large funding initiative starting in November A more compact definition of escience is proposed by the Cambridge e-science Center: e-science is research into new ways of using the Internet to do science Examples of this kind of science include social simulations, particle physics, earth sciences and bio-informatics. Let's take a closer look at bio-informatics and particle physics, as each in their domain provides useful insights. Validation of algorithms in bioinformatics Bioinformatics is the original breeding ground of e-science, and to this day remains the scientific domain where e-science seem to be best developed. Among the middleware platforms for e-science enumerated in Appendix A, all but one find their origin in a bioinformatics project. Closer to home, PRAXIS, the platform developed at ENST, also originates from that field. In it relevant to note the reasons that motivated the development of e-science platforms for bioinformatics: To facilitate the capture of meta-data: where does the data come from, which modifications have been performed by the user, what type of filtering has been applied, when was the data accessed, etc. To record the entire computation protocols for all experiments, and not only the results from the successful ones, and finally To facilitate communication among researchers, and the generation of reports.

13 Thus, it should be noted that e-science platforms have benefits beyond the obvious function of pooling computing resources and bringing online large databases [Gray03]. In a postgenomic research era, the intent of an e-science platform is to enable a peer review of the entire calculation protocol, and in general to facilitate the scientific work of a distributed research team [Sastry07]. The need for massive computing ressources in physics The Web was designed at CERN to facilitate the exchange of information between physicists working on different computers, and often scattered across many locations. The focus of e- Science in physics is on the pooling of computing resources needed to handle the quantity of data generated by such devise as the CERN Large Hadron Collider. The following quote is extracted from the presentation of the High Energy Physics laboratory at Imperial College [IC01]: Our group's e-science activities are aimed at enabling researchers to extract the greatest possible range of physics from these mountains of data in an efficient way. Our team has a high profile in a wide range of projects where we are working both on the development of core infrastructure (known as middleware) and on the Grid-enabling of experiment-specific applications. This aspect of e-science is particularly relevant to us, since the simulation experiments that will be needed in this project require calculation resources that are only available in some research centers and in large international investment banks. For most researchers, therefore, the ability to pool computing resources across research labs will be a basic requirement for conducting the research we have in mind. A short survey of existing e-science platforms With no claim to completeness, we have identified and tested a number of e-science platforms, in addition to ENST's PRAXIS. Screenshots are reproduced in Appendix A. We summarize our findings below, focusing on comparing PRAXIS to other platforms. We have surveyed and tested 5 platforms in addition to PRAXIS: Knime (www.knime.org).

14 To quote a white paper by the designer, The Konstanz Information Miner is a modular environment which enables easy visual assembly and interactive execution of a data pipeline. It is designed as a teaching, research and collaboration platform, which enables easy integration of new algorithms, data manipulation or visualization methods as new modules or nodes. The design of Knime is strongly influenced by its primary purpose as a data mining platform (for example, all data objects must be in tabular format). Its strong point is a remarkable user interface, and professional quality documentation and support. Kepler (www.kepler-project.org) Kepler and its predecessor Ptolemy is one of the oldest scientific workflow projects. The reference paper on Ptolemy was published in To quote the introductory page of the Kepler site: Kepler is designed to help scientists, analysts, and computer programmers create, execute, and share models and analyses across a broad range of scientific and engineering disciplines. Here again, we note that the major application domains are bioinformatics and environmental science. Taverna/MyGrid (taverna.sourceforge.net) A British project funded by the UK e-science program. The remarkable aspect of this project is the development of myexperiment, which initiates the convergence of scientific workflow engines and social networks. In the same spirit, Taverna/MyGrid seems to have a very active open source development community, supported by an impressive web presence. To quote the presentation of Taverna: The Taverna Workbench provides a desktop authoring environment and enactment engine for scientific workflows. The myexperiment social web site supports finding and sharing of workflows and has special support for Taverna workflows. The Taverna workbench, myexperiment and associated components are developed and maintained by the mygrid team, in collaboration with the open source community.

15 Triana (www.trianacode.org) Triana is presented as a problem solving environment. It is a workflow engine with an emphasis on engineering tasks: for example, it provides components that simulate oscilloscopes and other laboratory equipment. To quote the introduction on Triana's web site: [Triana is] an open source problem solving environment developed at Cardiff University that combines an intuitive visual interface with powerful data analysis tools. Already used by scientists for a range of tasks, such as signal, text and image processing, Triana includes a large library of pre-written analysis tools and the ability for users to easily integrate their own tools. SciRun (www.sci.utah.edu) SciRun is also described as a Problem Solving Environment. To quote the presentation page: SCIRun is a Problem Solving Environment (PSE), for modeling, simulation and visualization of scientific problems. Scirun has a strong emphasis on visualization, as demonstrated by the flexibility of its graphical components. Again, most of the applications of SciRun seems to be in the medical and biology fields. From a technology perspective, SciRun is the only system surveyed that is written in C++. Summary This rapid survey of 5 e-science platforms suggest the following observations: Just about every platform originates from a bio-informatics project With the exception of SCIRUN, every platform has been implemented in Java The connectivity of these platforms with the «R» statistical software is often native, reflecting the influence of the bio-informatics domain where «R» has a strong presence. The platforms have impressive documentation and a strong web presence. They seem to be the flagships of well-funded research projects.

16 The sophistication of the human interface varies significantly, from the very polished (Knime, SCIRUN) to the very simple (Taverna, Triana). Every platform is published under a GPL license (or equivalent), except Knime, for which commercial and academic licenses are available. Focus of this research project The purpose of the research project is three-fold: To precisely qualify the notion of model robustness, and quantify the risk of model mis-specification, by defining measurement criteria that take into account the multiple dimensions of risk. To develop a validation framework, based on a collaborative and open software platform. This framework will welcome and encourage contributions from variety of academic disciplines (statistics, mathematical finance, computer science). This framework will facilitate empirical studies in computational finance by providing access to historical data and calculation resources. To experiment with a new type of scientific production, based on the publication and peer review or entire experimental protocols. This should lead to a research product that is collaboratively produced and progressively enriched, ultimately creating a social network in this research domain. The scientific focus In this research project, we focus on the risk of model mis-specification, for both theoretical and practical reasons. From a theoretical perspective, the issue of model mis-specification is tractable. There is a body of literature on the diagnosis of mis-specification, and on robust methods for calibrating models. Despite this body of literature, however, there has been remarkably little theoretical research and even fewer empirical studies on the validity of financial models. The proposed research will fill a gap in the body of research in mathematical finance. From a practical perspective, we want to focus on the issue of model mis-specification because it is the constant concern of a trading desk. Any advance on this front can have direct, measurable effects on the quality of the risk management in any trading and hedging activity.

17 A computational environment Inspired by similar initiatives in bio-informatics and particle physics, the goal of this project is to build a computational environment to support research outlined earlier. This focus on e- Science is motivated by several considerations. We want to lift the roadblocks that currently inhibit empirical research on model validation. Following the example of bio-informatics and particle physics, we believe that the construction of an e-science platform is an essential step towards this goal, by: pooling computational resources, and providing easy access to historical data Appendix B illustrates the concept of an e-science platform for computational finance. The main contribution of this effort will be to identify elementary computational blocks of the domain, and specify standard communication protocols, so that, for example, the same instruments can be simulated with two different pricing libraries, or historical data can be retrieved from various databases with a minimum of work. On this front, the major challenge will be to define a generic representation of financial instruments, that can then be translated into the syntax that is expected by the various pricing libraries. A framework for communication and collaboration In addition to providing pooled computational resources and access to data, the escience platform will create new means of communication among the various actors interested in model validation. This is possibly the most innovative aspect of the research project, and opens many venues that are yet unchartered. A few developments already come to mind. In the academic environment, the main benefit of this platform, as already mentioned, will be to encourage empirical research by making the necessary data and computational resources more readily available. In addition, we hope that this platform will become a shared idiom among researchers in computational finance, and encourage collaborative work in the same way as the statistical software R has federated the community of statisticians around a software and a data format [R]. Consider next the corporate environment (the software platform will be made available to

18 private users, under conditions that are yet to be defined): The model validation team of an investment bank could use this platform not only to test model implementations, as it does now, but also to document and track all the details of the testing protocol. A software vendor would expose his pricing library as a web service, and an investment bank could use the platform to compare its internal models to the thirdparty implementation, without having to go through a time-consuming in-house installation of the third-party product. An investment bank could also publish its internal library as a web service, with access restricted to a rating agency or a regulatory body, so that the internal library would be subjected to stress tests without having to disclose the algorithms or the implementation details. Why PRAXIS? (www.bioside.org/www.diviz.org) PRAXIS is the work-flow engine developed at Télécom-Bretagne. It is used in a bio-informatic application (BioSide) and in a system for studying multi-criteria decision aid methods (DIVIZ). The presentation of DIVIZ illustrates the features of PRAXIS. To quote the DIVIZ introduction page, the goals of DIVIZ are: to help researchers to construct algorithmic MCDA work-flows ( = methods) from elementary MCDA components; to help teachers to present MCDA methods and let the students experiment their own creations; to help to easily compare results of different methods; to allow to easily add new elementary MCDA components; to avoid heavy calculations on your local computer by executing the methods on distant servers. Compared to existing work flows engines, we find PRAXIS to be particularly flexible, and simple to master. PRAXIS can orchestrate work flows made of components written in any language, exchanging data in an arbitrary format. The components can be executed locally, or remotely through a variety of invocation protocols. This flexibility is particularly useful as we apply PRAXIS to a domain that is very far from its original focus. On the flip side, PRAXIS is

19 probably not as user-friendly as its counterparts: the user interface is very simple, and the documentation minimal. This observation motivates the organization of the project in two separate tracks, and described in the next section. Project milestones The project involves two phases, that will partially overlap. Extended proof of principle The purpose of this phase is to develop by the end of 2009 a prototype that is sufficiently elaborate to be able to address a real-life validation problem. This prototype will use the PRAXIS platform. The purpose being to build a realistic illustration of what «e-science» for computational finance can represent. This prototype will also help us to identify the developments that will be needed on the PRAXIS platform. The problem to be addressed will be defined jointly with an industry partner (a bank or a consulting firm). Medium-term research plan The second phase will start simultaneously, but has a longer time frame. It involves software developments as well as a number of open research topics. Model Validation Framework The definition of a validation framework is at the core of this research project. Broadly speaking, the issue will be tackled from two angles: The first approach, that we will label the «static approach», will be concerned with the validation of various individual aspects: the robustness of the model calibration, the numerical stability of the «Greeks» calculation, etc. The second approach is concerned with the quality of the dynamic hedging (measured by the replication error) that can be achieved, using the risk indicators provided by the model. This dynamic approach is relevant on two counts: Firstly, it reflects the daily practice of risk management, and secondly, the existence of a replicating strategy is the cornerstone of the risk-neutral valuation framework. One should recognize that there are no universal criteria for measuring the replication quality. This research will be conducted with an industrial partner. Model of the Financial Domain The purpose of this research topic is to identify the components of the «e-science» platform, and to define abstractions for the components and their interfaces:

20 Data repositories and simulator of stochastic processes Financial calculation engines Components for simulation dynamic hedging strategies Components for visualization, statistical analysis of results and customized reporting. The most challenging aspect of this topic will be to define a generic representation of financial instruments, that is independent of the syntax required by the various pricing libraries Ideally, this research topic should be conducted a software vendor. Connectivity to Historical Databases Historical databases are essential components of a validation framework, yet academic researchers have a very hard time gaining access to such information. The objective is to provide a native connection to the historical databases that are currently under construction by the EuroFidai research lab [EuroFidai] and Finance Innovation [Fin- Inov]. Development of the PRAXIS Framework In order to broaden the scope of PRAXIS, we plan to further develop the platform in two directions: Firstly, a number of improvements are needed to improve the user-friendliness of the platform (look and feel, documentation, etc.) Secondly, new features are required in order to better model dynamical systems. The development effort is estimated at about 6 personyear.

21 Bibliography [Rebonato01] Rebonato, R. Managing Model Risk in C. Alexander (ed), Handbook of Risk Manage ment, FT-Prentice Hall, [Rebonato03] Rebonato, R. Theory and Practice of Model Risk Management (2003) [R-software] The R project for statistical computing (www.r-project.org) [E-Science01] e-science: Article on wikipedia: (en.wikipedia.org/wiki/e-science) [E-Science02] escience: University of Cambridge escience Centre (www.escience.cam.ac.uk/escience.html) [Gray03] W.A. Gray and C. Thompson Bioinformatics and escience in Proc. UK e-science All Hands Meeting, [Sastry07] L. Sastry et al. The Integrative Biology Grid Building on e-science Components in Proc. UK e-science All Hands Meetings, [IC01] Presentation of the High Energy Physics laboratory at Imperial College: [EuroFidai] Présentation du laboratoire EuroFidai: [Fin-Inov] Plateforme d'informations financières (www.financeinnovation.org/fiche_projet_2.htm) [Premia] Premia: A platform for pricing financial derivatives (www-roc.inria.fr/mathfi/premia/index.html) [Rmetrics] Rmetrics: an open source solution for teaching financial market analysis and valuation of financial instruments (http://www.rmetrics.org)

22 Appendix A: Survey of Workflow Engines Knime (knime.org) Technologie: Java+Eclipse+plug-ins. Noter la richesse de l'information visuelle sur les composants. Sans doutes la plateforme la plus élaborée à ce jour.

23 Kepler (kepler-project.org) Technologie: Java. Possibilité de définir interactivement des composants en Matlab ou R. L'exemple ci-dessous illustre l'intégration native avec R.

24 Taverna/MyGrid (taverna.sourceforge.net) Technologie: Java. Semble surtout donner lieu à des applications de bio-informatique. Documentation très bien faite. Noter la représentation simple des composants.

25 Triana (www.trianacode.org Technologie: Java. Illustration tirée du tutoriel de Triana, utilisant des composants standard de traitement du signal.

26 SciRun (http://www.sci.utah.edu/) Technologie: C++. Décliné en plusieurs applications dans le domaine bio-informatique. Illustration tirée du tutoriel SciRun. Noter la paramétrisation très fine de la représentation des composants, alors que la géométrie des icônes reste très stylisée.

27 Appendix B: Proof of Principle Using PRAXIS An escience platform is essentially a scientific work-flow engine. This proof of principle used the PRAXIS escience platform and built some work-flow components relevant to computational finance. Calculation components are defined by standardized inputs and outputs. A standardized syntax is also defined to describe these inputs and outputs. The work-flow engine provides a graphical user interface to define the sequence of calculation, and the engine automatically schedules the calculation tasks, taking due account of the dependencies among components. In practice, the power of such framework comes from the fact that remote computing and data resources can be combined with local resources. In this proof of principle, all resources are executed locally. The proof of principle involves the following components: Various components for defining assets, diffusion processes and management policies. A path simulator, that takes as input the description of a stochastic process and generates sample trajectories. An asset calculator that takes as input the simulated paths and an asset description, and computes the value and risk indicators for this asset along each path. Two asset calculators are implemented, one with the PREMIA library from ENPC/INRIA, while the second implementation uses the Rmetrics library from ETH Zurich. An Hedging simulator, that simulates a simple delta hedging strategy, and finally a component for computing statistics on the dynamic replication error The graphical representation of an asset calculator is shown in Figure 1.

28 Figure 1 Graphical representation of an asset calculator in Euclide proof of principle. With these components, one can build a simple work flow that tests a dynamic delta hedging strategy in a Black-Scholes framework. The work flow is represented in Figure 2. Figure 2 Work-Flow in PRAXIS The PRAXIS user interface includes three sections: The left panel contains a history of all the calculations tasks that have been performed. The system keeps track of these calculations, and of all the intermediate results generated by the calculation. The middle panel represents the work flow. During an execution of the work-flow, this panel provides indications about the progress of the calculation. The rightmost panel provides a list of the components that are available. New components can be dragged onto the middle panel for inclusion in the work-flow.

29 Appendix C: The Misspecification Risk: A Simple Example The purpose of this appendix is to illustrate the misspecification risk through a simple example. Let's consider the NYMEX futures on crude oil, and options written on these futures contracts. European options on futures are quite liquid, and it is straight forward to compute the implied volatility of at-the-money options on futures. Figure 3 represents this curve, computed on options quoted on 18-Dec Figure 3: Price (blue) and ATM Volatility (red) for WTI Futures on 18-dec The Black-Scholes implied volatility is the market estimate of the average volatility that will be experienced from today until the expiry of the option. Let's now observe time series of future prices, plotted against time to expiry of the futures contract. A casual observation reveals that volatility is not constant over time, but increases

30 as contracts come closer to expiry. Pric e (USD/bbl) Price vs. Time to Expiry May 08 Sep 08 Jun 08 Jul 08 Aug 08 Oct 08 Nov T ime to Expiry Figure 4: NYMEX WTI Futures Prices vs. Time to Expiry (in days) The December 09 contract settled at $56.64 on 18-Dec-09, with an implied volatility of 52%. We now want to price an option on the December 09 contract, that expires 6 month prior to expiry of the underlying contract, that is, the option will expire on 18-Jun-09. The Black-Scholes implied volatility for this underlying asset is 52%, and in a Black-Scholes world with constant volatility, this is also the volatility that will be used to price the option expiring in 6 months.

31 A better model would account for the empirical observation illustrated in Figure 3. One such model is the Gabillon model. Calibrated to the ATM volatility, this model will price the listed options at exactly the same value as the Black-Scholes model, but will yield an implied volatility of $40% for a 6 month expiry. The calculations are summarized in the table below. Black-Scholes Gabillon Listed ATM 1 year option Implied Volatility 52.00% 52.00% Price Delta Early Expiry option (6 months) Implied Volatility 52.00% 40.00% Price Delta To summarize, two models, calibrated on the same information, can yield prices that are over 20% apart, when applied to a simple OTC derivative. The effect can be much more spectacular when applied to complex exotic contracts.

32 Appendix D: Academic and Industry Partners of EUCLIDE Partenaire Contact Nature de la relation Laboratoire CERMICS / ENPC Bernard Lapeyre (Professeur) La librairie de calcul financier PREMIA, développée par l'inria et le CERMICS, est interfacée à EUCLIDE Laboratoire Rmetrics / ETH Zurich Diethelm Würtz (Professeur) La librairie de calcul financier Rmetrics est interfacée à EUCLIDE Zeliade Systems Claude Martini (CEO) Création d'un service WEB de calcul financier à partir de la librairie Zeliade, et interface avec EUCLIDE Laboratoire Eurofidai / CNRS Patrice Fontaine (Professeur) Projet de développer un composant EUCLIDE pour accéder aux données historiques d'eurofidai.

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