The MathFinance Newsletter, Edition 137, April 10 2006.

Previous editions and this edition in html format can be found on http://www.mathfinancenews.com/.

In this issue:

1. MathFinance Job Exchange
   1. Associate (m/w) Advisory für Bewertungsfragen im Financial Risk Management bei KPMG Frankfurt
   2. Mathematiker, Physiker oder Wirtschaftsinformatiker: d-fine GmbH, Frankfurt
   3. Mathematiker/Physiker/BWLer, Weber & Partner, Heidelberg
   4. Assistant Professor, Centre of Finance and Insurance, University of Amsterdam
   5. Derivatives Analyst at EIB, Luxemburg
2. MathFinance Events
   1. Advanced Interest Rate Modelling, 18 - 21 Apr 2006, Oxford
   2. WBS Training USA Fixed Income Derivatives Week: Inflation Linked Derivatives, Interest Rate/Hybrid Derivatives, Credit Derivatives, CDOs & CDO^2 Workshop Week, 15 - 19 May 2006, New York
   3. Daniel Duffy's Finite Difference Method for Quantitative Finance: Theory, Applications and Computation, New York, 16 - 17 May and 18 - 19 May 2006
   4. The Latest Developments: Interest Rate Modelling, 12 - 13 June 2006, Venice
   5. Einführung in Monte Carlo-Methoden und C++ im Financial Engineering, 10th-14th July 2006, HfB Frankfurt
   6. Bachelier Finance Society 2006 Fourth World Congress, August 17-20 2006, Tokyo
   7. Call for Papers: 10 - 11 January 2007 at the "WHU - Otto Beisheim School of Management" in Vallendar, Germany
3. MathFinance Resources
1. New book: "Biologically Inspired Algorithms for Financial Modelling", Brabazon and O'Neill
2. "Exponentials, Diffusions, Finance, Entropy and Information" by W. Stummer
3. Encyclopaedia of Cubature Formulas by Ronald Cools, Katholieke Universiteit Leuven
4. 20% discount for Wiley Finance Books for all participants of the Frankfurt MathFinance Workshop (http://workshop.mathfinance.de)
5. Canary Wharf Jobs.com

• place a student
• recommend your book or educational institute
• find a quant
• invite to a workshop
• contribute to our website
• pose questions about mathematical finance
• introduce your research to a wider audience

The MathFinance Newsletter: Established November 1999

Editor: Uwe Wystup, MathFinance
Assistant Editors: Susanne Griebsch, HfB, Frankfurt
Database Solutions: Dr. Thorsten Schmidt, Leipzig University

In detail:
 
 

1. MathFinance Job Exchange
   
   

   1. Associate (m/w) Advisory für Bewertungsfragen im Financial Risk Management bei KPMG Frankfurt

      Ihre Perspektive: Ist Risikomanagement bei Banken Ihr Thema? Dann sind Sie bei uns genau richtig.

      Ihre Aufgaben: Die Analyse und Entwicklung von Modellen für die Derivatebewertung und das Risikomanagement bilden Ihr Betätigungsfeld. Hier übernehmen Sie frühzeitig Verantwortung in Projekten zur fachlich-orientierten Beratung und Prüfungsunterstützung im Investment Banking, Treasury, Kreditmanagement, Risikocontrolling. Ihr analytisches Verständnis und Ihre Kreativität ermöglichen es Ihnen, innerhalb kurzer Zeit Problemstellungen zu strukturieren und zu lösen. Sie arbeiten in einem hoch qualifizierten und ambitionierten Team. Ihre Arbeitsergebnisse entwickeln und diskutieren Sie mit dem Mandanten, bei dem Sie Ihre Lösungsvorschläge in hochrangig besetzten Gremien präsentieren und vertreten.

      Ihr Profil: Sie haben ein Universitätsstudium der Mathematik, Wirtschaftsmathematik, Wirtschaftsingenieurwesen, Physik, BWL oder VWL mit quantitativem Schwerpunkt absolviert und Ihre überdurchschnittliche Qualifikation z.B. durch einen sehr guten Abschluss und/oder eine Promotion bewiesen. Sie haben Interesse an der Weiterentwicklung von Modellen, die die Bewertung und das Risikomanagement von neuen Produkten und in neuen Märkten ermöglichen. Der effiziente Einsatz numerischer Verfahren wie Monte Carlo Simulation und deren Umsetzung in C++ ist Teil Ihrer praktischen Erfahrung. Sie verfügen über außerordentliche analytische Fähigkeiten und haben großen Spaß daran, ständig neue Dinge zu lernen und zielorientiert umzusetzen. Sehr gute Englischkenntnisse setzen wir voraus. Sie sind sicher im Auftreten sowie team- und kundenorientiert. Ein Auslandsaufenthalt und/oder relevante Praktika runden Ihr Profil ab.

      Ihr Kontakt: Bewerben Sie sich online auf http://www.kpmg.de/careers
      
      oder senden Sie Ihre Bewerbung unter Angabe des Referenzcodes: AdvFestFSoJo50204504 an das
      
      Recruiting Team, KPMG,
      Klingelhöferstr. 18,
      10785 Berlin,
      eMail: .
      
      

      Für weitere Rückfragen steht Ihnen das HR Service Phone unter 0 800 KPMG JOB (0 800 5764 562) zur Verfügung.

      Profitieren Sie von den Entwicklungsmöglichkeiten bei KPMG, einem weltweiten Verbund national selbständiger Mitgliedsfirmen. Neben abwechslungsreichen Projekten im In- und Ausland bieten wir Ihnen Raum für Ihre persönliche Weiterentwicklung. Mehr wissen, mehr können - bei uns hat Erfolg, wer team- und mandantenorientiert arbeitet und gleichzeitig seine persönliche Entwicklung vorantreibt.

      
      
      

   2. Mathematiker, Physiker oder Wirtschaftsinformatiker: d-fine GmbH, Frankfurt

      Sie haben in der Wissenschaft viel bewegt? Dann können Sie auch in der Wirtschaft viel bewegen! Davon sind wir bei d-fine fest überzeugt.

      d-fine ist mit über einhundert Beratern eines der größten auf die Finanzwelt spezialisierten Beratungsunternehmen in Europa. Wir fokussieren höchste naturwissenschaftlich- technische Kompetenz auf die anspruchsvollen Herausforderungen unserer Kunden.

      Wir beraten Banken, Versicherungen und Industrieunternehmen beim Aufbau ihrer Handels- und Risikomanagementsysteme von der ersten Idee bis zur professionellen Implementierung der Lösung, vom finanzmathematischen Modell bis zur real-time Schnittstelle, vom einfachen Kredit bis zum exotischen Derivat, vom Ratingsystem bis zur Portfoliosteuerung, von IAS 39 bis Basel II.

      Unsere Kunden schätzen unseren kompromisslos hohen Qualitätsanspruch und vor allem, dass wir diesen Anspruch auch realisieren. Das beginnt schon bei der Auswahl unserer Mitarbeiter: Wir suchen Sie als Naturwisssenschaftler, Mathematiker oder Informatiker. Sie besitzen einen exzellenten Hochschulabschluss, sprechen fließend Englisch und haben überdurchschnittliche IT- sowie Programmierkenntnisse. Idealerweise sind Sie darüber hinaus mit Statistik, Numerik und Finanzmathematik vertraut und beherrschen Simulationsmethoden wie beispielsweise Monte Carlo.

      Unbedingt erwarten wir von Ihnen analytisches Denken, ergebnisorientiertes Vorgehen und exzellente Kommunikationsfähigkeiten. Sie sind teamfähig, erfassen auch sehr komplexe Aufgaben schnell und können sich rasch in neue IT-Umgebungen einarbeiten. Sie haben Beratungstalent, hohe Einsatzfreude und sind flexibel und belastbar.

      Selbstverständlich geben wir Ihnen eine intensive Einführung in Ihr zukünftiges Aufgabenfeld sowie ein anspruchsvolles finanzmathematisches Training auf höchstem Niveau in Zusammenarbeit mit führenden internationalen Universitäten.

      Wenn Sie in einem Team hoch begabter und hoch motivierter Kollegen mitarbeiten wollen, große individuelle Freiräume, viel Eigenverantwortung sowie hervorragende Entwicklungsperspektiven suchen, freut sich Frau Yasemin Keles auf Ihre Bewerbung.

      Willkommen im d-fine Team!
      
      Starten Sie durch!
      
      d-fine GmbH
      Opernplatz 2
      60313 Frankfurt am Main
      Telefon: +49-69-90737-0
      E-mail:
      Homepage:http://www.d-fine.de
      
      

   3. Mathematiker/Physiker/BWLer, Weber & Partner, Heidelberg

      Weber & Partner ist ein kleines Beratungsunternehmen in Heidelberg, das in enger Zusammenarbeit mit SciComp USA (www.scicomp.com) eine innovative Umgebung für die Entwicklung von Bewertungsroutinen für Finanzderivaten verkauft, entwickelt und für die Beratung von Kunden (Banken) einsetzt. Für diesen Bereich suchen wir ab sofort einen Uniabsolventen oder Studenten als zusätzliche Unterstützung.
      
      Ihr Profil:
      
      
      • Grundkenntnisse über Finanzderivate
      • Kenntnisse von numerischen Lösungsverfahren von partiellen Differentialgleichungen (Differenzenverfahren) und Simulation von stochastischen Prozessen (Monte Carlo Methode)
      • Gute C/C++ Programmierkenntnisse
      • Gute Englischkenntnisse in Schrift und Wort
      • PC-Kenntnisse, MS-Excel und Latex
      • Mathematica-Kenntnisse sind hilfreich
      
      
      Bei Interesse wenden Sie sich bitte an
      
      Herrn Dr. Thomas Weber,
      Tel. 06221/438509-10,
      e-mail:.
   
   
   

   4. Assistant Professor, Centre of Finance and Insurance, University of Amsterdam

      The faculty of Economics and Business at the University of Amsterdam is seeking candidates at the assistant professor level for a new Centre of Finance and Insurance. We welcome applications from excellent candidates in the areas of mathematical finance and actuarial science. Successful applicants will undertake and help coordinate research and teaching in the fields of actuarial science and finance broadly defined. The new Centre of Finance and Insurance has strong links with Netspar, a Dutch institute for research on pensions, aging, and retirement. In particular, the Centre will focus on applying option valuation techniques to value pension and insurance liabilities.

      Requirements are a PhD, the ability to initiate and implement international high-quality research and to stimulate and encourage the research of others, and demonstrated teaching excellence. Assistant professor appointments involve tenure-track positions, with an appointment for initially four years, to become tenured upon good research and teaching performance.

      The faculty of Economics and Business offers undergraduate and graduate courses and several Master programs. The teaching load is reasonable and can be concentrated both in time and in preparations.

      The University is located in the centre of Amsterdam in modern facilities. Amsterdam is a very friendly city in Europe with a high quality of life. Almost everyone in the Netherlands speaks good English. Compensation is very competitive relative to European salaries. Favourable tax agreements may apply to non-Dutch applicants.

      Applicants should submit their CV, research papers and at least three reference letters to .
      
      Further information can be obtained from Dr. Joost Driessen, tel. +31 20 525 5263 (http://www1.fee.uva.nl/fm/PEOPLE/driessen.htm).
   
   
   

   5. Derivatives Analyst at EIB Luxemburg

      The EIB, the European Union's financial institution, is seeking to recruit for its Risk Management Directorate (RM) - Financial Risk Department - Derivatives Division at its headquarters in Luxembourg a:

      Derivatives Analyst

      The Derivatives Division of the Financial Risk Department manages the credit exposure associated with Capital Market and Treasury transactions.

      In the context of the Basel II project, the successful candidate will help make the Derivatives Division compliant with supervisory requirements for Structured Transactions. In particular, s/he will: support the implementation of valuation models, their validation, update and documentation; develop econometric models for the estimation of market data; cooperate in the computation of the "fair price" of swap transactions and the determination of collateral requirements

      Responsibilities

      • Analyse new borrowing transactions and structured derivatives and assess risks
      • Develop and run valuation models for structured transactions
      • Validate, review, update and document swap valuation models and procedures
      • Specify market data requirements for valuation purposes in liaison with the Data Manager in FI
      • Develop econometric models for the estimation of relevant market data
      • Produce the "fair value" for swap transactions for accounting purposes
      • Verify the valuation of the "fair price" of transactions performed by counterparties
      • Define required collateral levels and verify counterparts' valuations
      • Contribute to the definition of: (a) exposure measures for derivative transactions, (b) bilateral counterpart limits and (c) more general policy guidelines to mitigate credit risks on the Bank's derivative portfolio

      Qualifications

      • University degree, preferably in mathematics, quantitative finance and/or statistics. Post-graduate studies in these subjects would be an advantage
      • Solid professional experience acquired with a major derivatives user, with extensive implication in derivatives control
      • Sound knowledge in the areas of derivatives valuation and statistics, as well as in derivatives valuation packages, such as NUMERIX and Algorithmics
      • Knowledge of econometric techniques to estimate model parameters and data
      • Expertise in mathematical programming languages, e.g. Visual Basic, MathLab or Mathematica
      • Familiarity with the main issues of credit risk quantification
      • Knowledge of financial models and credit portfolio management would be an advantage
      • Very good knowledge of English or French and good knowledge of the other. Knowledge of other EU languages would be an advantage

      Competencies

      • High level analytical capabilities
      • Ability to work in a team
      • Strong interpersonal skills
      • Strong verbal and written communication skills
      • Ability to organise, prioritise and work under tight deadlines

      Applicants must be nationals of a European Union Member State or one of the Acceding Countries. The EIB offers attractive terms of employment and remuneration with a wide range of benefits. The EIB is an Equal Opportunities Employer and particularly welcomes applications from women.

      To apply, please go to www.eib.org/jobs and click on reference number RM06WWW12.

      Applications will be treated in strictest confidence. They will not be returned. Personal Data are protected by Community Regulation.

      All current vacancies can be found on our website www.eib.org/jobs

      
      
      
   
   
   
2. MathFinance Events
   
   
   
   
   

   1. Advanced Interest Rate Modelling, 18 - 21 Apr 2006, Oxford

      Presenters: Piotr Karasinski (HSBC), Jochen Theis (Merrill Lynch), Chris Hunter (BNP Paribas), Riccardo Rebonato (RBOS)
      Organiser: Oxford University Centre for Professional Development & Oxford University Mathematcal Institute
      
      Topics Covered:
      
      
      • Motivational overview and historical data kara
      • Exotic interest rate derivatives theis
      • Term structure modelling
      • Smiles: Mechanisms, causes, financial explanation and modelling
      • Numerical techniques and example implementations
      • Calibration algorithms for different types of models
      • Hybrid products
      
      
      Contacts:
      
      Nynke Penninga, Anke Probst
      T: +44 (0)1865 286954 F: +44 (0)1865 286956
      Email:
      Weblink: http://www.conted.ox.ac.uk/cpd/mathsfinance/courses/msc/module9.asp
      Website: http://www.conted.ox.ac.uk/cpd/mathsfinance/
      Fee: £1500:00
      
      

   2. WBS Training USA Fixed Income Derivatives Week: Inflation Linked Derivatives, Interest Rate/Hybrid Derivatives, Credit Derivatives, CDOs & CDO^2 Workshop Week, 15 - 19 May 2006, New York

      Day 1:
      
      Introducing Inflation-linked Securities and Derivatives: Introductory / Intermediate
      
      Presenters: David Murphy & Andrew Street
      
      Topics Covered:
      
      
      • Understanding Inflation
      • Inflation-Linked Securities: The Standard Bond Structure
      • Investors and the Demand for Inflation-Linked Products
      • Inflation-Linked Securities: Perspectives for Traders and Issuers
      • Building the Inflation Curve
      • Structuring Effective Inflation-Linked Products
      • Pricing and Trading Derivatives on Inflation
      
      
      Day 2:
      
      Latest Developments of Inflation-linked Derivatives
      
      Presenters:
      
      Gang Hu: Associate Director of U.S. Inflation Trading, Barclays Capital
      Lane P Hughston: Professor of Financial Mathematics, King's College
      Dariush Mirfendereski: Head of Inflation Linked Trading, UBS
      
      Topics Covered:
      
      
      • Models for real interest rates and inflation: New Directions
      • General theory of inflation dynamics
      • "Hidden variables" models for inflation
      • Practical Perspectives on Pricing, Trading, and Hedging Inflation-Indexed Derivatives - from the Dark Ages to the Present
      • The Road Ahead: what to watch out for in this fast developing market
      • A Users' Manual on Inflation Derivative Products
      • iStrips
      • Structured Products on the market
      • Potential structures that might be of interest to the market, and general view on the outlook of the inflation derivative market.
      
      
      Day 3:
      
      Latest Developments: Interest Rate Derivatives / Interest Rate Hybrid Products
      
      Presenters:
      
      Tariq Dennison: Vice President, Bear Sterns
      Lane P Hughston: Professor of Financial Mathematics, King's College
      Chris Hunter: Managing Director: BNP Paribas
      John Uglum: Executive Director: Morgan Stanley
      
      Topics Covered:
      
      
      • Overview of the General Theory of Interest Rate / Hybrid Models
      • Pricing and Hedging of Callable Exotic Swaps
      • The LIBOR market model and stochastic volatility extension
      • Solving the stochastic control problem using Monte Carlo
      • Practical implementation issues and variance reduction techniques
      • Complete overview of Interest Rate / Equity Hybrids
      • Correlation Smile and Hybrid Pricing
      
      
      Day 4:
      
      The Latest Developments: Credit Derivatives Presenters:
      
      Jon Gregory: Global Credit Derivatives: Barclays Capital
      Paul Glasserman: Professor of Risk Management, Columbia Graduate School of Business
      Marco Naldi: Lehman Brothers
      
      Topics Covered:
      
      
      • The Correlation Skew and Correlation Modelling
      • The Gaussian Copula Model and Beyond
      • The Correlation Skew and Base Correlations
      • Monte Carlo for Credit Risk and Credit Derivatives
      • Fast pricing of basket default swaps
      • Accelerating Monte Carlo by increasing default rates
      • Pricing Exotic Tranches / Relative value trading of liquid tranches
      
      
      Day 5:
      
      The Latest Developments: CDOs & CDO^2
      
      Presenters:
      
      Terry Benzschawel: Director of Qualitative Credit Modeling and Analytics, Citigroup
      David Li: Head of Quantitative Analytics Credit Derivatives, Barclays Capital
      Michael liang: Quantitative Analytics Credit Derivatives, Barclays Capital
      Maximo Silberberg: Vice President, Structured Credit, JP Morgan
      
      Topics Covered:
      
      
      • Overview of CDOs
      • CDOs: Credit Selection, Trade Construction, and Portfolio Optimization
      • CDO Equity as an Asset Class
      • CDOs in Portfolios of Traditional and Alternative Assets
      • Customizing CDO Tranche Trades
      • Credit Portfolio Correlation Skew Modelling
      • Alternative Bespoke CDO pricings
      • Market overview for synthetic CDO^2
      • CDO2 pricing: Price a CDO2 consistently with the pricing of the underlying CDOs
      • Construction of synthetic CDO^2
      • Further extensions of CDO^2 technology
      
      
      Fees: $1399:00 each day
      
      Discount Structure
      
      2 days $200 Discount
      3 days $300 Discount
      4 days $400 Discount
      5 days $600 Discount
      
      Contact:
      
      Neil Fowler
      T: +44(0) 1273 674400 F: +44(0) 1273 672333
      Weblink: http://www.wbstraining.com/?m=WS&p=courses/5daynymay2006.php
      Website: http://www.wbstraining.com
      Email:
   
   
   

   3. Daniel Duffy's Finite Difference Method for Quantitative Finance: Theory, Applications and Computation, New York, 16 - 17 May and 18 - 19 May 2006

      Course fee: 2 days: 1.790,-- euro or 4 days 3.180,-- euro.
      
      Register on-line
      
      This course introduces and applies robust and efficient finite difference schemes to partial differential equations (PDE) that model financial instruments. In particular, we approximate the one-factor and multi-factor Black Scholes equations by finite differences. This course assembles some of the most powerful and proven finite difference schemes and applies them to approximating the PDEs for financial instruments.
      
      Your trainer is Dr Daniel J. Duffy.
      
      Special Features of this Course
      
      
      • New, revised and optimized finite difference schemes
      • Full documentation and C++ source code (and a copy of Duffy's book 'Finite Difference Methods in Financial Engineering, a Finite Difference Approach' Wiley 2006)
      • Using the C++ framework on your laptop. Output in the Excel visualization package. The focus is not C++ programming but on changing parameters and adding a few lines of strategic code to test new models.
      • If you wish you can bring your own models to test FDM
      
      
      After having completed this course you will be in a position to apply FDM to Quantitative Finance applications. You can bring your own test cases and examples as input. The focus is on the full project, from the financial model through PDE, FDM and numerical experimentation in C++ and Excel.
      
      Bring your own laptop if you want to try out the provided code during the course.
      
      What past attendees have said of this Course
      
      
      • "The best and most extensive documentation I have ever received"
      • "Good value for money"
      • "Goes beyond basic schemes, real problems and details discussed"
      • "Fills a gap in the training landscape"
      
      
      Please note that in-company courses are possible and can be customized to your wishes. The course is given in London and New York on a regular basis.
      
      This course will be given in English.
      
      Course contents
      
      Part I (Day 1): Finite Difference Fundamentals
      The goal of the first day is to give a complete overview of the Finite Difference Method (FDM) and it applications to QF.
      
      Overview of Partial Differential Equations
      
      
      • Parabolic, hyperbolic and elliptic PDE
      • Boundary and initial (payoff) conditions
      • One-factor and multi-factor PDE
      • Existence and uniqueness results
      
      
      PDE and its Relationships with Stochastics
      
      
      • Motivating FDM by Brownian motion
      • Stochastic Differential Equations (SDE) and their approximations
      • Ito calculus and the Feynman-Kac equation
      • Comparing FDM and Monte Carlo methods
      
      
      The Black Scholes PDE and its Generalisations
      
      
      • The PDE taxonomy in Quantitative Finance
      • Properties of the original and generalised PDEs
      • Fixed and free boundaries
      • PDE and payoffs for correlation options
      • Heston stochastic PDE
      • Jump models and Partial Integro-Differential Equations (PIDE)
      
      
      Introduction to FDM for PDE
      
      
      • Meshes, divided differences and finite difference schemes
      • Semi-discretisation (Method of Lines, Rothe's method)
      • Full discretisation in time: Euler, Crank-Nicolson, Runge-Kutta
      • Solving discrete sets of equations
      
      
      Theoretical Issues
      
      
      • Consistency, stability and convergence
      • Conditional and unconditional stability
      • Von Neumann stability analysis versus M-matrix approach
      • Examples from QF
      
      
      Important Issue: Matrix Computation
      
      
      • Overview of Numerical Recipes and Golub/Van Loan
      • Direct and iterative methods for solving linear systems of equations
      • LU decomposition and solution of tridiagonal systems
      • Cholesky decomposition and applications in QF
      • FDM algorithms and their mapping to matrix systems
      
      
      C++ Workshop
      
      
      • Testing and using explicit and implicit schemes
      • What-if scenarios with discontinuous payoff functions
      • Convection-dominated problems
      • Writing your own mini Crank-Nicolson scheme
      
      
      Part II (Day 2): One-Factor Models and Efficient Schemes
      In this part we apply the FDM from day 1 to the pricing and hedging of one-factor European and American options using FDM. We also touch on N-factor models.
      
      One-factor Models
      
      
      • Explicit and implicit schemes
      • Discretisation of boundary conditions (Dirichlet, Neumann, linearity)
      • Payoff and smoothing effects
      • Setting up the discrete systems of equations
      
      
      Barrier and Lookback Options
      
      
      • Continuous and Discrete monitoring
      • Modelling jumps and time-marching schemes
      • Approximating the greeks (delta, gamma, theta, vega)
      
      
      Asian Options
      
      
      • Parabolic and hyperbolic components
      • The problems with centred differencing and numerical boundary conditions
      • Upwinding and downwinding schemes
      • Stability and convergence
      
      
      One-factor Models (early exercise)
      
      
      • Penalty methods, change of variables, LCP: comparisons
      • The Landau transformation in detail
      • The penalty method in detail
      • Implicit, semi-implicit and explicit schemes
      • The (ubiquitous) predictor-corrector method
      
      
      C++ Workshop: Plain and Barrier Options
      
      
      • Creating a generic time-marching scheme
      • Implementing boundary conditions: first-order and second-order schemes
      • Solving tridiagonal systems
      • Modelling integral equations and jumps
      
      
      C++ Workshop: American Options
      
      
      • Approximation of the smooth pasting conditions
      • Comparing the performance of the different schemes
      • Predictor-corrector versus penalty method
      • Calculating greeks near the strike price
      • C++ payoff classes and integration into framework
      
      
      Part III (Day 3): N-Factor Financial Modelling
      The goal of this part is to develop the theory of FDM for n-factor pricing models. We shall deal with robust and efficient finite difference schemes that we subsequently use in QF.
      
      An Overview of the Candidates
      
      
      • Overview and summary of the schemes from the first two days
      • Alternating Direction Implicit (ADI)
      • Soviet Splitting and Locally One-Dimensional (LOD) schemes
      • ADE: explicit and unconditionally stable methods
      • Rothe's method and iterative elliptic systems
      • Comparing the different schemes
      
      
      Attention Points and Challenges
      
      
      • Achieving good accuracy and performance
      • Approximating mixed derivatives
      • Convection-dominated problems and spurious oscillations
      • Exponential fitting Algorithms and closing to code
      
      
      ADI in Detail
      
      
      • ADI classico
      • Craig-Sneyd scheme for problems with mixed derivatives
      • Solution by LU decomposition
      • Examples
      
      
      Splitting in Detail
      
      
      • Explicit and implicit methods
      • Approximate factorization methods
      • Handling Dirichlet, Neumann and linearity boundary conditions
      • Examples
      
      
      PIDE
      
      
      • The Merton jump model
      • Approximation of PIDEs
      • Splitting and predictor-corrector methods
      
      
      Two-factor American Options
      
      
      • Formulation and PDE
      • Using the penalty method
      • Semi-implicit and explicit methods
      
      
      Part IV (Day 4): Applications
      In this part we examine a number of 2-factor and 3-factor pricing problems whose solutions we approximate using FDM. The students can test the models using the C++ software provided with the course. The focus will be on practical problems in QF.
      
      Stochastic Models
      
      
      • Defining the PDE model
      • Approximation using FDM
      • Boundary conditions
      • European and barrier options
      • Approximating the greeks
      
      
      Correlation Options
      
      
      • A common PDE framework
      • Mixed derivatives
      • Solving the system of equations
      • Multi-asset payoff function: handling non-smooth payoffs
      • Approximating the greeks
      
      
      N-Factor Models, N = 3, 4, …
      
      
      • Using approximate factorization
      • ADE and sweeping schemes
      • Why no! matrix inversion is needed when using ADE
      
      
      C++ Workshop
      
      
      • Using splitting and ADI schemes
      • Stress and performance testing
      • Visualisation
      • Extending the C++ framework: some hints and guidelines
      
      
      Who should attend?
      
      This course is for anyone who wishes to know the details of how to price derivatives using the Finite Difference Method. The course suitable for the following kinds of attendees:
      
      • Those who wish to learn the basics of FDM and apply it to one-factor models (the first two days)
      • Those who have experience of FDM and who wish to skip the first two days (these students can then attend the last 2 days of the course)
      • Those who wish to attend the full 4-day course
   
   
   

   4. Einführung in Monte Carlo-Methoden und C++ im Financial Engineering , 10th-14th July 2006, HfB Frankfurt

      Christoph Becker und Uwe Wystup

      HfB - Business School of Finance and Management