Day Three - Latest research in interest rate modellingInnovations in existing models are contrasted with a new geometric methodology for interest rate modelling in a specially extended masterclass. Leading names will provide thecontent and a practitioner's orientation will be upheld by Dr. Peter Jäckel from The Royal Bank of Scotland in his role as chairman.08.0008.3008.4009.4010.4011.0012.0013.00Registration and breakfastChairman's opening remarksMARKOV INTEREST RATE MODELS AND CALIBRATION· Short rate models· Market rate models· Numerical implementation· Calibration to options· Calibration to volatility smiles· Pricing complex interest rate derivativesMONTE CARLO IN THE BGM/J FRAMEWORK: using a non-recombining tree todesign a new pricing method for Bermudan swaptions· Choosing an appropriate instantaneous volatility structure· Calibrating to European swaptions· Predictor-Corrector handling of the state dependent drift coefficients· Using a non-recombining tree to select the best coordinate system for the parametrisation ofthe exercise boundary· Numerical resultsMorning breakA VARIANCE GAMMA BGM MODEL FOR PRICING EXOTIC INTEREST-RATEDERIVATIVES· Review of the variance gamma model for stock evolution.· Fitting forward rates into the variance gamma setting; changes of numeraire· Time-dependent instantaneous volatility in the variance gamma model· Smiles produced by the modelA MARTINGALE APPROACH TO RISK COMPUTATION· Background- Gradual retirement of long-dated US Treasuries; MBS used as substitution- "Monte Carlo over Monte Carlo" in risk computation for portfolios with significant positions inMBS or other agency issues· Discrete-Time Analysis- Tree Construction- Markov Property- Girsanov Transformation- Prepayments· Continuous-Time Analysis- Boundary Conditions- Fokker-Planck Equation- Jump Conditions- Computational Considerations· Empirical AnalysisLunchDr. Peter Jäckel, Quantitative Research Centre, The Royal Bank of ScotlandAnlong Li, Director of Quantitative Research, Citadel Investment Group, L.L.C.Before joining Citadel Investment Group, Mr Li was Senior Vice President and head of Structured ProductsGroup for fixed-income derivatives at ABN AMRO North America in Chicago, responsible for structuring,trading and the development of new derivative products, from 1996 to 1999. He was head of ProductDevelopment and Derivative Research for Global Derivatives at the First National Bank of Chicago in Chicago,IL, from 1994 to 1996. He also worked in derivative products at both Salomon Brothers and Lehman Brothers.Mr Li received his Ph.D. in Operations Research from Case Western Reserve University. His work appears inmany academic as well as professional journals.Dr. Peter Jäckel, Quantitative Research Centre, The Royal Bank of ScotlandDr. Peter Jäckel received his DPhil from Oxford University in 1995. In 1997, he moved into quantitative analysisand financial modelling when he joined Nikko Securities. Currently, he works as a Senior Quantitative Analyst inthe Quantitative Research Centre of the enlarged Royal Bank of Scotland Group. His primary responsibilitiesare independent model validation and derivatives modelling research but he is also consulted firm-wide onvarious risk assessment and derivatives pricing methodology issues.Dr Mark S. Joshi, Quantitative Research Centre, Group Risk, Royal Bank of ScotlandBiographical note:BA (Oxon) 1990, Phd (MIT) 1994 In the theory of PDEs. 1994-1999 Assistant Lecturer, Department of PureMathematics and Mathematical Statistics, University of Cambridge, 1999-<strong>2000</strong>, Senior Quantative Analyst,Quantitative Research Centre, Natwest Group Risk the RboS Group Risk, researching derivatives pricing anddoing model validation.Bernard Lee, Director of Financial Engineering Consulting, SunGard Trading and Risk SystemsProfessor Nicos Christofides, Director, Centre for Quantitative Finance, Imperial College <strong>London</strong>Bernard Lee, CFA, is Director of Financial Engineering Consulting at SunGard Trading and Risk Systems andResearcher at the Centre of Quantitative Finance at Imperial College, <strong>London</strong>. He holds undergraduate andpostgraduate degrees in finance, applied mathematics and computer science from Princeton and Stanford, andis a charter holder of the CFA designation. Prior to joining SunGard, he worked for two proprietary tradingdesks and ran a relative-value arbitrage book, among taking other "quant" positions in the industry. Mr. Lee haspublished in Risk Magazine, Journal of Risk Finance, Derivatives Strategy, Derivatives Week and FinancialEngineering News, as well as co-edited the Infinity Guide to FAS 133/IAS 39 Compliance. (At press time, Mr.Lee has accepted an offer to join the Financial Commodities Risk Consulting Group at Arthur Andersen LLP inNew York.)Professor Nicos Christofides graduated from Imperial College in 1963 (BSc) and 1966 (PhD) in ElectricalEngineering. He has been a member of academic staff at Imperial College since 1967 and was appointed theProfessor of Operational Research in 1984. His teaching and research includes Graph Theory, Networks, andOptimisation. Since its inception in 1992 he has been a Director of the Centre for Quantitative Finance andconcentrates on the application of mathematical techniques to financial problems. Professor Christofides hassupervised over 80 successful PhD students in Imperial College and published over 100 papers and fourbooks in fields as diverse as distribution systems (location, routing and scheduling), cost benefit analysis,computer vision and quantitative finance.
14.0015.0016.0016.3017.3017.40MASTERCLASSSTATISTICAL GEOMETRY IN TERM STRUCTURE MODELLING: THEORY ANDAPPLICATIONPart 1: Theory· Review of information geometry and its applications to modern statistics· Theory of probability distribution comparisons and statistical manifolds· General characterisation of positive interest rate term structures by use of statistical geometry· New formulation for Heath-Jarrow-Morton term structure dynamics as a process on a statisticalmanifoldMASTERCLASS (CONTINUED)STATISTICAL GEOMETRY IN TERM STRUCTURE MODELLING: THEORY ANDAPPLICATIONPart 2: Application· Principal moment dynamics for yield curve structures· Statistical divergences for term structures· Quasi-lognormal models· Canonical parametric models and calibration· Hilbert space dynamics for infinite dimensional term structure movements: statistical geometryas a natural setting for interest rate string theoryAfternoon breakMATHEMTAICAL FOUNDATION OF CONVEXITY CORRECTION CALUCLATIONS FORPRICING EXOTIC INTEREST RATE DERIVATIVES· Convexity Correction and Change of Numeraire· Options on Convexity Corrected Rates· Linear Swap Rate Model· Single Index Products- LIBOR in Arrears- Constant Maturity Swap- Diffed LIBOR- Diffed CMS· Multi-Index Products- Rate Based Spread Options- Spread Digital- Other Multi-Index Products- Comparison with Market Models· A Warning on Convexity CorrectionChairman's closing remarksEnd of day threeDr. Dorje C. Brody, Royal Society University Research Fellow, Imperial CollegeDr. Brody is a Royal Society University Research Fellow at Imperial College, <strong>London</strong>. He also holds a ResearchFellowship at Churchill College, Cambridge, where he is based at the Centre for Mathematical Sciences,Cambridge University. His research specialities include mathematical finance and its applications to interestrate modelling, statistical mechanics, and the foundations of quantum theory.Professor Lane P. Hughston, Centre for Financial Mathematics, King's College <strong>London</strong>Lane Hughston is Professor of Financial Mathematics at King's College <strong>London</strong>. He received his D. Phil. inMathematics from Oxford University. Before joining King's he was Director of Derivative Product RiskManagement at Merrill Lynch, where he was responsible for managing the development of pricing models forinterest rate and foreign exchange derivatives, and other products. His research interests include: mathematicalfinance and its applications in an investment banking context; the pricing and risk management of derivatives;martingale models for interest rates and foreign exchange; the impact of transaction costs; stochastic volatilitymodels; and applications of information geometry and stochastic differential geometry. For more informationsee: http://www.mth.kcl.ac.uk/Dr Antoon Pelsser, Sr Actuary, Nationale-NederlandenDr. Antoon Pelsser is a Senior Actuary at the insurance company Nationale-Nederlanden (part of ING group)and is responsible for the calculation of market values and risk measures of the insurance portfolio. From 1993until <strong>2000</strong> he was Vice President at ABN-Amro Bank in Amsterdam, where he was responsible for thedevelopment of pricing models for exotic interest rate derivative products. During that time he also held apart-time position as an assistant professor at the Erasmus University of Rotterdam in the Department ofFinance. In 1999 his PhD thesis on interest rate derivative models has been awarded by the Royal DutchAcademy of Sciences the Christiaan Huygens prize. Dr. Pelsser has been published in several academicjournals including Finance and Stochastics, European Journal of Operational Research, Journal of FinancialEngineering and the Journal of Derivatives. He is also author of the book Efficient Methods for Valuing InterestRate Derivatives, published by Springer Verlag.DAY THREE
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