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FUNCTIONAL CALCULUS FOR FINANCE – January 12, 2009

Claudio Albanese, Level 3 Finance
8:00-8:30 Registration and Opening Address
Petter Kolm, Deputy Director of Mathematics in Finance M.S. Program, Courant Institute
Morning Session(8:30-12:30)

Part I. Stochastic Processes

  • Constructive probability theory
  • Markov processes
  • Martingales and monotonic processes
  • The Fundamental Theorem of Finance
  • Application: Regime switching dynamics for equity derivatives

Part II. Convergence and Smoothness

  • Spectral Methods
  • Fast Exponentiation
  • Smoothness and the Courant condition
  • Brownian Motion
  • Diffusion Processes
  • Application: Sensitivities and single precision arithmetic
Afternoon Session(2:00-5:00)

Part III. Moment Methods

  • Markov Bridges
  • Stochastic integrals
  • Moment expansions for stochastic integrals
  • Application: Volatility derivatives

Part IV. Pricing Methods

  • Backward Induction
  • Long step Monte carlo and malliavin calculus
  • Abelian processes in continuous Time
  • Feynman-Kac formula and other block diagonalizations
  • Abelian processes in Discrete Time and non-Resonance Conditions
  • Block factorizations
  • Application: Cliquets

 

Day 2 - DERIVATIVE MODELS - 13 January 2009

Claudio Albanese, Level 3 Finance
Morning Session(8:30-12:30)

Part I. Stochastic Monetary Policy Models for Interest Rate Derivatives

  • Short rate models in the operator formalism
  • Modelling stochastic monetary policy
  • Discounted transition probability kernels
  • Discounted functions and swap rates
  • Backward induction
  • Forward induction
  • Monte Carlo scenario generation
  • Callable swaps
  • Target redemption notes Snowballs

Part II. Calibration, Valuation and Risk Management of Exotic Interest Rate Derivatives

  • Levenberg-Marquardt and differential evolution
  • The Rotating Frames algorithm
  • Calibration baskets with exotics
  • Cash flow synchronization for VAR calculation
  • Historical calibration and risks
  • Application: Callable CMS spread options
  • Calibration baskets with exotics
  • Cash flow synchronization for VAR calculation
  • Historical calibration and risks
  • Application: Callable CMS spread options
Afternoon Session(2:00-5:00)

Part III. FX Derivatives and Hybrids

  • Designing FX models
  • Stochastic volatility and stochastic reversals
  • Embedding mean reversion in risk neutral dynamics
  • Joint calibration to European and barrier options
  • Long dated FX models
  • Dynamic copulas for Monte Carlo Pricing
  • Example: PRD TARNs

Part IV. Structural Credit Models

  • Designing and calibrating single name credit-equity models
  • Dynamic conditioning
  • CDO tranche pricing and calibration

 

Day 3 - GPU-BASED QUANTITATIVE FINANCIAL MODELING - January 14, 2009
8:30-9:00 Registration and Welcome Address
Petter Kolm, Mathematics in Finance M.S. Program, Courant Institute
Morning Session(9:00-12:30)

9:00-9:50 Tesla and CUDA Overview, John Milner, Director of GPU Computing, NVIDIA

10:00-11:30 Programming financial computations on multi-GPU configurations, Claudio Albanese, Professor, Imperial College London

11:30-12:30 The use of architecturally diverse systems to accelerate the performance of Monte Carlo simulations, Naveen Singla, Exergy, Inc.

12:30-2:00 Lunch
Afternoon Session(2:00-5:00)

2:00-3:00 CUDA and Options Pricing, Gerald Hanweck, Jr .PhD, Principal, Hanweck Associates

3:15-4:15 Parallel computing and financial instrument modeling, Dean Tallam, SciComp

 
 
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