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Course Calendar Course Calendar

BGM Models and Advances: Basis, CSA, Credit and Funding

Day One

Foundations and the new markets

  • The interest rate market and the foundations of modelling
  • What has changed in the market with the crisis. Libor, OIS, the basis. Collateral agreements. The new relations among market quotes
  • Practical advantages and shortcomings of different modelling approaches in the new market. Short rate modelling, HJM, Libor and Swap Market Models (BGM)
  • Understanding Market Models: from market Black formulas to the Libor Market Model
  • From the basic Libor Market Model to a Dual Libor Market Model with CSA discounting

Volatility and the cap market

  • Parameterising the model: the choice of the Volatility Structure. Future evolution and implications on pricing and stability. The evolution of the Term Structure of Volatility during the Financial Crisis
  • Calibrating different volatility structures to cap quotes. The relation between volatilities for different tenors (i.e three month, six month, one year)

Volatilities, correlations and the swaption market

  • Correlation Modelling:  Desirable properties, Historical Estimations, Parametric Forms for today’s decorrelation
  • Controlling Model Dimension. The number of factors
  • Establishing a one-to-one relationship between parameters and market quotations for precise volatility bucketing
  • Calibrating exactly and instantaneously to swaptions. Analysis of calibration market cases. Diagnostics of Calibration: controlling realism, stability and consistency of the results. Joint Calibration. Possible inconsistencies between cap and swaption markets

More Analytics and Numerics for the BGM

  • Accurate approximations for efficient calibration to swaptions. Testing the approximations on crisis stressed data
  • Monte Carlo Pricing in the LMM:  from Log-Euler to Milstein to Predictor-Corrector  schemes
  • Efficiency, Variance Reduction and Control Variates

Workshop: Volatility and correlation structures

Day Two

Smile, SABR and today “exotics”

  • Different ingredients for smile modelling. Local-stochastic. The Local volatility skew backbone of stochastic volatility model. The issue of the smile dynamics for Local volatility, uncertain volatility, Stochastic volatility
  • SABR model. The precision of the approximation. SABR in a multicurve context. Dynamic behaviour of smile and hedging issues. Arbitrage issues. How to solve the calibration problem
  • Convexity adjustments and freezing drifts in Libor Market Model. Application to CMS derivatives. Analysis and comparison in different market situations. The problems of standard approximations with an anomalous shape of the term structure and the changes in volatility and correlation

Stochastic volatility in the Libor Market Model

  • Heston stochastic volatility Libor Model. Different choices for parameterisations. Empirical testing of Heston stochastic volatility Libor Model in practice. How to perform the calibration. Nested calibrations. Model diagnostics. Evolution of volatility term structure in case of stochastic volatility. The future smile
  • An arbitrage-free term structure market model for Libor exotics with SABR dynamics. Calibration, approximations, empirical testing on market prices. Modelling correlation of rates with stochastic volatility
  • Comparing Heston volatility vs SABR volatility in Libor Market Model

Pricing Bermudans in practice

  • LS Monte Carlo for Bermudans. Parameterising exercise boundary. Choice of explanatory variables. Sensitivities
  • Dealing with exotic callable interest rate products. Calibration and model adjustments. Efficiency issues and sensitivities
  • Comparing the pricing of Bermudans with different models. The role of correlations

Workshop: CMS and Bermudans

Day Three

Latest advances and Multicurve Modelling

  • Something more on efficient sensitivities in the Libor Market Model. Pathwise greeks. Computing global and bucketed delta and vega. Some more numerical tricks
  • A fully multicurve Libor Market Model with stochastic volatility and stochastic basis. Parameterisation and calibration issues
  • Other modelling approaches for pricing derivatives with multicurves. Short rate models and the Hull&White and CIR dual-curve models. HJM and the tractable solutions for modelling a stochastic basis. Modelling the credit factor in these frameworks

Credit and Funding in Pricing Interest Rate derivatives

  • A hint at Standard CSA and the pricing of cross-currency interest rate derivatives in the current market
  • Understanding the post-crisis market: heterogeneous and volatile credit and funding risk. Explaining and modelling the anomalies in interest rate products. The effect of credit risk on Libor and on the basis. A new structural foundation for interest rate modelling
  • Computing the funding cost. Funding charge and its interactions with credit charge. Different funding strategies and different shapes for funding charge

Workshop: Simulating stochastic volatility and forward smile

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