BGM Market Models: Calibration, Smile, Pricing, and Advances

Course Outline

The BGM Libor and Swap Market Models are the last generation of financial models for interest rate derivatives, with an importance in pricing and hedging financial products that has grown in the recent market turmoil.

Discover new developments and cutting edge techniques in Libor and Swap Market Models. This in-depth course reviews foundations and illustrates the latest advances, including lessons learned from the financial crisis. This will give participants the opportunity to apply new methodologies in a practical context for the current needs of the market.

The course analyzes techniques and structures for crucial points such as volatility and correlation modelling. It further investigates calibration techniques on market data, presents problematic scenarios and identifies appropriate solutions. The various pricing problems with real-world payoffs are examined and practical solutions are described. Volatility smile and skew are explored and captured with tractable dynamics and the introduction of stochastic volatility, analyzing in practice the most recent stochastic volatility term structure models. Finally, how to deal with credit and liquidity risk in this framework is explained.

Who The Course is For

  • Exotic Products Managers (pricing strategy development)
  • Quantitative Analysts
  • QA Managers
  • Fixed Income Managers
  • Interest Rate Derivatives Managers & Teams
  • Managers of Financial Engineering
  • Portfolio Managers
  • Traders
  • Risk Managers or Directors

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Prior Knowledge

The Black-Scholes Model and Formula.


This program is eligible for 24 Continuing Education credit hours from the CFA Institute. If you are a CFA Institute member, CE credit for your participation in this program will be automatically recorded in your CE Diary.


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Day One

  • Practical advantages and shortcomings of different approaches for pricing and hedging interest rate derivatives/Short rate modelling, HJM, Market Models (BGM). The capability to fit current market data
  • Understanding Market Models: from market Black formulas to the Libor Market Model
  • The Libor and Swap Market Models. Theoretically inconsistent but practically compatible
  • Parameterising the model: the choice of the Volatility Structure. Future evolution and implications on exotics pricing and stability. The evolution of the Term Structure of Volatility during the Financial Crisis
  • Calibrating different volatility structures to cap quotes. Examples
  • Correlation Modelling:
    • Desirable properties
    • Historical Correlations
    • Parametric Forms for Correlation
    • Controlling Model Dimension. The number of factors
    • Parameterising the Decorrelation seen from summer 2008
  • Accurate approximations for efficient calibrating to swaptions. Testing the approximations on stressed data
  • Monte Carlo Pricing in the LMM:
    • Euler scheme
    • Log Euler
    • Milstein scheme
    • Predictor-Corrector scheme
    • Efficiency and Variance Reduction
    • Control Variates
  • Calibrating exactly and instantaneously to swaptions. Analysis of calibration market cases
  • Establishing a one-to-one relationship between parameters and market quotations for precise volatility bucketing
  • Diagnostics of Calibration: controlling realism, stability and consistency of the results
  • Joint Calibration. Possible inconsistencies between cap and swaption markets

Workshop: Volatility and correlation structures

Day Two

  • Modelling smile and skew in interest-rate derivatives markets
  • Deciding the backbone by models for the skew (ingredients for stochastic volatility models): CEV and shifted lognormal Libor Model. Pricing formulas
  • Local volatility Libor Market Models. Choosing a model with well-defined dynamics
  • Uncertain volatility models. Simplest choice for embedding smiles in the Libor Market Model. Limitations
  • SABR model. Dynamic behaviour of smile and hedging issues
  • Indetermination problems and effect on pricing exotics. 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
  • Convexity adjustments with smile for CMS products
  • Stochastic Libor Market Models
  • Heston stochastic volatility Libor Model. Approximations for efficient pricing. 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
  • Practical problems in implementing stochastic volatility Libor Models. Modelling correlation of rates with stochastic volatility
  • Cutting edge: an arbitrage-free term structure market model for Libor exotics with SABR dynamics. Calibration, approximations, empirical testing on market prices
  • Comparing Heston volatility vs SABR volatility in Libor Market Model

Workshop: Pricing spread options with stochastic volatility

Day Three

  • Implementing a Libor Market Model that can automatically price derivatives based on nonstandard rates. Interpolating realisations, interpolating dynamics, stochastic interpolation. Using LMM rates to rebuild a future general term structure. Testing interpolations. Practical pricing of path-dependant derivatives
  • Efficient sensitivities in the Libor Market Model. Pathwise greeks. Computing global and bucketed delta and vega
  • Simulation issues. Simulation of stochastic volatility. Controlling negative values. Predictor-corrector and other tricks
  • Bermudan-style products:
    • 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 products. The role of correlations

Workshop: Pricing Bermudan derivatives

  •  Making the model robust to cope with the new market after the credit crunch. Explaining and modelling the anomalies in interest rate products that aroused from the subprime crisis
  • A new foundation to interest rate models to account for counterparty and liquidity risk
  • Decoupling discounting from forwarding when there is collateralisation. Libor and OIS Market Model. Modelling basis swap spreads
  • A Libor Market Model for a plurality of curves
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