BGM MARKET MODELS:
Advances, Calibration, Smile, Pricing

Course Outline

The BGM Libor and Swap Market Models are the last generation of financial models for interest rate derivatives and have growing importance in pricing and hedging modern financial products. Discover new developments and cutting edge techniques in Libor and Swap Market Models. This in-depth course reviews foundations and illustrates the latest advances. This will give participants the opportunity to apply new methodologies in a practical context for the current needs of the market.

The course analyses present 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, analysing in practice the most recent stochastic volatility term structure models.

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

• Interest Rate Derivatives
• Practical advantages and shortcomings of different approaches for pricing and hedging interest rate derivatives/ Short rate modelling, HJM, Market Models (BGM)
• 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
• Calibrating different volatility structures to cap quotes. Examples

• Correlation Modelling:

- Desirable properties
- Historical Correlations
- Parametric Forms for Correlation
- Terminal Correlations
- Controlling Model Dimension. The number of factors

• Accurate approximations for calibrating efficiently to swaptions
• 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

Workshop: Volatility and Correlation Structures

Day Two

• Diagnostics of Calibration: controlling realism, stability and consistency of the results
• Joint Calibration. Possible inconsistencies between Cap and Swaption markets

Workshop: LMM and the Swaption Market

• Efficient Computation of Sensitivities
• Accurate and Fast Vegas in the Libor Market Model
• Computing exact closed-form formulas for products setting In Arrears. Examples
• Pricing efficiently with one-step Monte Carlo. Trigger swaps pricing example
• Efficient approximations for pricing derivatives depending on rates outside the model tenor structure. How to compute and assess pricing formulas. Zero-coupon swaptions example
• Convexity Adjustments in the Swap Market Model and freezing drifts in the Libor Market Model. Application to CMS derivatives. Analysis and comparison
• Pricing path-dependent products linked to the observations of non-standard reference rates. Techniques: Interpolating realisations, Interpolating dynamics, Stochastic Interpolation. Practical Pricing Range Accruals example
• Efficient Drift Approximations for Options: Ratchets and Average Rate Caps
• 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

Workshop: Pricing with Approximations

Day Three

• Interpreting and modelling smile and skew in interest-rate derivatives markets
• Libor Dynamics for Volatility Smile and Skew
• Local volatility models with a well-defined dynamics:
  - Models for the skew (ingredients for stochastic volatility models): CEV and Shifted Lognormal Libor Model. Pricing formulas
  - Capturing curvature: Mixture of Lognormals Libor Model. Pricing formulas
• Uncertain Volatility and Uncertain Shifts models. The simplest choice for embedding current smile in the Libor Market Model. Local and Uncertain Volatility: Limitations
• Adding Stochastic Volatility to Libor Models
• Modelling skew with a local volatility function, or with rate volatility correlation?
• SABR Model. Dynamic Behaviour of the Smile and Issues for Hedging
• Indetermination Problems and effect on Pricing Exotics. How to solve the problem in calibration
• Convexity adjustments with smile for CMS products
• Stochastic Volatility Term Structure Models
• Heston Stochastic Volatility with Libor Model. Stochastic volatility Libor Model with time-dependent and Libor-specific parameters
• Empirical Testing of Stochastic Volatility for Libor and Swap Models in practice. Issues in Calibration, Pricing, Hedging
• Problems and advantages of different models, comparisons
• Cutting Edge: an arbitrage-free Term Structure Market Model for Libor Exotics with SABR Dynamics. Calibration, Approximations, Empirical testing on market prices

Workshop: Capturing Smile and Skew