Bgm Market Models: Advances, Calibration, Smile, Pricing
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
Prior Knowledge:
The Black-Scholes Model and Formula
Course Programme*
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
* Subject to change. Contact centre for more information.
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.
