BGM Market Models Calibration Smile Pricing and Advances with lessons from the Crisis
Training
Provided by London Financial Studies
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 learnt 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 analyses 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. 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
Prior Knowledge
The Black-Scholes Model and Formula
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BGM Market Models Calibration Smile Pricing and Advances with lessons from the Crisis
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
- Terminal Correlations
- Controlling Model Dimension. The number of factors
- Parameterising the Decorrelation seen from summer 2008
* Accurate approximations for calibrating efficiently 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
* 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 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
* 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
* 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
* 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
Day Three
* The case for Negative rates
* Capturing smile 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 Hedge: an arbitrage-free Term Structure Market Model for Libor Exotics with SABR Dynamics
Calibration, Approximations, Empirical testing on market prices
* Practical problems in implementing stochastic volatility Libor models. Modelling correlation of rates with stochastic volatility
* Modelling counterparty and liquidity risk in Libor and in the interest rate curves
* A Libor Market Model for Credit Spreads
* A Swap Market Model for Credit Index Options. The importance of Correlation and Armageddon probability for pricing Index Options in a credit crunch
* 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
- Terminal Correlations
- Controlling Model Dimension. The number of factors
- Parameterising the Decorrelation seen from summer 2008
* Accurate approximations for calibrating efficiently 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
* 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 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
* 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
* 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
* 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
Day Three
* The case for Negative rates
* Capturing smile 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 Hedge: an arbitrage-free Term Structure Market Model for Libor Exotics with SABR Dynamics
Calibration, Approximations, Empirical testing on market prices
* Practical problems in implementing stochastic volatility Libor models. Modelling correlation of rates with stochastic volatility
* Modelling counterparty and liquidity risk in Libor and in the interest rate curves
* A Libor Market Model for Credit Spreads
* A Swap Market Model for Credit Index Options. The importance of Correlation and Armageddon probability for pricing Index Options in a credit crunch
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