Day 1: Interest Rate Modelling: From Basic - Hybrids Workshop

Presenters:

Dorje C. Brody: Royal Society University Research Fellow, Imperial College London
Lane P Hughston: Professor of Financial Mathematics, King's College London

Topics Covered:

• Interest-rate modelling: the basics
• Applications: short rate models, positive-interest models, chaotic models
• Interest rate and foreign exchange hybrids
• Conditional variance models for foreign-exchange volatility
• Interest rate and inflation hybrids
• Payout structures for inflation-linked hybrid products
• Interest rate and credit hybrids
• Market-information models for credit-linked structures

Day 2: Latest Developments: Interest Rate Modelling Techniques

Presenters:

Claudio Albanese: Chair of Mathematical Finance, Imperial College London
Dariusz Gatarek: Glencore International
Fabio Mercurio: Head of Financial Models, Banca IMI
Raoul Pietersz: Senior Derivatives Researcher, ABN Amro

Topics Covered:

• Stochastic volatility term structure models for callable swaps
• Modeling challenges with callable swaps
• The Swaption Smile and CMS Convexity Adjustments
• Introducing the displaced diffusion LIBOR model with uncertain shifts
• Approximations of Libor market model
• Linear and Nonlinear Pricing of Swaptions
• Generic and CMS Market Models and Measures
• Extending LIBOR and swap market models

Day 3: Latest Developments: Interest Rate Hybrid Products

Presenters:

Alain Chebanier: Head, FX and Commodities Derivatives Research, Deutsche Bank
Messaoud Chibane: Senior Quantitative Analyst, Bank of America
Chris Hunter: Managing Director, BNP Paribas
Jakob Sidenius: Senior Quantitative Analyst, Royal Bank of Scotland

Topics Covered:

• On the Term Structure of Portfolio Loss Distributions
• FX Hybrids Modelling
• Modelling the long-dated FX smile
• Skew dynamics on FX and interest rates
• Impact of skew dynamics on exotics
• Correlation Smile and Hybrid Pricing
• Evolution of the Correlation Smile

Day 1: Basic - Advanced - Hybrids Workshop

08:30 – 17:30 Dorje C. Brody: Imperial College London & Lane P Hughston: King's College London

08:30 – 10:30 Interest-rate modelling: the basics

• Probabilisitic foundations (the essentials, less the irrelevancies)
• Discount bonds and interest rates, dynamics of discount bonds
• Interest-rate modelling: why take an axiomatic approach?
• Axiom one: the money-market account
• Axiom two: arbitrage-free asset-price dynamics
• Axiom three: the floating rate note
• Axiom four: the discount-bond system
• What is the difference between the "pricing kernel method" and so-called "risk-neutral valuation"?
• Relation to Baxter, Constantinides, Flesaker-Hughston,
• Heath-Jarrow-Morton, Hunt & Kennedy, Rogers, Rutkowski, etc.
• Market completeness issues: pricing vs hedging
• Pricing kernels: the economic foundations, and why we cannot do without them
• Applications: short rate models, positive-interest models, chaotic models
• Swaptions, caps, and CMS products
10:30 - 10:45 Break

10.45 – 12.30 Interest rate and foreign exchange hybrids

• Matrix models for exchange-rate systems
• Geometrical interpretation of foreign exchange volatility
• On the relation between market price of risk and volatility
• Foreign pricing kernels
• Conditional variance models for foreign-exchange volatility
• Applications for FX-IR and equity-index products

12:30 - 13:45 Lunch

13.45 – 15.15 Interest rate and inflation hybrids

• Inflation-linked bonds
• Payout structures for inflation-linked hybrid products
• General theory of inflation dynamics
• The foreign-exchange analogy for inflation models
• Price processes for real and nominal discount bonds
• Models for real pricing kernels
• Valuation of inflation-linked derivatives

15:15 - 15:30 Break

15.30 – 17.30 Interest rate and credit hybrids

• Market-information models for credit-linked structures
• Price processes for credit-risky bonds
• Options on credit-risky debt
• Correlation issues: introducing the X-factor approach
• Extension to equity-linked products and IR/credit/equity hybrids

Cocktail Party Tuesday 21st March 17:30 – 19:00 (All delegates are invited to the cocktail party)

Day 2: Latest Developments: Interest Rate Modelling Techniques

08:30 – 10:30 Claudio Albanese: Imperial College London

2 Hours

Stochastic Volatility Term Structure Models for Callable Swaps

• Modeling challenges with callable swaps
• Local calibration and risk management with SABR
• Stochastic volatility and regime switching term structure models
• Implementation on functional lattices
• Global calibration
• Using the Markov functional model for local calibration refinements
• Case study: Constant maturity callable swaps and callable swap spreads
• Stochastic skew models for FX options and PRDCs

10:30 – 10:45 Break

10:45 – 12:45 Fabio Mercurio: Banca IMI

2 Hours

The Swaption Smile and CMS Convexity Adjustments

PART I

• The swaption smile quoted by market
• Calibration with the SABR functional form
• Introducing the CMS convexity adjustments
• Valuing CMS convexity adjustments with the SABR functional form
• A joint calibration to swaptions and CMS swap spreads

PART II

• Introducing the displaced diffusion LIBOR model with uncertain shifts
• Exact calibration to at-the-money swaptions
• Model implications
• Examples of calibration

12:45 – 13:45 Lunch

13:45 – 15:15 Dariusz Gatarek: Glencore

1 Hour 30 Minutes

Approximations of Libor Market Model

• LIBOR rate lognormal approximations
• Linear and nonlinear pricing of swaptions
• Swap rate lognormal approximation
• Numerical example of European swaptions
• Brownian bridge drift approximation
• Comparison of pricing methods & potential extensions

15:15 – 15:30 Break

15:30 – 17:30 Raoul Pietersz: ABN Amro

2 hours

Generic and CMS Market Models and Measures

• Extending LIBOR and swap market models
• Ease of volatility calibration
• Expressions for drift under terminal and spot measures
• Reduced factor fast drift calculations for LIBOR, swap and CMS models
• Applications to callable CMS swaps

Cocktail Party Tuesday 21st March 17:30 – 19:00 (All delegates are invited to the cocktail party)

Day 3: Latest Developments: Interest Rate Hybrid Products

09:00 – 10:30 Messaoud Chibane: Bank of America

1 Hour 30 Minutes

FX Hybrids modelling

Examples of typical products
• Power Reverse Dual Currency knock outs and cancellables
• FX inverse floaters
• FX tarns
• Quantoed structures

History of FX model for long dated structures
• The standard model: the Two Currency Hull-White
• Cross-Currency Libor Market Models
• Modelling the long-dated FX smile

10:30 – 10:45 Break

10:45 – 12:30 Alain Chebanier: Deutsche Bank

1 Hours 45 Minutes

Skew dynamics on FX and interest rates

• Impact of skew dynamics on exotics
• Model choice
• FX calibration
• Interest rates calibration
• Comparison of the two models

12:30 – 13:30 Lunch

13:30 – 15:00 Jakob Sidenius: Royal Bank of Scotland

1 Hour 30 Minutes

On the term structure of portfolio loss distributions
• Kinematics and constraints
• Calibration to market
• Dynamics and constraints
• Calibration of dynamics
• Applications to deals
15:00 – 15:15 Break

15:15 – 17:15 Chris Hunter: BNP Paribas

2 Hours

Correlation Smile and Hybrid Pricing

• Term structure of correlation
• Modeling correlation tails
• Implied Correlation
• Local Correlation
• Evolution of the Correlation Smile