Advanced Interest Rate Models - Construction, Implementation and Applications
Duration:
2 days
2 days
Location:
Prague, Mövenpick Hotel
Prague, Mövenpick Hotel
- The Term Structure of Interest Rates
- The Term Structure of Volatility
- Equilibrium and No-Arbitrage Models
- The BDT and the Hull-White Models
- The Libor Market (BGM) Model
- Calibrating and Implementing Interest Rate Models
- Using Term Structure Models to Price Interest Rate Options
The purpose of this advanced-level seminar is to give you a good understanding of interest rate models and their uses in option pricing and risk management.
We first present and explain important concepts such as the term structure of interest rates and the term structure of volatility. We then take at closer look at various processes for interest rate evolvement over time, and we explain how interest rate volatility can be modelled into these processes.
Next, we present and explain a number of models for interest rate processes, including “Equilibrium” models such as the Rendleman-Barter and Cox-Ingersoll-Ross and “No-arbitrage” models - with and without mean reversion features. This class of models includes single-factor models such as the Ho-Lee, Vasicek, Hull-White, Black-Derman-Toy as well as two-factor models such as Longstaff-Schwartz. We also present the popular “Libor Market”, or BGM (Brace-Gatarek-Muselia), model, which is widely used by practitioners. We discuss the important characteristics and parameters of these models, and we demonstrate how they can be constructed, calibrated and implemented in practice using tree-building procedures and Monte Carlo simulation.
Further, we explain and illustrate how these models can be used for pricing and risk assessment of interest rate options such as Caps, Floors, Swaptions, Delivery Options, Prepayment Options and Defaultable Bonds. We also demonstrate the pricing and hedging of more advanced structures such as “Constant Maturity Swaps” (with convexity adjustment) and of path-dependent option structures such as barrier, look-back and Asian options.
Finally, we look at how interest rate models can be used for various risk management purposes, including calculating key ratios and estimating return distributions for “Value-at-Risk” estimation.
We first present and explain important concepts such as the term structure of interest rates and the term structure of volatility. We then take at closer look at various processes for interest rate evolvement over time, and we explain how interest rate volatility can be modelled into these processes.
Next, we present and explain a number of models for interest rate processes, including “Equilibrium” models such as the Rendleman-Barter and Cox-Ingersoll-Ross and “No-arbitrage” models - with and without mean reversion features. This class of models includes single-factor models such as the Ho-Lee, Vasicek, Hull-White, Black-Derman-Toy as well as two-factor models such as Longstaff-Schwartz. We also present the popular “Libor Market”, or BGM (Brace-Gatarek-Muselia), model, which is widely used by practitioners. We discuss the important characteristics and parameters of these models, and we demonstrate how they can be constructed, calibrated and implemented in practice using tree-building procedures and Monte Carlo simulation.
Further, we explain and illustrate how these models can be used for pricing and risk assessment of interest rate options such as Caps, Floors, Swaptions, Delivery Options, Prepayment Options and Defaultable Bonds. We also demonstrate the pricing and hedging of more advanced structures such as “Constant Maturity Swaps” (with convexity adjustment) and of path-dependent option structures such as barrier, look-back and Asian options.
Finally, we look at how interest rate models can be used for various risk management purposes, including calculating key ratios and estimating return distributions for “Value-at-Risk” estimation.
Equilibrium Models
- Rendleman and Barter
- Vasicek
- Mean reversion in the Vasicek model
- Term structures in the Vasicek Model
- Cox, Ingersoll, & Ross (CIR)
- General form of CIR
- Mean reversion in the CIR model
- Term structures in the CIR model
- Examples and Exercises
12.00 - 13.00 Lunch
13.00 - 16.30 No-arbitrage Models
- Markov vs. Non-Markov Models
- The Ho and Lee Model
- The BDT Model
- General form
- Deriving the model from zero curve and volatility structure
- The Hull-White Model
- A general tree-building procedure
- Building the tree – stage one
- Calculating branching probabilities
- Building the tree – stage two
- The Swap Market Model
- The Libor Market (BGM) Model
- Using Monte Carlo Simulation with Interest Rate Models
- Exercises
Day Two
09.00 - 09.15 Recap
09.15 - 12.00 Pricing Interest Rate Options Using Term Structure Models
- Pricing Options on Zero Coupon Bonds
- Pricing Options on Coupon-Bearing Bonds
- Pricing Libor Options
- Interest Rate Guarantees
- Caps and Floors
- Swaptions
- “Cancellation Swaps”
- Pricing Structured Interest Rate Products
- “Capped FRNs”
- “Inverse Floaters”
- “Callable Snowball Notes”
- “Targeted Redemption Notes”
- “Fairway Bonds”
- Pricing Exotic Structures
- Captions, floptions and other compounds
- Ratchet caps, sticky caps, and flexi caps etc.
- Examples and Exercises
12.00 - 13.00 Lunch
13.00 - 16.30 Pricing Callable and Defaultable Bonds
- Pricing Callable Bonds
- Single-call and multiple-call bonds
- Prepayment Models
- Integrating Prepayment Models into an Interest Rate Model
- Pricing Defaultable Bonds
- Incorporating credit spreads into term structure models
- Examples and Exercises
Using Interest Rate Models in Risk Management
- Hedging Instruments and Hedging Process
- Calculating Key Ratios and Hedge Ratios
- Generating Return Distributions and Calculating “Value-at-Risk”
Evaluation and Termination of the Seminar
