Interest Rate Models - Advanced Pricing and Risk Management

The objective of this advanced-level seminar is to give you a good understanding of modern 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 a 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 “classical” 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 present and explain a double-curve framework, adopted by the market after the liquidity crisis started in summer 2007. We revisit the problem of pricing and hedging plain vanilla single currency interest rate derivatives using different yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. We also derive the no arbitrage double curve market-like formulas for basic plain vanilla interest rate derivatives and show how they can be used for pricing of FRA, swaps, cap/floors and swaptions etc.

Further, we present models for stochastic volatility, exemplified by the widely used Heston Model today. We motivate the uses of such models, and we show how the model is computationally validated, calibrated and applied in the pricing of standard and more exotic interest rate 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” calculation.

 

Day One

09.00 - 09.15 Welcome and Introduction

09.15 - 12.00 Introduction to Interest Rate Modelling

• Interest Rates and their Behavior
• The Term Structure of Interest Rates and Volatility
• Features of Interest Rate Models
  • No-arbitrage
  • Mean reversion
  • Spot or forward rates
  • Stochastic volatility
• New Challenges in Interest Rate Modelling

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
  • Term structures in the CIR model
• Examples and Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Classical No-arbitrage Models - Single Curve Environment

• The BDT Model
  • General form
  • Deriving the model from zero curve and volatility structure
• The Hull-White Model
  • A general tree-building procedure
• The Swap Market Model
• The Libor Market (BGM) Model
• Using Monte Carlo Simulation with Interest Rate Models
• Single-Curve Pricing & Hedging Interest-Rate Derivatives – Examples
  • Swaps
  • Caps, floors, swaptions
  • Exotic interest rate options
  • Structured interest rate products
• Exercises

Day Two

09.00 - 09.15 Recap

09.15 - 12.00 Modern Libor Market Models

• From Single to Double-Curve Paradigm
• Double-Curve Framework, No Arbitrage and Basis Adjustment
  • General Assumptions
  • Pricing Procedure
  • No Arbitrage Revisited and Basis Adjustment
• The Double Curve Libor Market Model
• Foreign-Currency Analogy and Quanto Adjustment
  • Forward Rates
  • Swap Rates
• The Double-Curve Lognormal LMM
• Foreign-Currency Analogy and Quanto Adjustment
  • Forward Rates
  • Swap Rates
• Double-Curve Pricing & Hedging Interest Rate Derivatives (Examples)
  • Swaps
  • Caps, floors, swaptions
  • Exotic interest rate options
• Examples and Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Stochastic Volatility Models

• The World of Stochastic Volatility
• The Heston Model
  • Motivation and parameters
  • Computational valuation
  • Calibration
  • Generating volatility surfaces and skews
• Pricing Options Using Stochastic Volatility 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