Délka:

2 dny

2 dny

Místo:

Praha, hotel NH Prague

Praha, hotel NH Prague

- The Term Structure of Interest Rates
- Volatility and Mean Reversion
- The Vasicek and CIR Models
- Simulating Interest Rates and Yield Curves
- The Ho and Lee, BDT and the Hull-White Models
- The Modern Swap Market and Libor Market (BGM) Models
- Double-Curve Pricing & Hedging Interest Rate Derivatives
- Stochastic Volatility Models
- Using Interest Rate Models in Risk Management

The purpose of this advanced-level seminar is to give you a good and practical 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 and "mean reversion" can be modelled into these processes.

Next, we present and explain widely used "equilibrium" models such as the Vasicek and Cox-Ingersoll-Ross models. We explain the general forms of these models and demonstrate how they can be estimated and used for simulating interest rate processes and for constructing yield curves. We also discuss how these models can be extended to multi-factor models such as the Brennan-Schwarz model.

We then turn our focus to look at "no-arbitrage" models. This class of models includes models such as the Ho-Lee, Vasicek, Hull-White and the Black-Derman-Toy models. We also present the popular "Swap Market" and "Libor Market" (BGM) model, which are widely used by practitioners. We discuss the important characteristics and parameters of these models, and we demonstrate how they can be constructed, calibrated and used under the double-curve framework which was introduced following the liquidity crisis that started in the 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.

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 and "mean reversion" can be modelled into these processes.

Next, we present and explain widely used "equilibrium" models such as the Vasicek and Cox-Ingersoll-Ross models. We explain the general forms of these models and demonstrate how they can be estimated and used for simulating interest rate processes and for constructing yield curves. We also discuss how these models can be extended to multi-factor models such as the Brennan-Schwarz model.

We then turn our focus to look at "no-arbitrage" models. This class of models includes models such as the Ho-Lee, Vasicek, Hull-White and the Black-Derman-Toy models. We also present the popular "Swap Market" and "Libor Market" (BGM) model, which are widely used by practitioners. We discuss the important characteristics and parameters of these models, and we demonstrate how they can be constructed, calibrated and used under the double-curve framework which was introduced following the liquidity crisis that started in the 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.

- Paradigm Shifts in Interest Rate Modelling
- Multi-curve pricing and extremely low interest rates

- Features of Interest Rate Models
- No-arbitrage
- Mean reversion
- Spot or forward rates
- Stochastic volatility

- Dothan / Rendleman and Bartter
- The Vasicek Model
- General form
- Mean reversion in the Vasicek model
- Term structures in the Vasicek Model
- Discretizing the Vasicek Model
- Estimating the parameters with maximum likelihood methods
- Simulating the short term rate and estimating yield curves

- Applications of the Vasicek Model
- Pricing bonds and interest rate options using the Vasicek model

- Multifactor Extensions of the Vasicek Model
- Practical Examples and Exercises

- The Cox, Ingersoll, & Ross (CIR)
- General form
- Mean reversion in the CIR model
- Term structures in the CIR Model
- Discretizing the CIR Model
- Estimating the parameters with maximum likelihood methods
- Estimating spot and forward yield curves
- Simulating the short term interest rate
- Pricing bonds and interest rate options using the CIR model

- Applications of the CIR Model
- Pricing interest rate options using the Vasicek model

- Multi-Factor Extensions of the CIR Model
- Examples and Exercises

- Risk Neutral Valuation and the Ito-Process
- The Ho and Lee Model
- The BDT Model (Extended Dothan)
- Deriving the model from zero curve and volatility structure

- The Hull-White Model (Extended Vasicek)
- A general tree-building procedure

- Modelling Market Rates
- The Swap Market Model
- The Libor Market (BGM) Model

- Single-Curve Pricing & Hedging Interest-Rate Derivatives – Examples
- Caps, floors, swaptions, exotics
- Structured interest rate products

- Modern Libor Market Models
- From Single to Double-Curve Paradigm
- Double-Curve Framework, No Arbitrage and Basis Adjustment
- The Double Curve Libor Market Model
- Foreign-Currency Analogy and Quanto Adjustment
- The Double-Curve Lognormal LMM

- Double-Curve Pricing & Hedging Interest Rate Derivatives
- Caps, floors, swaptions, exotics

- Examples and Exercises

- The World of Stochastic Volatility
- The Heston Model
- Motivation and parameters
- Computational valuation and calibration
- Generating volatility surfaces and skews

- Pricing Options Using Stochastic Volatility Models

- Hedging Instruments and Hedging Process
- Calculating Key Ratios and Hedge Ratios
- Generating Return Distributions and Calculating “Value-at-Risk”

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