Risk management, Arbitrage and Scenario generation for interest rates

61 Pages·2010·0.38 MB·English

by  Josef Teichmann

Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Risk management, Arbitrage and Scenario
generation for interest rates
Josef Teichmann
ETHZu¨rich
Toronto, June 2010
(cid:73) Generated scenarios should share the most important stylized
facts of the respective time series of risk factor (mean,
covariance, skewness, kurtosis, heavy tails, stochastic
volatility, etc) in order to reflect the market’s information.
(cid:73) The actual generation of scenarios must be quick (up to one
hour) and flexible (changes of markets should be directly
implemented into the scenario generator).
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
Motivation
(cid:73) Scenarios of risk factors are needed for the daily risk analysis
(1D and 10D ahead) due to Basel II legislation.
(cid:73) The actual generation of scenarios must be quick (up to one
hour) and flexible (changes of markets should be directly
implemented into the scenario generator).
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
Motivation
(cid:73) Scenarios of risk factors are needed for the daily risk analysis
(1D and 10D ahead) due to Basel II legislation.
(cid:73) Generated scenarios should share the most important stylized
facts of the respective time series of risk factor (mean,
covariance, skewness, kurtosis, heavy tails, stochastic
volatility, etc) in order to reflect the market’s information.
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
Motivation
(cid:73) Scenarios of risk factors are needed for the daily risk analysis
(1D and 10D ahead) due to Basel II legislation.
(cid:73) Generated scenarios should share the most important stylized
facts of the respective time series of risk factor (mean,
covariance, skewness, kurtosis, heavy tails, stochastic
volatility, etc) in order to reflect the market’s information.
(cid:73) The actual generation of scenarios must be quick (up to one
hour) and flexible (changes of markets should be directly
implemented into the scenario generator).
(cid:73) Risk factors are yield curves, exchange rates, etc.
(cid:73) Usually the number of risk factors N is (substantially) larger
than the number of observations K.
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
The data
(cid:73) A time series of risk factors of length K.
(cid:73) Usually the number of risk factors N is (substantially) larger
than the number of observations K.
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
The data
(cid:73) A time series of risk factors of length K.
(cid:73) Risk factors are yield curves, exchange rates, etc.
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
The data
(cid:73) A time series of risk factors of length K.
(cid:73) Risk factors are yield curves, exchange rates, etc.
(cid:73) Usually the number of risk factors N is (substantially) larger
than the number of observations K.
(cid:73) Control the generation of scenarios by stochastic differential
equations, which describe the local dynamics of the
respective risk factors and which are standard models in
finance.
(cid:73) Impose no arbitrage conditions.
(cid:73) a robust and quick calibration method (no optimization!).
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
Proposed approach
(cid:73) Dynamize the simulation (continuous time instead of discrete
time).
(cid:73) Impose no arbitrage conditions.
(cid:73) a robust and quick calibration method (no optimization!).
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
Proposed approach
(cid:73) Dynamize the simulation (continuous time instead of discrete
time).
(cid:73) Control the generation of scenarios by stochastic differential
equations, which describe the local dynamics of the
respective risk factors and which are standard models in
finance.
(cid:73) a robust and quick calibration method (no optimization!).
Riskmanagement,ArbitrageandScenariogenerationforinterestrates
Introduction
Proposed approach
(cid:73) Dynamize the simulation (continuous time instead of discrete
time).
(cid:73) Control the generation of scenarios by stochastic differential
equations, which describe the local dynamics of the
respective risk factors and which are standard models in
finance.
(cid:73) Impose no arbitrage conditions.