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Introduction
The user can specify stochastic processes at the curve level (one for real world process, one for risk neutral process). In a credit simulation, all rates within each curve are evolved according to the stochastic process assigned to the curve, with each term within a curve having different parameter values. A parameter estimation function generates maximum likelihood estimators of the parameters for each rate point using historical rate values.
Supported Estimation Functions
Parameter Estimation generates unconditional maximum likelihood estimators of the parameters in the normal, lognormal, Ornstein–Uhlenbeck (OU) , Ornstein–Uhlenbeck standard (OU standard) and normal mean reverting stochastic processes. In the case of the OU, OU standard and normal mean reverting processes, the user may choose to supply either long term average or mean reversion factor and the process parameters calculated will be conditioned on this supplied fixed parameter.
Historic rates within the specified window are retrieved from the RiskEngine database and the parameters are then calculated from the rate change between consecutive business days. Therefore, if there are some missing days in the historic data, parameters can still be calculated. If there are no consecutive days with rates in the time window however, no parameters can be calculated and a warning will be returned.
The Parameter Estimation results are saved to the RiskEngine database, which are then used to run Monte-Carlo Simulation.
Real World Process Parameters
|
Stochastic Process |
Parameters |
Possible Fixed Parameter |
|
NORMAL |
Drift, Volatility |
None |
|
LOGNORMAL |
Drift, Volatility |
None |
|
OU |
LTAverage, ReversionFactor, Volatility |
LTAverage, ReversionFactor |
|
OUSTANDARD |
LTAverage, ReversionFactor, Volatility |
LTAverage, ReversionFactor |
|
NORMALMR |
LTAverage, ReversionFactor, Volatility |
LTAverage, ReversionFactor |
Risk Neutral Process Parameters
|
Stochastic Process |
Parameters |
Possible Fixed Parameter |
|
RNFX |
None |
None |
|
CVRNFX |
Volatility |
None |
|
HWAUTO |
ReversionFactor |
None |