The Challenges of Long Horizon Simulations in the context of Counterparty Risk modeling : CVA, PFE and Regulatory reporting.
This joint presentation reviews the key decisions that need making regarding the choice of risk factor evolution models and calibration methods. In particular, we will analyse the performance of classical historical calibration methods (such as Maximum Likelihood and the Efficient Method of Moments) in estimating the volatility and drift terms of the Hull & White class of Interest Rate models ; both in terms of convergence and stability.
As most methods perform satisfactorily for volatility but disappoint on the mean reversion estimation, we propose a new modified Variance Estimation method that significantly outperform the classical approaches.
Lastly, after reviewing historical economic evidence of mean-reversion dynmics in high interest rate regime, we propose modifying classical models by making mean reversion non-linear and accelerating for high rates - that can be referred as "+R" models.
This model address unrealistically large and persistent interest rates values often observed at high quantile in PFE and CVA simulations.