1. Numerical Results
In this section, we present some numerical results for CVA calculation based on the theory described above. First, we study the impact of margin agreements on CVA. The testing portfolio consists of a number of interest rate and equity derivatives. The number of simulation scenarios (or paths) is 20,000. The time buckets are set weekly. If the computational requirements exceed the system limit, one can reduce both the number of scenarios and the number of time buckets. The time buckets can be designed fine-granularity at the short end (e.g., daily and then weekly) and coarse-granularity at the far end (e.g. monthly and then yearly). The rationale is that the calculation becomes less accurate due to the accumulated error from simulation discretization, and inherited errors from calibration of the underlying models, such as those due to the change of macro-economic climate. The collateral margin period of risk is assumed to be 14 days (2 weeks).
For risk-neutral simulation, we use a Hull-White model for interest rate and a CIR (Cox-Ingersoll-Ross) model for hazard rate scenario generations a modified GBM (Geometric Brownian Motion) model for equity and collateral evolution. The results are presented in the following tables. Table 2 illustrates that if party A has an infinite collateral threshold i.e., no collateral requirement on A , the CVA value increases while the threshold increases. Table 3 shows that if party B has an infinite collateral threshold , the CVA value actually decreases while the threshold increases. This reflects the bilateral impact of the collaterals on the CVA. The impact is mixed in Table 4 when both parties have finite collateral thresholds.