- 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.