and BCVA was shown to be the value and characteristics of the derivative that the two quantities are being evaluated on. For entities of fair credit quality default happens latter in a dervatives deal than when the deal has just comemnced. This has the consequence that in IRSs entered into at the fair rate when the interest rate curve is upward sloping, the counterpary credit exposure faced by the fixed rate payer larger than that faced by floating rate payer. This is due to the fact that towards maturity the cashflows are more likely to be positive towards the fixed leg. The second study focused on correlation effects and, instead of using fair IRSs, an IRS with initial positive value towards the floating leg was investigated. More precisely, a R100 million notional IRS was investigated and it was shown that cor- relation had significant effect.
8.2
Future Work
It was mentioned earlier that there have been many studies across instrument classes on CVA/BCVA but there is still a lot to be done in this area apart from using more sophisticated processes to model the asset value of the firm, short rate and the intensities of the various entities. The issues arising when incorporating funding and collateral into CVA/BCVA have not been investigated in detail. We discuss their importance and complexities below and also briefly describe how a more realistic volatility can be achieved in a CIR++ model.
8.2.1 Incorporating Collateral into a CVA/BCVA
In Chapter 3, collateral posting was described and its mitigating effect was illustrated with an example. It is however very important to note that even with frequent collateral posting, counterparty credit risk is not eliminated. The introduction of collateral introduces a collateral rate which is earned by the collateral after being posted. The existence of the collateral rate may introduce re-hypothecation, that is, the holder will be able to use the posted collateral. If re-hypothecation is allowed, then a model for the collateral rate is required when calculating a CVA/BCVA. The framework would need to account for the fact that the holder of the collateral can possibly default on the collateral itself. There has been no work investigating the effects of collateral on a CVA/BCVA in the South African market.
When an OTC derivative is protected by a CSA included in the ISDA master agreement, the collateral is usually posted if the value of the derivative is greater than a particular threshold. From time to time both sovereign governments and big companies are downgraded. It is thus beneficial in long dated contracts when calculating a CVA/BCVA in the presence of a CSA to consider making the threshold
8.2. FUTURE WORK 115
rating dependent. To the best of our knowledge this is not available in the literature. Collateral posting in the South African market context is also going to a complex exercise as the collateral posted might have to be invested with the clearing houses which are the South African banks, who each have a positive probability of default. The analysis required in solving this cyclic problem would be very interesting.
8.2.2 Incorporating Funding into a CVA/BCVA
The choice of a discounting curve is important. A discounting curve should be risk free and most certainly one that represents interest in money invested without an option to redeem it before maturity. There are different choices that may be made for this curve which will affect CVA/BCVA calculations. For example, it could be constructed using JIBAR or OIS (Overnight Index Swap) rates. There are papers that have dealt with funding such as the one by Piterbarg [65] but overall this subject is still open for debate, especially in the South African market, given the fact that there are no overnight index swaps in the market.
8.2.3 Choice of Intensity Process
The intensity of default for all the entities investigated was assumed to follow a CIR++ process. While it has many attractive features, this model has a shortcoming in that its implied volatility is small compared to those implied for similar entities in the CDS options market. One reason is that the calibration process produces small values for k, θ, σ. The other reason is that the Feller condition,
2kθ > σ2, (8.1)
is imposed in order to prevent the process from attaining zero. This implies that to obtain larger values of σ, the values of k and θ would have to be made larger, which has undesirable consequences. A bigger θ means that the intensities will revert to a bigger value and a bigger value for k means the process will revert too quickly which may inhibit the stochastic nature of the process by attaining values that cluster around θ. A way to achieve better levels of implied volatility would be the introduction of jumps in the intensity process which has not been implemented in this work and to the best of the authors knowledge there has been no literature on its application in the South African market. The reason may stem from the fact that there is no active swaptions market in the South African market and the credit market is also relatively immature which means that calibration may be very hard.
Appendix A
Pricing Pre-requisites
A.1
Pricing Curves
In-order to price it is necessary to obtain the pricing curves, the discount factor curve and the survival probability curves for the different entities. The strip- ing/bootstrapping of the discount factor curve is done using short dated instruments such as FRA’s and long dated instruments which would be IRSs in our case, the table A.1 summarizes the values of the curves at different points in time.