The impact of collateralization on swap curves and their users
In recent uncertain times, derivative contracts are increasingly being collateralized in order to mitigate credit risk, which is achieved. The fact that collateralization makes the contract (close to) riskless, has consequences for the discount rate used. This discount rate should not be based on the swap curve, but on the growth rate of the collateral specified in the Credit Support Annex (CSA). If the collateral is cash based, which it usually is, the overnight index rate (OIS) is closest to matching the single day credit risk of collateralized derivatives and should therefore be used as the discount rate. The result is a different valuation which can have big impact if the spread between the swap curve and the overnight curve increases. This is what happened in 2007, resulting in a new financial order in which a double curve approach is required. This means using separate curves to determine the forward and discount rates, resulting in delta exposure to the instruments used to build these curves. The theoretical evidence leaving no doubt, an attempt is made to empirically determine the impact on different hedging strategies in the stress scenario that has occurred during the credit crunch. This stress test leads us to conclude that there is a significant difference in hedge effectiveness when switching to OIS discounting, confirming the theoretical need for proper accounting. One the side it is determined that bucket hedging outperforms a single swap hedge, and that more sophisticated hedging methods are promising but require more testing and support in the form of liquid OIS markets. It can be concluded that there is little doubt that collateralized derivatives should be discounted based on the underlying CSA and that, when setting up a hedge, multiple curves have to be accounted for.