Swaptions from a Clearinghouse perspective : Hedging swaptions, an option on interest rate swaps, using compression

Abstract: With the increasing popularity of interest rate swaps the need to understandswaptions, an option of an interest rate swap, is of great importance. A swap-tion can be used in both speculative purposes and to hedge against changesin interest rates. The most important thing to understand is the pricing for-mula. By starting at the basic rate instrument, bonds, we will work our waytowards the pricing formula for a swaption, the Black76 model. The Black76model is a variant of the Nobel prize winning formula Black-Scholes-Merton.With the pricing model we can start looking at the main scope of this thesis,a hedging strategy against swaptions from a clearinghouse perspective.Clearinghouses are central to the modern financial market. They act asa middleman in order to clear trades from clearing members and have anoversight of the financial market. In case a clearing member defaults, theclearinghouse will gain control over the defaulted portfolio. The clearing-house will host an auction of the portfolio which they strive to hold after5 to 15 days. When they hold the portfolio, they are exposed to the risksand therefore it’s of great importance to be able to hedge the assets in theportfolio. In this thesis a strategy and algorithm have been developed todelta-hedge swaptions in order to be delta-neutral under stable market con-ditions.In the thesis we will consider two cases. The first case is when the clear-inghouse receives the portfolio long before the swaptions maturity. In thiscase forward swaps are used to hedge and in order to reduce the number offorward swaps obtained, compression is used. The second case is when theswaption maturity will be reached within the period the clearinghouse holdsthe portfolio. For the days before maturity is reached, forward swaps andcompression is used. After maturity is reached interest rate swaps is used tohedge.For both cases the result is very close to achieving delta-neutrality. Withnormalized deltas with respect to the notional amount the mean delta ex-posure is of the magnitude 10−4 for the first case and 10−6 for the second.However, one thing to keep in mind is that everything is based on simu-lated values under some simplifying assumptions. This thesis should be asolid ground for future studies where more extreme scenarios are considered.With more extreme scenarios one could investigate the possibility to hedgewith Gamma or another Greek such as Vega.