The CMS Triangle Arbitrage (Slides)

For much of 2009 there was a static arbitrage in Euro CMS spread options, a consequence of the dislocation between the markets for options on CMS rates and CMS spreads. High volatility of volatility in the vanilla rates market pushed up the prices of long-dated CMS rate options, as these options are static replicated using the vanilla rates smile. In contrast, supply pressures kept the prices of CMS spread options suppressed. The requirement to maintain mark-to-market for CMS spread options led quants to consider models that do not directly reference the CMS rate marginals, choosing instead to model the CMS spread distribution directly. This allowed prices in these two markets to drift apart, with essentially independent models marked to increasingly disconnected markets. In some cases, the gap that opened up was sufficient to create an exploitable arbitrage between the markets. This article considers the construction of the CMS triangle arbitrage, its mathematical limits, and strategies for maximising the benefit