Arbitrage Algebra and the price of Multi-Peril ILS

At this year’s third annual Bond Market Association Risk-Linked Securities Conference, John Seo gave an excellent address entitled “Risk Management Tools for Investors." The more colorful subtitle was along the lines of “evaluating multi-peril bonds and avoiding the Bermuda rectangle." Yes, rectangle. We will leave the Bermuda angle (rect- or tri-) for John to explain and he can be found (together with his brother Nelson) at Fermat Capital Management LLC managing a fund specializing in investing in cat bonds and other exotica. However, this article takes advantage of his basic plea (simplification) to further explore a favorite topic of ours-how should cat bonds be priced? In particular, to explore the vexing question of multi-peril bonds compared to single peril bonds. Our approach is to explore “arbitrage-equivalent” pricing in which covers can be either bought or sold. We do not yet know how to determine how the absolute level of cat bond prices should be set-although we expect it must be driven by two old friends (a.k.a. supply and demand)-but the Seo simplification allows greater insights into relative prices of single vs. multi-peril bonds even in our arbitrage context. We begin with a reprise of John’s examples (see Exhibit 1).