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).