The Mathematics of Risk Transfer

Canadian winters are extreme: cold and snow are a fact of everyday life. Canada spends over $1Bn every year removing snow. As one example, consider the city of Montreal. The city spends over $50M every year removing snow, about 3% of its total budget. It does that through a fixed-price contract agreement with a third party, which starts on November 15 and ends in April 15 – the snow season. During this time, the city’s exposure to snow removal costs are – to a large degree – predictable. However, snow precipitation outside of this period can become very costly: it is outside of the contractual arrangement, and the city may incur into expenses which may, on a relative basis, exceed the ones during the snow season. The city is exposed to snow financial risk. But snow financial risk affects also other corporations, such as ski resorts. For them, the snow financial risk is opposite: low precipitation during the late part of the fall or early spring will yield operational losses compared to years when snow fall is ample early in the fall or late into the spring. They also face snow financial risk.

Today, credit risk has been regulated in BIS-II, the resolution of the Bank for International Settlements, but the credit market has just started (although at the present time its volumes are very high). A host of new credit products are created everyday. Later in the paper we will explore some of the newest ones, the Collateralized Fund Obligations, or CFOs, designed to provide financing to investors in hedge funds. What is interesting, from a mathematical viewpoint, is that the arrival of new credit-sensitive products is accompanied with new risks, which need to be determined, and priced.

We will review some of the earlier properties of financial risk, and we will focus on the analysis of CFOs as a means to highlight some of the new paradigms that we will likely face in the near future.