Loading [Contrib]/a11y/accessibility-menu.js
Mildenhall, Stephen J. 2023. “Pricing Seasonal Peril Catastrophe Bonds: A Simplified Approach.” Variance 16 (1).
Download all (6)
  • Figure 1. Kernel density estimate of the date (in years) of landfall for all U.S. hurricanes based on data from 1851-2018 and for severe storms, Safir Simpson 3 and above.
  • Figure 2. The survival probability of a bond written on January 1 with annual event intensity \(\lambda=0.0725\) over a 3-year term. The straight line shows probabilities using a constant hazard rate of \(\lambda\).
  • Figure 3. Determining the price of a seasonal catastrophe bond. Left: the expected present value of benefit factor, \(\bar A^{1}_{x:\overline{n}\kern{-1.0pt}|}\). Middle: the expected present value factor for the coupon, i.e., premium income, over the life of the bond, \(\bar a_{x:\overline{n}\kern{-1.0pt}|}\). Right: the price \(c\) assuming \(Y=1\).
  • Figure 4. Price \(c_x\) against annual intensity \(\lambda\) for January 1, March 1, June 1, September 1, and December 1 effective dates, realistic range of \(\lambda\). The gray line shows the identity \(c=\lambda\).
  • Figure 5. Price \(c_x\) against annual intensity \(\lambda\) for January 1, March 1, June 1, September 1, and December 1 effective dates, large \(\lambda\) to show trends.
  • Figure 6. The value of a bond written January 1 through the year. Assumes \(\lambda=0.0725\), \(i=0.02\), and no partial losses. Par value 100.


We show a catastrophe bond’s economically meaningful cash flows are the same as a fully continuous term life insurance policy. As a result we obtain a simple catastrophe bond pricing formula expressed in standard actuarial notation. Catastrophe bonds covering seasonal perils have a periodic event intensity and so their issue price varies with effective date during the year. We quantify this variation. We also show how the current value of a seasonal bond varies during the year and explain how a variable coupon would remove this effect. A simple seasonal model produces a flat term structure. We consider how a non-flat pricing yield curve could arise. In addition to providing the first explicit quantification of the impact of seasonality on price, the paper highlights the synergies between property casualty and life insurance actuarial practice groups and illustrates the benefits of a general actuarial education.

Accepted: July 23, 2021 EDT