Mildenhall, Stephen J. 2023. “Pricing Seasonal Peril Catastrophe Bonds: A Simplified Approach.” Variance 16 (1).
• 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.