• pricing
• risk
• insurance
• incompleteness
• Esscher
• derivative
• catastrophe
• CAT

The devastating calamitous events of the last decades have raised a widespread interest in the still unexploited coverage opportunities offered by the CAT derivatives, especially in the height of the global financial crisis; this concerns not only primary insurers but also governments seeking assistance with the huge costs of emergency and reconstruction by the transfer of natural risk to capital market investors in lieu of reinsurers. Hence, such economic reasons, encompassing the preservation of financial stability, behind the development of the market for insurance-linked securities (ILS) urge a thorough analysis of their fair valuation as a crucial requisite for liquidity. Indeed, the catastrophic jumps of their underlying loss index raise the issue of market incompleteness, whereby a natural solution is found in the pricing approach based on Esscher Transforms; in fact, such actuarial tool proves particularly intuitive yet effective when dealing with the ILS. Once its theoretical foundations have been outlined, a straightforward application leads to a closed-form pricing formula for a PCS option. Furthermore, Monte Carlo simulations allow a numerical analysis of fair prices and yield spreads of an index-triggered CAT bond. Such analysis, original to the best of our knowledge in that it accounts for both a general class of Lévy-type underlying and global Transforms to justify jump risk premia, makes an interesting contribution also to the issue of the choice between alternative pricing measures; moreover, it opens wide perspectives of research, bridging a gap between actuarial tools and financial theory, thanks to the dual nature of the presented approach.