Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts

Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts

Abstract

Catastrophe risk is a major threat faced by individuals, companies, and entire economies. Catastrophe (CAT) bonds have emerged as a method to offset this risk and a corresponding literature has developed that attempts to provide a market-consistent pricing methodology for these and other long-dated, insurance-type contracts. This paper aims to unify and generalize several of the widely-used pricing approaches for long-dated contracts with a focus on stylized CAT bonds and market-consistent valuation. It proposes a loading pricing concept that combines the theoretically possible minimal price of a contract with its formally obtained risk neutral price, without creating economically meaningful arbitrage. A loading degree controls how much influence the formally obtained risk neutral price has on the market price. A key finding is that this loading degree has to be constant for a minimally fluctuating contract, and is an important, measurable characteristic for prices of long-dated contracts. Loading pricing allows long-dated, insurance-type contracts to be priced less expensively and with higher return on investment than under classical pricing approaches. Loading pricing enables insurance companies to accumulate systematically reserves needed to manage its risk of ruin in a market consistent manner.

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JEL Classification: G10, G13
1991 Mathematics Subject Classification: primary 65C20; secondary 60H10.
Key words and phrases: long-dated contracts, CAT bonds, real world pricing, risk neutral pricing, loading pricing, benchmark approach, market-consistent valuation.

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