Abstract

The increasing frequency and severity of natural catastrophes call for comprehensive strategies to manage, mitigate, and transfer catastrophe (CAT) risk. In response, a variety of financial instruments, such as CAT bonds, CAT derivatives, and industry loss warranties, have been created. This paper investigates the pricing of CAT risk, focusing on two main challenges. First, catastrophe risk is increasingly intertwined with financial risk due to evolving physical and economic environments, driven by climate change and socio-economic factors, respectively. Second, the cyclical nature of the two environments reshapes both catastrophe and financial risks. We model the occurrence of CAT events using a doubly stochastic Poisson process. Three underlying rate processes—a hazard rate process governing the occurrence of CAT events, a risk-free rate process for discounting, and a floating coupon rate process determining floating coupon payments—are assumed to jointly follow an affine jump-diffusion model, influenced by the regimes of the physical and economic environments. We develop a general pricing framework and derive semi-analytical expressions that, when combined with simulation techniques, enable an effective computational scheme. We illustrate this using a standard CAT bond. Extensive numerical studies underscore the importance of accounting for the interplay between catastrophe and financial risks, as well as the cyclical nature of the physical and economic environments.

Abstract

Green bonds, as an innovative financial instrument, have been playing an important role in capital mobilization towards climate change mitigation and adaptation. The market was established in 2007, gained momentum from 2014 onwards, and has since accumulated approximately US$3.3 trillion globally as of September 2024. The rapid market growth calls for a rigorous pricing task, an area of burgeoning importance. At the core of green bond pricing is the ‘greenium’—a premium that arises from investors’ pro-environmental motives. Green bonds are also subject to deep uncertainties, which encompass three dimensions: the physical and transition risks of climate change, market dynamics, and human perception of non-pecuniary utilities. This study establishes an integrated pricing framework that accounts for the uncertainties across these three dimensions and captures their effect on the ‘greenium’.

Abstract

In the aftermath of the global financial crisis, regulators worldwide have promoted the use of central clearing counterparties (CCPs) for credit default swaps (CDS) and other credit derivatives. While CCPs have greatly reduced counterparty risk and enhanced financial stability, they have simultaneously created a new risk channel, where a CCP’s failure, though unlikely, could lead to catastrophic, systemically relevant consequences. To protect themselves, modern CCPs often implement loss-sharing rules to mutualize default losses among surviving members. Consider a centrally cleared CDS, where the buyer may be required to absorb losses from a CCP default as part of the recovery process. Consequently, the buyer is exposed to two layers of risk, stemming from both the default of the reference entity and the default of the CCP. Our goal is to develop a rigorous pricing framework for such CDS contracts. To achieve this, we model both losses from the reference entity’s default and the CCP’s default in a hybrid structure composed of two components: one contingent on historical information up to the time of default, and the other linked to the economic regime at the default and subject to additional unpredictability risk. Following the reduced-form approach, we assume that default intensities and interest rate jointly follow an affine jump-diffusion model, governed by the regime shifts of the economy. Extensive numerical studies are conducted to assess the impacts of regime-shift risk, unpredictability risk, and central clearing on CDS valuation.