Pauline Barrieu

Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs

In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability properties are obtained through some useful exponential submartingale inequalities. Then, a general stability result, including the strong convergence of the martingale parts in various spaces ranging from H1 to BMO, is derived under some mild integrability condition on the exponential of the terminal value of the semimartingale. This can be applied in particular to BSDE-like semimartingales. This strong convergence result is then used to prove the existence of solutions of general quadratic BSDEs under minimal exponential integrability assumptions, relying on a regularization in both linear-quadratic growth of the quadratic coefficient itself. On the contrary to most of the existing literature, it does not involve the seminal result of Kobylanski [Ann. Probab. 28 (2010) 558–602] on bounded solutions.

Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges*

This article investigates the latest developments in longevity-risk modelling, and explores the key risk management challenges for both the financial and insurance industries. The article discusses key definitions that are crucial for the enhancement of the way longevity risk is understood, providing a global view of the practical issues for longevity-linked insurance and pension products that have evolved concurrently with the steady increase in life expectancy since s. In addition, the article frames the recent and forthcoming developments that are expected to action industry-wide changes as more effective regulation, designed to better assess and efficiently manage inherited risks, is adopted. Simultaneously, the evolution of longevity is intensifying the need for capital markets to be used to manage and transfer the risk through what are known as Insurance-Linked Securities (ILS). Thus, the article will examine the emerging scenarios, and will finally highlight some important potential developments for longevity-risk management from a financial perspective with reference to the most relevant modelling and pricing practices in the banking industry.

On Precautionary Policies

In the United States and most industrialized countries, regulatory policies pertaining to food safety, occupational health, and environmental protection are (according to laws and statutes) science based. The complexity of some ecosystems and new technologies, however, makes it increasingly necessary to deal with situations where scientists cannot yet provide a definite picture. In this context, a widely invoked (but debated) rule, known as the Precautionary Principle, says to address potential hazards right away with preventive measures. We develop an intuitive formalization of this rule, which allows us to infer what an appropriate precautionary policy should do. Implications for resource conservation and the regulation of technological risks are then explored.

Assessing Financial Model Risk

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk and the local measure of model risk. Each of the measures has a specific purpose and so allows for flexibility. We illustrate the various notions by studying some relevant examples, so as to emphasize the practicability and tractability of our approach.

Reinsuring Climatic Risk Using Optimally Designed Weather Bonds

The aim of this paper is to determine the optimal structure of a weather bond, i.e. a bond whose coupons depend on the occurence of a weather event. The stress is put more on the structuration than on the simple pricing of the bond. Therefore, instead of looking only at the bond issue, we consider it as a part of a more general transaction, involving three agents: a firm, which wants to be hedged against its weather risk, an investor, which buys the bond and a bank, which has an intermediary key role. Then, we derive the optimal characteristics of the whole transaction. But the bond structure which is obtained, corresponds to a minimal structure: indeed, only the bond optimal price function and its optimal reimbursement level (amount which is paid back when an event occurs) can be determined while there is a degree of freedom in the choice of the optimal coupon. Therefore, this indeterminacy may be interpreted as a marketing tool and it could play an important role in the negotiation process between the issuer and the investor.

Decision SupportAssessing financial model risk

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk and the local measure of model risk. Each of the measures has a specific purpose and so allows for flexibility. We illustrate the various notions by studying some relevant examples, so as to emphasize the practicability and tractability of our approach.

Market-Consistent Modeling for Cap-and-Trade Schemes and Application to Option Pricing

In this paper we refer to the requirement for industrialized countries to reach a domestic target for greenhouse emissions, as ratified in the Kyoto Protocol, and propose a market-consistent model of futures price dynamics for cap-and-trade schemes designed in the spirit of the European Union Emissions Trading Scheme EU ETS. Historical price dynamics for the EU ETS suggest that both European emission allowance EUA and certified emission reduction CER certificates, generated by a nondomestic offset mechanism, are significantly related. We use an equilibrium framework to demonstrate that compliance regulation singles out special price dynamics. Based on this result, we propose an arbitrage-free model and apply it to the pricing of spread options between EUAs and CERs.

A primer on weather derivatives

We give a short introduction to weather derivatives. We discuss what they are made for. We describe the markets on which they are exchanged, and how they are used to promote agricultural risk transfer in developing countries via the World Bank program. We also treat some specific issues such as basis risk, pricing and design.

Innovations in Insurance Markets: Hybrid and Securitized Risk-Transfer Solutions

One of the most significant economic developments of the past decade has been the development of innovative risk-financing techniques in the insurance industry. Innovation has been driven by the increase in the frequency and severity of catastrophic losses, capital management needs in the life insurance industry, market inefficiencies created by (re)insurance underwriting cycles and regulation, advances in computing and communications technologies, and other factors. These developments have led to the development of hybrid insurance/financial instruments that blend elements of financial contracts with traditional reinsurance as well as new financial instruments patterned on asset-backed securities, futures, and options that provide direct access to capital markets. This chapter provides a survey and overview of the hybrid and pure financial markets instruments, not only emphasizing CAT bonds but also covering futures, options, industry loss warranties, and sidecars. The chapter also covers life insurance securitizations executed to provide capital release, respond to reserve regulations, and hedge mortality and longevity risk.

Integrated EUA and CER Price Modeling and Application for Spread Option Pricing

In this paper we propose a market consistent futures price dynamics model for cap-andtrade schemes, designed in the spirit of the European Union’s Emissions Trading Scheme (EU ETS). Historical price dynamics for the EU ETS suggest that, both, European emission Allowances (EUAs) and Certified Emission Reductions (CERs), certificates, which are generated through the Clean Development Mechanism (CDM) - a non-domestic offset mechanism - are significantly related. We use an equilibrium framework to demonstrate that compliance regulation singles out special joint futures price dynamics. Based on this result we propose an arbitrage free futures price model and apply it to the pricing of spread options between EUAs and CERs.