Catastrophe Risk Bonds Pricing Models And Its Simulation Research

According to Swiss Re Sigma world insurance database, there is a clear upward trend in both the frequency of catastrophe and property damage and insurance losses caused by catastrophes since the late1980s. The Fourth Assessment Report of Intergovernmental Panel on Climate Change (IPCC) in2007forecasts that the frequency of global extreme disasters will continue to increase in the21st century. Faced with severe global climate changes, the traditional insurance and reinsurance instruments have fallen short of meeting the demands for the catastrophic risk diversification due to their limited underwriting capacity and risk transfer mode. Alternative risk transfer(ART) vehicles invented in the1990s provide an option to manage and diversify the catastrophic risk. In recent years, a major approach to managing catastrophic risk is to issue Insurance-linked securities(ILS) which transfer risks from insurance market to capital market. Among them, catastrophe risk bonds are by far the most successful and important financial innovation. Therefore, pricing catastrophe risk bonds are not only of theoretical value, but of practical significance.Drawing on previous relevant findings, this dissertation sets out to research into the catastrophe risk bonds pricing theory, model solving and its parameter estimation from both theoretical and empirical perspectives. The results are summarized as follows:First, Using the risk-neutral approach, this dissertation derives and empirically analyzes catastrophe risk bond pricing theory in a Vasicek or Cox-Ingersoll-Ross model of the term structure under the hypothesis that the cumulative loss process follows compound Poisson process. A nonlinear function of claim arriving intensity at claim time is constructed to replace the existent deterministic function, which better reflects the periodicity of catastrophe risk rate, thereby further improving the characterization of its periodicity. Furthermore, we estimate and calibrate the parameters of the pricing model using the catastrophe loss data provided by Property Claim Services(PCS) from1985to2010. As no closed-form solution can be obtained, this dissertation proposes a hybrid approximation method to find the numerical solutions for the price of catastrophe risk bonds. Finally, numerical experiments demonstrate how financial risks and catastrophic risks affect the prices of catastrophe bonds, and numerical experiments show that the hybrid approximation method described in this dissertation is effective and feasible.Second，to characterize extreme features in catastrophes, this dissertation adopts the Block Maxima Method(BMM) and the Peak Over Threshold(POT) in extreme value theory to characterize the tail characteristics of the loss in catastrophic risk events. With the risk-neutral approach, the pricing formula of catastrophe risk bonds is derived in a Longstaff model of the term structure under the hypothesis that the cumulative loss process follows a compound Poisson process. Panjer discrete recursion formula and fast Fourier transform algorithm are used to solve the model numerically rather than the hybrid approximation algorithm because of its limitation. The parameters of the generalized extreme value distribution and the generalized Pareto distribution are estimated with the PCS loss index data provided by the US Insurance Services Office. And the loss distribution is analyzed and assessed using the graphics technology, the goodness-of-fit test, and model evaluation. Finally, numerical experiments are conducted to verify the feasibility of this model.Third, due to global warming, the climate changes over time will become more serious, and the occurrence and severity of abnormal climate change presents an irregular cycle with upward trend. A pure Poisson process with deterministic intensity function does not adequately explain this phenomenon of CATs. Therefore, we construct a doubly stochastic Poisson process provides flexibility by letting the intensity not only depend on time but also allowing it to be a stochastic process. The Black Derman Toy(BDT) model is introduced in this dissertation to characterize this random intensity, and a doubly stochastic compound Poisson Process is built to depict the threshold time. Using the forward risk-adjusted measure approach, the pricing formula is derived in Hull-White model of the term structure and the doubly stochastic compound Poisson loss process. Quasi Monte Carlo simulation is conducted and the sensitivity of the major parameters is also investigated. The results show that simulated catastrophe bonds yield spreads exhibit the similar trend with the arithmetic average secondary market yield spreads, which validates the model.In summary, focusing on characterizing the catastrophe risk loss distribution and the claim arriving intensity at claim time, this dissertation constructs pricing models using extreme theory, the doubly stochastic compound Poisson loss processes and various stochastic interest rate models, including the Vasicek interest rate model, the CIR interest rate model, the Hull-White interest rate model and the Longstaff interest rate model. Different algorithms in line with the characteristics of the different models are proposed, including the hybrid approximation algorithm, the Panjer discrete recursion algorithm, the fast Fourier transform algorithm and the Quasi Monte Carlo simulation algorithm. Simulation results verify the validity and the applicability of these models. This research would provide practical guideline for the development of catastrophe risk bonds，and help the investors to make rational investment decisions in financial markets.