Index-linked catastrophe instrument valuation - Giuricich, Mario Nicolo (Division of Actuarial Science, 2019)
This thesis proposes four contributions to the literature on index-linked catastrophe instrument valuation. Invariably, any exercise to find index-linked catastrophe instrument prices involves three key steps: construct a suitable arbitrage-free valuation model, estimate the parameters for the underlying loss process and simulate the instrument prices. Chapters 3 to 5 of this thesis loosely follow this process. In Chapter 3 we propose an index-linked catastrophe bond pricing model, which pervades in subsequent chapters. We furthermore show how, under certain assumptions, our model can use real-world catastrophe loss-data to find arbitrage-free, index-linked catastrophe bond prices. Chapter 4 demonstrates how we estimate parameters for the catastrophe-related insuranceloss process on which our pricing model relies. In practice, data from such insurance-loss processes is both left-truncated and heavy tailed. We build on ? ]’s procedure for modelling left-truncated data via a compound non-homogeneous Poisson process, and modify their fitting process so that it becomes systematically applicable in the context of heavy-tailed data. We close this chapter by presenting an importance sampling technique for simulating index-linked catastrophe bond prices. Chapter 5 treats the new problem of finding simple, closed-form expressions for indexlinked catastrophe bond prices. By using the weak convergence of compound renewal processes to α-stable Levy motion, we derive weak approximations to these catastrophe bond prices. ´ Their applicability is then highlighted in the context of our catastrophe-bond pricing model. Chapter 6 deviates from the ambit of catastrophe bond pricing, and considers a new type of insurance-linked security, namely the contingent convertible catastrophe bond. Our foremost contribution is that we comprehensively formalise the design and features of this instrument. Subsequently, we derive analytical valuation formulae for index-linked contingent-convertible catastrophe bonds. Using selected parameter values in line with earlier research, we empirically analyse our valuation formulae for index-linked contingent-convertible catastrophe bonds.