Essays on insurance-linked securities and foreign exchange options

This dissertation consists of three papers referring to the pricing of insurance-linked securities, while a fourth one deals with investigating the dynamics of foreign exchange implied volatility and correlation surfaces. The first paper proposes a novel risk-neutral pricing approach for industry loss warranties, where the dependence of losses on individual policies in an insurance portfolio is explicitly considered. These joint claim events are modeled in a Lévy-Frailty framework with a stochastic time change. The model is estimated on historical quotes, obtaining excellent fit statistics. The second paper focuses on natural catastrophe risk, increasingly insured through alternative capital. Since most instruments are missing an active secondary market, their ongoing valuation poses a challenge. Thus, information contained in regularly observed catastrophe bond prices is extracted by means of a reduced-form model. The Poisson intensity of the latter is found to depend on time to maturity and default probability. Based on these two dimensions, smooth implied intensity rate surfaces are estimated, allowing to mark any catastrophe risk contract to market. The third paper investigates the dynamics and determinants of implied Poisson intensities. These are derived from observed catastrophe bond prices using a reduced-form model. A principal component analysis shows that the factors level, slope and curvature explain most of the variation. Evidence of macroeconomic and natural catastrophe events to influence these intensities is found by means of fixed effects models. A risk-neutral valuation framework is thus suitable for pricing natural catastrophe risk. In the fourth paper, smooth implied volatility and correlation surfaces are constructed that depend on option delta and time to maturity. These surfaces exhibit both skew/smile features and term structure effects, and change shape over time. The fluctuations are then studied by applying a Karhunen-Loève decomposition, where the largest share in the dynamics are explained by exactly the same three factors. This finding confirms interdependences between implied correlation and implied volatility.