Abstract: The discrete-time multifactor Vasiček model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditions leads to model parameters that change over time. Therefore, the model parameters should be understood as being time-dependent or even stochastic. Following the consistent re-calibration (CRC) approach, we construct models as concatenations of yield curve increments of Hull–White extended multifactor Vasiček models with different parameters. The CRC approach provides attractive tractable models that preserve the no-arbitrage premise. As a numerical example, we fit Swiss interest rates using CRC multifactor Vasiček models.
Abstract: We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival times depending on the claims that arrive within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the bonus-malus (BM) feature of pricing car insurance. We discuss first the asymptotic results of ruin probabilities for different regimes of claim distributions. For numerical results, we recognise an embedded Markov additive process, and via an appropriate change of measure, ruin probabilities could be computed to a closed-form formulae. Additionally, we employ the importance sampling simulations to derive ruin probabilities, which further permit an in-depth analysis of a few concrete cases.
Abstract: This paper studies the dependence between coupled lives, i.e., the spouses’ dependence, across different generations, and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. We find that a generation-based model is important, since spouses’ dependence decreases when passing from older generations to younger generations. The independence assumption produces quantifiable mispricing of reversionary annuities, with different effects on different generations. The research is conducted using a well-known dataset of double life contracts.
Abstract: Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging binomial schemes with a particular application to barrier options.
Abstract: This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class of Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterisations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges that are amenable to practitioners when fitting such models is to perform robust estimation of the model parameters. In this paper we develop a novel, efficient, and robust procedure for estimating the parameters of this family of Tukey transform models, based on L-moments. It is shown to be more efficient than the current state of the art estimation methods for such families of loss models while being simple to implement for practical purposes.
Abstract: Traditionally, actuaries have used run-off triangles to estimate reserve (“macro” models, on aggregated data). However, it is possible to model payments related to individual claims. If those models provide similar estimations, we investigate uncertainty related to reserves with “macro” and “micro” models. We study theoretical properties of econometric models (Gaussian, Poisson and quasi-Poisson) on individual data, and clustered data. Finally, applications in claims reserving are considered.