Description: Prior work indicates that a regime-switching stochastic model with randomized regime parameters creates a more plausible set of extreme paths than do the usual stochastic interest rate models. Generalizing the Black-Karasinski model by randomizing the mean reversion target provides an example. Better to understand such models, as well as to calibrate their parameters without trial and error runs of a stochastic model, this paper uses an asymptotic expansion to estimate the moments of the integrated stochastic process over time. Mention is made of a family of related asymptotic expansions that could be of wider interest.

Description: Read the April 2020 issue of The Modeling Platform, published by the Modeling Section. Newsletters provide practical information for the working actuary, articles on trends that impact sections and news about section activities.

Description: Read the November 2019 issue of The Modeling Platform, published by the Modeling Section. Newsletters provide practical information for the working actuary, articles on trends that impact sections and news about section activities.

Description: Principle-based reserving requires modeling assets and liabilities across a range of scenarios to assess the sufficiency of assets when determining reserves, a major shift from the current formulaic framework. These changes will require valuation actuaries to evolve their skill set by heightening their focus on creative analysis, gaining deeper understanding of complex projections and clearly communicating drivers of reserve movements to stakeholders in order to influence strategic decision-making. The panelists will discuss the way that they see the role of the valuation actuary changing in response to the change in focus in reserving requirements. They will also discuss successful characteristics along with best practices for understanding and explaining results in the new paradigm. The audience will be given the opportunity to interact through polling and facilitated discussion of their stories, experiences and observations.

Description: A classical risk model with a multi-layer premium rate is considered in this paper. In the two-layer case, an explicit expression is obtained for the joint distribution of the maximal surplus up to ruin, the surplus immediately before ruin and the deficit at ruin. Such an expression involves some known results on the joint distribution at ruin for a risk model with a constant premium rate. In the multi-layer case, a scheme is proposed to compute its ruin probability.

Description: This article is based on an excerpt from a Milliman Research Report on universal life insurance with secondary guarantees, ULSG. It discusses stochastic profit analysis and the impact of investment volatility of two common variants of ULSGs - level specified premium and single-fund shadow account designs.

Description: 2011 Enterprise Risk Management Symposium, Chicago. This study investigates whether simulation-based models can be used to predict liquidity risk for banks, which must comply with Basel III by January 2015. The paper looks at the process of developing a measurement framework using Black-Scholes and Merton’s asset-based models to measure liquidity risk.

Description: Feature article discussing numerical short cuts, rules of thumb, estimators, modeling tips, etc. The featured problem is fitting the intermediate points for a real-world stochastic model of interest rates.

Description: This presentation considers the pricing of European derivatives in a Black-Scholes model with stochastic volatility. The presentation shows how Parseval’s theorem may be used to express those prices as Fourier integrals. This is a significant improvement over Monte Carlo simulation in many cases. The main ingredient in this presentation's method is the Laplace transform of the ordinary [constant volatility] price of a put or call in the Black-Scholes model, where the transform is taken with respect to maturity [T]. The presentation derives these formulas and then applies them to the case where volatility is modelled as a Markov chain in continuous time, the so-called 'Markov regime switching model'. This model has been used previously in stochastic volatility modelling, but mostly with only N=2 states. The presentation shows how to use N=3 states without difficulty, and how larger number of states can be handled. Numerical illustrations are given, including the volatility smile in a three-state model.

Description: An overview of guaranteed lifetime withdrawal benefits (GLWB) on registered index-linkedannuity (RILA) products and a stochastic analysis of market risks.