Description: In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. This presentation offers a quantitative analysis of this brand new financial innovation. First of all, the presentation sets up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices [spreads] that are fairly close to the spreads that Goldman Sachs currently offers. The presentation then explores the uncertainty involved in this model-based pricing framework. Specifically, it studies parameter risk by using Markov Chain Monte Carlo [MCMC] and model risk by examining structural changes in mortality dynamics. The results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap.

Description: This session from the 2003 SOA Orlando Meeting discusses the new risk-based capital RBC requirements for variable annuities with guranteed benefits such as guaranteed minimum death benefits - GMDBs and guaranteed minimum income benefits - GMIBs. From the Society of Actuaries Record, Volume 29, No. 3.

Description: This session at the SOA 2001 Toronto Spring Meeting offers an overview of stochastic pricing including stochastic variables, equity market models, interest rate models and policyholder behavior. An example is given using a variable annuity product.

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: This session of the SOA 2003 Washington, DC Spring Meeting covers the basics of stochastic modeling with focus on random number and scenario generation, steps in creating models, and verification of models and assumptions.

Description: Provides a how-to session on modeling assets and liabilities in the Valuation Actuary's work to comply with the Standard Valuation Law. Comparisons of the methods discussed are occasionally made with the requirements of New York Regulation 126. Session 12 of the 1991 Valuation Actuary Symposium.

Description: 1998 Valuation Actuary Symposium. The panelists discussed how asset liability management is synonymous with a dynamic financial analysis and quantitative risk management. Topics covered were systems implementations including asset risk exposure optimization given a company-specific set of liabilities and total risk exposure optimization, which includes stochastic analysis of alternative asset and liability strategies.

Description: 2003 Valuation Actuary Symposium, San Diego, CA. This panel discussion provided an overview of the current risk-based capital RBC requirements for life insurers as well as insight into topical issues and potential changes to RBC. Discussion topics included: 1. Recap of RBC law and RBC calculation rules. 2. Modeling potential impact of alternative actions. 3. The tax impact of the factors. 4. Stochastic capital requirements for variable products. 5. The role of reinsurance and offshore solutions.

Description: This session from the 1995 SOA Boston Meeting discusses constructing and using a comprehensive, credible risk management system with a concentration on C-3 risk. It also covers an example of option adjusted spread analysis for a single premium deferred annuity SPDA. From the Record of the Society of Actuaries, Vol. 21, No. 4b.

Description: 2003 Valuation Actuary Symposium, San Diego, CA. In this Teaching Session the instructor discussed the importance of making sure the correct inferences were drawn from stochastic testing exercises. Topics included: 1. Applying the assumption of a normal distribution. 2. Drawing inferences about, and creating confidence intervals around, a population mean. 3. Drawing inferences about, and creating confidence intervals around, tail percentiles. 4. Certifying anticipated mortality under XXX in a mathematically concise way.