Description: From a session at the Spring meeting of the Society of Actuaries held in San Antonio, Texas, June 14-15, 2004 The panelists discuss the benefits of hedging variable annuity guarantees, the challenges they face and how they keep score.

Description: This presentation introduces the Threshold Life Table as a solution to the problem of modeling mortality for extreme ages. This method is based on extreme value theory, and it avoids the need to extrapolate beyond an arbitrary age. This method produces an omega, the highest attainable age, without it being chosen arbitrarily.

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: These are Charts 1-4 from a presentation entitled 'Stochastic Immunization' From a session at a meeting of the Society of Actuaries held in San Diego, CA, June 22-23, 2000

Description: These are Charts 5-8 from a presentation entitled 'Stochastic Immunization'. From a session at a meeting of the Society of Actuaries held in San Diego, CA, June 22-23, 2000

Description: Presentation discussing modeling of daily and hourly rainfall, both occurrence and amount. These distributions would be needed to price derivative or insurance contracts involving rainfall amounts.

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: From a session at a meeting of the Society of Actuaries held in San Diego, CA, June 22-23, 2000 A discussion of how stochastic modeling techniques can be used to efficiently and effectively consider a wide variety of scenarios and outcomes and how these tools can be used to optimize portfolio performance?

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.