PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

MODELING FINANCIAL SCENARIOS 191the stock market in October 1987. This single observation mayappear to be too “extreme” and very unlikely given a singlevarianceassumption. Instead, suppose that equity returns at anypoint in time are generated from two distinct distributions, a“high volatility” regime or a “low volatility” regime. The chanceof switching from one regime to the other over the next timestep is dictated by transition probabilities. During times of economicinstability, the returns on equities may be more uncertain,representing a transition to the high volatility regime. Thus, theobservation from October 1987 may simply be a draw from thehigh volatility regime.We use Hardy’s approach for equity returns but apply theregime-switching process to excess returns over and above thenominal risk-free rate. At any point in time, the excess return ofstocks is a draw from a normal distribution that is conditionalon the current regime. 4 For each period, there is a matrix ofprobabilities that dictate the movement between regimes. Whilethere is no limit to the number of regimes that can be embeddedin the model, Hardy finds only marginal improvement in fit whenextending the equity return model to more than two regimes.Given two regimes (i.e., i and j), Hardy uses these transitionprobabilities to determine the unconditional probability ¼ iof being in state i at any point in time:p j,i¼ i = , ¼p i,j + p j =1¡ ¼ i : (2.9)j,iActuarial ModelsRedington [34] pioneered the work in modeling insurers. Thisearly work introduced the concept of immunization against interestrate risk and introduced the “funnel of doubt” terminologyto convey uncertainty in outcomes. Modern approaches to modeling(including this research) focus first on assumptions of the4 Ahlgrim and D’Arcy [1] extend this regime-switching approach to international equities.