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

MODELING FINANCIAL SCENARIOS 193Dynamic financial analysis (DFA) has become the label underwhich these financial models are combined with an insurer’soperations when performing a variety of applications includingpricing, reserve adequacy, and cash flow testing. D’Arcy et al.[15, 16] walk through the development of a public-access DFAmodel and illustrate the use of the model in a case study.3. DESCRIPTIONS OF THE FINANCIAL SCENARIO GENERATORAND DATAIn this section, detailed descriptions are provided for eachof the economic time series included in our model. Embeddedin these descriptions are references to the sources of historicaltime-series data used to select the parameters of the model.InflationInflation (denoted by q) is assumed to follow an Ornstein-Uhlenbeck process 5 of the form (in continuous time):dq t = ·q(¹ q ¡ q t )dt + ¾ q dB q : (3.1)The simulation model samples the discrete form equivalent ofthis process as¢q t = q t+1 ¡ q t = ·q(¹ pq ¡ q t )¢t + " q ¾ q ¢tq t+1 = q t + ·q(¹ q ¡ q t )¢t + " q ¾ qp¢t= ·q¢t ¢ ¹ q +(1¡ ·q¢t) ¢ q t + " q ¾ qp¢t:(3.2)From this last equation, we can see that the expected level offuture inflation is a weighted average of the most recent valueof inflation (q t ) and a mean reversion level of inflation, ¹ q .Thespeed of reversion is determined by the parameter ·q. Inthecontinuous model, mean reversion can be seen by consideringthe first term on the right-hand side of Formula (3.1) (which iscalled the drift of the process). If the current level of inflation q t is5 The Vasicek process discussed in Section 2 is also an Ornstein-Uhlenbeck process.