All simulators except custom

For all capital market simulators except the custom type, ProVal uses the inflation parameters to simulate the total rate of inflation, reflecting both expected and unexpected (sometimes referred to as surprise) inflation. Simulated inflation affects future liabilities (through its effect on salaries, benefits, etc.) as well as future asset values (as a component of the nominal return rate of an investment).

In general, inflation is described as being mean-reverting (trending toward long term expected inflation) and serially correlated (affected by the prior year's value). The resulting distribution is essentially a normal distribution. The mathematical equation used to develop the current year inflation rate, Inf(t), is the following:

 Inf(t) = [ (Inf(t-1) * w ] + [ LTInf * (1-w) ] + e

Where:

• Inf(t-1): Previous year inflation is the annual rate of inflation in year t-1. For the previous year’s (actual) inflation, specify any rate between -0.2 and 1, inclusive. Enter the rate as a decimal number (not as a percentage).

• w: Lagged inflation coefficient indicates the relationship between the prior year’s inflation and the current year’s inflation. The value 1 – w is sometimes referred to as the speed of mean reversion. The rate of expected inflation is defined as w times the prior year’s inflation plus (1 –w) times long-term expected inflation, i.e., the sum of the first two terms of the equation. Specify any rate between 0 and 1, inclusive. Enter the rate as a decimal number (not as a percentage).

• LTInf: Long term inflation is your expected long-term, or equilibrium, rate of inflation. Specify any rate between 0 and 2, inclusive. Enter the rate as a decimal number (not as a percentage).

• sd(e): Standard deviation of unexpected inflation is the specified standard deviation of the rate of unexpected inflation, e, in year t. The error term (e), generated by the simulator, accounts for unexpected inflation. It is based on a normal distribution with an expected value of zero and a standard deviation as defined by this parameter. For the classic mean variance simulator (but not the multi-factor term structure or explicit corporate yield curve simulators), the error term is lognormally transformed, so that it has a positive bias. Specify any rate between 0.000001 and 0.4, inclusive. Enter the rate as a decimal number (not as a percentage).

When you specify the standard deviation of unexpected inflation, consider the amount of deflation that may be generated. Check the resulting distribution of overall inflation. For example, if mean inflation of 3.0% with a 3.0% standard deviation is generated, then inflation has (roughly) a 67% probability of being between 0.0% and 6.0% and a 16% probability of being below 0%. This is typically too much deflation to be considered reasonable. Note that the value of the parameter w plays an important role in the volatility of overall inflation as well.