I have a financial model that generates future values for a present sum of money based on its growth by investment minus inflation adjusted expenditure. Rather than use fixed rates for growth and inflation (say over the next 20 years), I'd like to use a range with a probability distribution. e.g. inflation "normally" distributed between 1 to 5 percent (90% confidence). Question is, is a normal distribution a good choice for modeling future inflation rates? Or does the history of inflation point towards some other distribution?
With many financial variables you can deduce the distribution from the options market , but there isn’t a sufficiently developed inflation options market (at least in the US). However, experience shows that market participants are unwilling to sell options with strikes either very low (say 0%) or very high (say 5%) at anywhere near theoretical prices, suggesting that the right distribution might be more fat tailed than a normal distribution. This wouldn’t be shocking , since many financial variables have similar characteristics.
It also matters what measurement period you are working with. The inflation rate for a given 12month period in the future could have a wider distribution than the average inflation over a 20year period, which might be better behaved.
In the US , the center of the distribution can be estimated from the inflation bond and derivatives markets , and is in the area of 2% for long term forecasts, in line with the target of the Federal Reserve.