====== Math - Calculate Tolerance ======

Volatility varies through assets and this model adapts to asset’s individual characteristics.  Dynamic tolerance levels will be used based on confidence levels, allowing the use of thresholds more aligned to the price variation of a particular asset.

A generic formula will be used to set these dynamic tolerance levels using a rolling 30 or 60 or 90 days prices volatility. 

{{:math:tolerance.png?800|}}

S[t-1] * exp (-z[a] * O[30 or 60 or 90 days] <= S[t] <= S[t-1] * exp (Z[a] * O[30 or 60 or 90 days])

where

  * S[t]:  Simulated Price.  S[t] is the price to be verified.
  * S[t-1]:  Current Price.  S[t-1] is the previous price.
  * Z[a]:  Critical value associated with confidence level = 3 or 4 or 5 depending on the confidence level that is wanted.  The values proposed are 3 or 4 with a probability of a minimum 99% to be in the confidence interval.
  * O[30 or 60 or 90 days]:  Rolling 30 or 60 or 90 days volatility of the underlying classification.  30, 60, 90 days is assumed to be describing the time period rather than number of previous prices. So for example if a fund is priced monthly it does not mean we go back 90 months, just 3 months for a 90 day period. 

For all assets that have a history below 60 data points, default tolerance level will be set to:

Fixed Income – 5%
Equity – 10%
Funds – 10%
Structured Products – 10%
Forex – 1%