Cost of living index adjustment is driven by changes in the purchasing power of an assignee in the host location. The purchasing power is based on both the exchange rate and inflation, relative between the home and host countries.
Hyperinflation causes rapidly increasing prices, and thus increases cost of living indices. However, hyperinflation is often accompanied by local currency depreciation, which has an opposite impact. The balance between these two opposing forces on the index will determine how much change is seen. When depreciation lags or a currency is pegged, the impact on an index can be considerable.