I'm calibrating a multiplier for a correlation matrix. For low values it's simple, I multiply the correlations by a value. So if I apply an adjustment of 1.1, then correlations of 0.2 go to 0.22. I need some way to handle large |correlations|, e.g. if the original correlation is 0.98, and I apply the factor of 1.1. I'd get a correlation of 1.078, which makes no sense. Is there a mathematically correct way to handle this scaling so correlations remain in the range of -1 to +1 ?
If there is no single correct solution, can someone suggest a formula/model that behaves sensibly/smoothly as correlations approach 1 or -1. Ideally something reversible, so that applying a factor and then 1/factor gets me back to where I started, which max(-1, min(1, original_correlation * factor)) does not achieve!