Futures Price In Variance Units to Volatility Units Translation

This translation functionality is for the user that wishes to answer the question "What is the implied volatility associated with the current displayed futures price in variance units?".

Solving Equation 5 for implied volatility yields the following formula, which maps an observed futures price in variance points to an equivalent futures price in volatility points:

The "Futures Price to Traded Volatility" Variance Calculator functionality uses Equation 6 to translate a variance unit futures price into an equivalent implied volatility. The user inputs an estimate for the end of day S&P 500 Index level (P^*_n), which is the key input that bridges the variance unit prices to volatility units. Rather than being viewed as a prediction of the actual closing index level, this input should be viewed as an input that enables the assessment of the sensitivity of the equivalent volatility unit price to variations in the end of day index observation. Users may input the instantaneous index level or another index level as an estimate of the end of day index observation.

It should be noted that Equation 6 could result in imaginary implied traded volatility values (i.e., a negative number under the square root sign). The Variance Calculator implements a check on user inputs for this translation and displays a user-friendly error message to increase the futures price (F^*) and/or decrease the index level (P^*_n) as necessary to prevent a negative value under the square root sign.