CFADS Volatility Calibration

When the volatility of CFADS $//<![CDATA[ \begin{array}{l}\sigma_{CFADS}\end{array} //]]>$ increases, a firm's debt value declines. This is because it cannot benefit from the larger CFADS, so rising volatility only increases the risk of CFADS falling below the debt service costs. However, the equity value could increase as there would a greater chance of larger CFADS. Consequently, the firm value - the sum of the equity and debt values - is also a function of   $//<![CDATA[ \begin{array}{l}\sigma_{CFADS}\end{array} //]]>$. 

We estimate the proper  $//<![CDATA[ \begin{array}{l}\sigma_{CFADS}\end{array} //]]>$ by matching the firm value equal to asset value within a tolerance range (+/- 10%).  

$$//<![CDATA[ \begin{array}{l}\displaystyle FirmValue(\sigma_{CFADS}) = EquityValue(\sigma_{CFADS}) + DebtValue(\sigma_{CFADS}) = TotalAssetValue.\end{array} //]]>$$

Once  $//<![CDATA[ \begin{array}{l}\sigma_{CFADS}\end{array} //]]>$ is calibrated, the possible future scenarios of CFADS are determined and their probabilities are estimated. The credit risk metrics, such as PD, LGD and EL can be computed.