\(f_{nd} – CVA + DVA\)
where
\(f_{nd}\) is the value assuming no defaults on either side
\(DVA = \sum_{I=1}^{N} q_i^* v_i^*\)
where
where \(s(t_i)\) is the counterparty’s credit spread at time \(t_i\) , and R is the recovery rate if counterparty defaults
The default of an entity occurs if the linear combination of these factors falls below a certain threshold, which is linked to the entity’s creditworthiness.
\(x_i = a_i F + \sqrt{1 – a_i^2} Z_i\)
where,
\(Q_i(T|F) = N \left( \frac{N^{-1}[Q_i(T)] – a_i F}{\sqrt{1 – a_i^2}} \right)\)
\(Q(T|F) = N \left( \frac{N^{-1}[Q(T)] – \sqrt{\rho} F}{\sqrt{1 – \rho}} \right)\)
where,
Example
showing that the 99.9% worst case default rate is 12.8%. The 1-year 99.9% credit VaR is therefore \(100 \times 0.128 \times (1 – 0.6) \ \text{or} \ \$5.13 \ \text{million}\).