new trade HVA

The new trade HVA (or marginal HVA) is the incremental change in a book’s Hedging Valuation Adjustment when a new trade with gamma ${\gamma }_i$ is added. Derived in Burnett (2021), it is:

${\text{HVA}}_i^{\text{new}}(t,T)\approx -2{\int }_t^T{\mathbb{E}}_t\left[{\mathcal{D}}_r(t,u)\frac{\psi }{D^2}{\sigma }^2\Gamma {\gamma }_i\right]\mathrm{d}u.$

The factor of 2 is crucial and counterintuitive. It arises from the quadratic dependence of HVA on book gamma: since $(\Gamma +{\gamma }_i{)}^2\approx {\Gamma }^2+2\Gamma {\gamma }_i$, the marginal impact of a new trade on friction costs is twice what one would naively compute by looking at the trade’s gamma ${\gamma }_i$ in isolation.

This provides healthy incentive alignment: a trade that reduces the book’s net gamma (offsetting risk) gets a positive HVA attribution (benefit), while a trade that increases gamma gets a negative attribution (cost). The “naive” HVA — computed using only the trade’s own gamma ${\gamma }_i$ — underestimates the true cost by a factor of $2\Gamma /{\gamma }_i$, which can be an error of both sign and order of magnitude.

Key Details

• The allocation ${\text{HVA}}_i=-\int \mathbb{E}[{\mathcal{D}}_r\cdot (\psi /D^2){\sigma }^2\Gamma {\gamma }_i]\mathrm{d}u$ gives per-trade HVA summing to total book HVA (symmetry, zero for ${\gamma }_i=0$)
• The factor of 2 is the origin of the super-contingency multiplier $m\approx 2$ in the XVA-consistent framework
• This is directly analogous to how CVA must be computed at portfolio level, not per-trade

---

concept