  Although not a formal pricing consideration, gap risk or hedging errors are
the norm of derivatives businesses. Starting with the gap risk during a margin
period of risk of a repurchase agreement (repo), this article extends the
Black-Scholes-Merton option pricing framework by introducing a reserve capital
approach to the hedging error's irreducible variability. An extended partial
differential equation is derived with two new terms for expected gap loss and
economic capital charge, leading to the gap risk economic value adjustment and
capital valuation adjustment (KVA) respectively. Practical repo pricing
formulae is obtained showing that the break-even repo rate decomposes into cost
of fund and economic capital charge in KVA. At zero haircut, a one-year term
repo on main equities could command a capital charge as large as 50 basis
points for a 'BBB' rated borrower.
