The presence of hedging errors is practically a norm of derivatives businesses. Using the unhedgeable gap risk during a margin period of risk as a starting point, this article introduces a reserve capital approach to the hedging error and its inclusion in derivatives pricing and valuation. Specifically, we define economic capital associated with the gap risk hedging error and build the cost of capital into the Black-Scholes-Merton option pricing framework. An extended partial differential equation is derived, showing terms for expected gap loss and economic capital charge, corresponding to capital valuation adjustment--KVA. For a repurchase agreement, economic capital is computed under a double-exponential jump-diffusion model, either estimated from historical data or calibrated to options smile. We find that the expected loss of a repo is very small and that cost of economic capital is the dominant component of the repo pricing spread. A repo therefore constitutes an ideal case to study economic capital and its valuation impact. The approach taken can be extended into margined OTC derivatives and more generally derivatives in incomplete markets.
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