Hedging Valuation Adjustment : Fact and friction

We develop a simple and generic expression for the impact of transaction costs on the value of a derivative portfolio, expressed as a 'Hedging Valuation Adjustment' (HVA). We provide expressions for the HVA in two cases: when it is included as part of the value to be hedged, and when it is left as an unhedged reserve. The hedged case shows an interesting feature we term 'imaginary volatility'. We show numerical results, and extend the formalism to the pricing of individual trades and to the multi-asset case