Quadratic hedging of risk neutral values

Risk neutral valuation determines no arbitrage values for financial or real assets, including ones that are exposed to energy price risk. It is always uniquely associated with a hedging strategy if and only if markets are complete, which is the exception in theory and never the case in practice. We apply quadratic hedging, which is both conceptually simple and partially analytically tractable, in a nonstandard fashion to approximately offset the change in the value of an asset obtained from using any chosen risk neutral measure when markets are incomplete. Consistency between valuation and hedging conditional on this value is thus ensured. Achieving this goal with standard quadratic hedging requires employing the so called variance optimal martingale measure for valuation, which can be problematic in general because this measure can fail to be a risk neutral one. Heuristics that rely on a complete market assumption are compatible with the proposed conditional quadratic hedging approach. Simple examples suggest that such techniques can perform near optimally. The methodology put forth therein applies to fully risk neutral valuation of assets with cash flows that depend on both market and private risks, reducing to quadratic hedging if markets are partially complete, which we show provides a novel justification for this valuation strategy in this case. It can be extended beyond the single and fixed-date cash flow purview of this research.