  We investigate a statistical-static hedging technique for pricing assets
considered as single-step stochastic cash flows. The valuation is based on
constructing in a canonical way a European style derivative on a benchmark
security such that the physical payoff distribution coincides with the
(corrected) physical asset price distribution. It turns out that this pricing
technique is economically viable under some natural cases. The fundamental
properties of the pricing rule arising in this way are investigated here. This
gives rise to a novel way of estimating state price density. Our approach has
some tangible benefits: its principle is transparent, and it is easy to
implement numerically while avoiding many issues typically involved in such an
estimation. As an application, it is shown how this method can be used in
performing kurtosis corrections to the standard Black-Scholes-Merton model by a
mixture of several types of distributions. In fact, the technique is
non-parametric in nature, and it can handle in principle any physical
distribution, e.g., a multimodal one. Some other interesting applications are
discussed as well.
