Optimal Spot Slides

Spot slides record the impact on the market value of existing positions in derivative markets in response to an immediate movement in the underlying asset’s spot price. The question of an optimal spot slide is then one of designing this response to be optimal among the set of possible risk exposure functions. Structurally as a nonzero constant cannot be an exposure, its role as a numeraire asset is replaced by the selection of a numeraire exposure. The design objective replaces expected utility that is not a financial objective by a monetary utility that we define to be a Financial Finance Objective (FFO). An FFO valuation, by virtue of being a market valuation, also avoids the use of physical probabilities in designing exposures. The FFO values risk by the maximal level of the numeraire exposure that may be extracted from a position subject to the resulting risk maintaining its acceptability. Risk acceptability is defined by a convex set that may or may not contain a convex cone larger the nonnegative variables. Such a larger cone is referred to as an embedded Conic Finance Cone (CFC). The absence of a CFC embedding limits risk taking and is a simpler design problem. The more general problem with a CFC embedding is numerically solved using Disciplined Saddle Point (DSP) programming. An FFO maximizes a conservative valuation obtained on minimizing over a set of admissible measure changes. Consequently the general problem is always a saddle point problem. We therefore envisage an enhanced role for DSP in finance with applications revising hedging, investment, and both active and passive wealth management strategies.