Abstract
An operative framework for valuations is presented based on the absence of acceptable deals rather than just arbitrages. Specifically, the valuation functional U(Y) of a future cash flow Y is defined as the infimum over Z of E[ZY]+r(Z) for Z in a set M determined by the dual of a distortion function and r an appropriate floor function. It will be shown that the solution Z to such a minimization problem admits a semi-explicit formula, which can be approximated by the solution to a finite-dimensional version of the problem itself. Two applications are explored. First, this valuation framework allows one to design capital structures that maximize the enterprise value implied by the volatility surface and to test whether current capital requirements imposed by Basel III regulations are adequate. Secondly, an optimal hedging strategy that maximizes a derivative position is devised based only on forward-looking risk-neutral measures rather than estimated physical ones. The associated maximin problem is solved efficiently via Lagrange duality by converting the inner minimization problem into a maximization one.
Organized by: Umberto Cherubini