Nonlinear equity valuation using conic finance and its regulatory implications

Abstract

Economic enterprises are modeled to have the return distributions of pure jump limit laws. Specifically the four parameters of a bilateral gamma process synthesize the up and down moves in returns with differing mean and variance rates for the two motions. Prudential capital assessments value a distant terminal payout defined by the accumulated returns. The valuation incorporates risk charges based on measure distortions that generalize the concept of distorted expectations. Particular risk charges are calibrated to data on S&P 500 index options and their associated time series. On the other hand regulatory capital evaluates extreme loss levels possible over a short time interval. For equity market returns the two calculations yield comparable magnitudes displaying enterprises with both sufficient and insufficient capital. Enterprises invested in Treasury bonds have regulatory capital requirements that are well below their prudential capital levels for long positions. Short positions may have insufficient prudential capital values relative to their regulatory counterparts. The additional prudential and regulatory capital costs of leveraged positions are illustrated. Hedge funds reflect high levels of prudential capital associated with low levels of required regulatory capital reflecting the access of good drifts at low risk levels.