Enterprise, Capital and Risk

Abstract

Economic enterprises are represented by their return processes modeled in efficient markets by pure jump limit laws. In particular four parameters of a bilateral gamma process are used to synthesize the up and down moves with differing mean and variance rates for the two motions. Prudential capital requirements value a distant terminal payout given by accumulated returns. The valuation incorporates risk charges based on measure distortions generalizing distorted expectations. The risk charges are calibrated to data on S&P 500 index options and their associated time series. Regulatory capital evaluates extreme loss levels possible in a short interval. For the equity space the two calculations yield comparable magnitudes displaying enterprises with sufficient and insufficient capital. Enterprises invested in Treasury bonds have regulatory capital is 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.