Exposure valuations and their capital requirements

Risk exposures are defined to be the change in financial valuation induced by a movement an underlying factor. For derivative valuations, asset's price is primary determining When there no move factor also and therefore exposure functions zero at zero. With delta hedging may taken have derivatives As consequence first order of quadratic variation. These considerations lead us value units variation as numeraire. The theory acceptable risks then extended with pricing reformulated units. Explicit computations made using hyperbolic cosine for numeraire bilateral gamma law motion asset price. Capital requirements risk measure distortions develop conservative valuation. Computations illustrate applications options on ten assets over six year period. capital increase moneyness volatility decrease maturity premium puts calls.