As has been shown almost two years ago , generalized vector dominance (GVD) quite successfully quantitatively accounts for the data on deep inelastic electron nucleon scattering. There is, however, one principal feature within this approach, which became more and more unsatisfactory as progressively higher energy data on e+e-+hadrons became available: these showing roughly a 1/s law in the Frascatil 3 1range, and an even slower fall off for c.m. energies /8 beyond about 3.5 GeV has been reported by CEAI 4 1 and more recently by the SLAC-LBL collaboration at SPEARisl. The problem, as discussed in I 1 I, with a 1/s law for e+e-annihilation is that in the usual diagonal form of GVD (i. then for p''(1600) photoproduction one expectswhere the addition.e e ann1h1lat1on result Experimentally one finds I 11 I Denoting the ratio of the first off-diagonal to the diagonal (t = 0) transition amplitude as (3) we thus obtain the isovector photon part of the transverse virtual photon ab- which for large N gives (negJ.ecting order I/~)Then the sum in (4) turns out to be convergent, provided the constant in (5) and (6) is chosen to be 1/2. Thus inserting (2) and (6) 2Generalizing to include the isoscalar parts and evaluating (7) The only free parameter introduced, o, which fixes the magnitude of the off-diagonal transitions, may now be determined fromfue normalization ( Although (II) may easily be evaluated numerically from the tables for 1/J (z), it is advantageous to give a much simp lac formula for oT' which for A = 2 approximates (II) extremely well, the error being at most 2% (around (13). (14) -6 -It is amusing to note that the simple pole formula (14) which is equivalent to(ll); had p~evi~u~~y'fgf be~n ~how~::tO'to de~c~ib~ extremely weilthe.•. Agreement of (II) and (14) •· are substantially unchanged.From our Ansatz (5), we note that diffraction dissociation, as exemplified by a single, effective off-diagonal term parametrized with CN, increases with N, becoming a constant fraction of the elastic reaction. This feature seems a necessary one for convergence and scaling. We have checked that a constant, N independent CN gives a logarithmically divergent non-scaling expression except for the singular point CN = 1/2, for which case the result is convergent, but also non-scaling with a leading term proportional to (1/q 4 ) ln (q 2 tm 2 ).

No abstract

No abstract

No abstract

No abstract

No abstract

We investigate what can be learned from a purely phenomenological study of options prices without modelling assumptions. We fitted neural net (NN) models to LIFFE "ESX" European style FTSE 100 index options using daily data from 1992 to 1997. These non-parametric models reproduce the Black-Scholes (BS) analytic model in terms of fit and performance measures using just the usual five inputs (S, X, t, r, IV). We found that adding transaction costs (bid-ask spread) to these standard five parameters gives a comparable fit and performance. Tests show that the bid-ask spread can be a statistically significant explanatory variable for option prices. The difference in option prices between the models with transaction costs and those without ranges from about −3.0 to +1.5 index points, varying with maturity date. However, the difference depends on the moneyness (S/X), being greatest in-the-money. This suggests that use of a five-factor model can result in a pricing difference of up to £10 to £30 per call option contract compared with modelling under transaction costs. We found that the influence of transaction costs varied between different yearly subsets of the data. Open interest is also a significant explanatory variable, but volume is not.

Absrracf-This paper describes a generally applicable robust method for determining prediction intervals for models derived by non-linear regression. Hypothesis tests for bias are applied. The concept is demonstrated by application to a standard synthetic example, and is then applied to prediction intervals for a financial engineering example viz. option pricing using data from LlFFE for 'ESX' European style options on the FTSE 100 index. Unbiased estimates of the standard error are obtained. The method uses standard regression procedures to determine local error bars and avoids programming special architectures. It is appropriate for target data with non-constant variance.