Mirror-time diffusion discount model of options pricing
  The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an equivalent martingale measure is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution, correspondent to the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S&P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives. The method allows increasing the number of asset price probability distribution parameters. 
Pavel Levin