In Black-Scholes delta-hedging method generalization, a "mirror-diffusion" inverse stochastic process is introduced with condition determined by the underlying price variance and payoff function. The process reduces an expected option value at maturity under equivalent martingale measure back to the current time. The normalized ksi-returns , correspondent to the kernel function in the found general solution and not dependent explicitly on time, were used for verification of the one-parameter model inherent efficiency, i.e. self-calibration using only historical volatility data. The model minimizes implied volatility bias (for 2004-2007 S& P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives. It allows increasing the number of stock price distribution parameters.
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.
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In Black-Scholes delta-hedging method generalization, a "mirror-diffusion" inverse stochastic process is introduced with condition determined by the underlying price variance and payoff function. The process reduces an expected option
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
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under
of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an
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back to the current time. The normalized ksi-returns
is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution
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kernel function in the
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and not dependent explicitly on time, were used for verification of the one-parameter model inherent efficiency, i.e. self-calibration using only historical volatility data. The model minimizes implied volatility bias (for
of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered
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P100 index options) and
P 100 index data. The model
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The method
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stock price
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