A Mirror-Diffusion Model of Options
Pricing
Pavel Levin, Department of Physics,
St. John’s College of Liberal Arts and Sciences
Abstract: 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 ?-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.