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.