Profitable forecast of prices of stock options on real market data via the solution of an ill-posed problem for the Black-Scholes equation

TL;DR

This paper introduces a novel regularized approach to solve an ill-posed Black-Scholes equation for option pricing, demonstrating profitability on real market data and proposing a new trading strategy.

Contribution

It presents a new mathematical model with reversed time Black-Scholes equation and regularization, avoiding traditional maturity and strike price notions.

Findings

Method is profitable on tested options

Regularization effectively solves ill-posed problem

Potential for significant profits in large-scale trading

Abstract

A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. This idea is verified on real market data for twenty liquid options. A trading strategy is proposed. This strategy indicates that our method is profitable on at least those twenty options. We conjecture that our method might lead to significant profits of those financial institutions which trade large amounts of options. We caution, however, that detailed further studies are necessary to verify this conjecture.