Black Scholes with Fewer Assumptions - Economics and Finance
Speakers: Dean Buckner (email@example.com) is the founder of The Eumaeus Project and Kevin Dowd (firstname.lastname@example.org) is a professor of finance and economics at Durham University Business School, Durham University.
This paper provides a new derivation of the Black-Scholes-Merton option pricing formula that relies on fewer assumptions than were made in their original article. The unnecessary conditions include some that are commonly believed to be essential to the formula, such as a log-normal stock price, no arbitrage and Ito’s Lemma. Our more parsimonious derivation reveals that the formula is valid for any of a number of non-log-normal stock price processes. It resolves several problematic implications of the original derivation, helps to explain the ‘holes in Black Scholes’ paradox and raises questions about the logic of risk-neutral valuation methodology. It also has major practical implications. Amongst these, it provides for rational valuations in situations where options markets are incomplete or non-existent, for ‘fair value’ valuations in a normative accounting sense and for ‘market consistent’ valuations as that term is used in actuarial science. It also provides for a radical overhaul of the way in which option valuation and pricing can be taught.