The Pivotal Roles of Supply and Demand in Option-Pricing: The Reality Beyond Black-Scholes

For at least the past several decades (and arguably much of the past century), our understanding of the dynamics of option pricing has centered almost entirely on either the implied volatility surface or upon stochastic volatility models, both of which are predicated upon the Black-Scholes-Merton (BSM) assumptions regarding the stochastic process governing the underlying and the resulting equilibrium dynamics. However, existing approaches to calibrate these models and their variants for even a single underlying asset run into the serious empirical contradictions presented by the implied volatility skew/smile.

Nevertheless, BSM rests upon a fairly rigorous foundation, and it is difficult even for detractors to deny the equilibrium principles that underly the framework, if for no other reason than put-call parity. Nevertheless, the skew has persistently presented theorists and practitioners with a serious and unyielding puzzle since the advent of options contracts themselves. One problem we identify is that many actors, because of taxation, portfolio size, and other factors, do not hold completely liquid portfolios. We show here that, as a result, BSM is in fact an incomplete partial equilibrium framework. Within this framework, skew dynamics arise from heterogeneous agents who inhabit the market. Our model extends the BSM approach to develop an extended equilibrium theory that better explains the skew. This finding is supported both by a theoretical proof and by our discovery that price chart patterns do have direct effects on the price of options. This latter observation is in part an extension of the admirable work of MIT's Andrew Lo regarding technical analysis.

In our model, delta hedgers act as ‘insurance agents,’ who allow for increased risk-taking on the part of major firms with larger, less liquid portfolios. This has direct policy implications with respect to short sale bans, the severity of the great stock crash of 2008, and the real positive value that options markets provide as an institution.

Perhaps most importantly, our work indicates that the current deltas produced by the BSM model are not correct and therefore can lead to imperfect delta hedging. As a result, some market-makers and participants are exposed to considerably more risk around technical barriers than the current BSM model would indicate.

These findings are supported by a proof that substantially extends the classic Black-Scholes-Merton derivation. Additionally, a year's worth of index options prices on the S&P 500 are analyzed in the context of our model, in order to show the real world effects and practical implications of our theoretical proof. To the best of our knowledge, our finding is the first of its kind, as market data has heretofore created an irreducible identification problem in the literature.