Sustainability-valued discrete option pricing in complete markets

Abstract

ABSTRACT We consider option pricing using recombining binomial trees, with a two-fold purpose. The first is to introduce environmental, social and governance (ESG) sustainability valuation into option pricing. We explore this in a number of scenarios, including enhancement of yield due to trader information and the impact of the past history of a market driver. The second is to emphasize the use of discrete dynamic pricing, rather than continuum models, as the natural model that governs actual market practice. Furthermore, use of continuous, rather than discrete, compounding (e.g. of the risk-free rate) in discrete option pricing models violates conditions of the fundamental theorem of asset pricing and no-arbitrage. By considering models based upon both compounding methods, we show explicitly where this violation occurs and demonstrate computational differences that arise as a result.