Sustainability arbitrage pricing of ESG derivatives

Abstract

This study aims to propose a new model of ESG derivative pricing by introducing a new concept of sustainability arbitrage arising from ES components vertical to market risk and examine the model’s usefulness in practice by focusing on the mean-reverting properties of ESG asset prices. The ESG derivative pricing model, an extension of good-deal bounds (GDB) in an incomplete market, can overcome the arbitrariness of setting the exogenous Sharpe ratio necessary for the GDBs. The empirical studies using ESG indices of S&P, MSCI, and STOXX demonstrate that the price boundaries from sustainability arbitrage pricing of ESG futures and call options are much tighter than those from the original good-deal bounds with twice the Sharpe ratio, which is the maximum of any portfolio performance as assumed in Ross (1976) and which Shanken (1992) calls “approximate arbitrage.” Sustainability arbitrage pricing generates relatively tight price boundaries consistent with sustainable concepts. Then, empirical studies find the long-term mean of ESG indices strongly affects ES risk premiums in sustainability arbitrage pricing. The results confirm the importance of mean-reversion of ESG indices in ESG derivative pricing. Sustainability arbitrage pricing produces a positive relationship between economic and ESG value, symmetric information holding of ES risk between buyers and sellers, and reasonable upper limits in ES risk premiums. These three features of the ES risk premium may prove that sustainability arbitrage pricing is valid for ESG derivative pricing in practice. Finally, we discuss the validities of the proposed models and empirical studies using an econometric analysis, model parameter estimation using more recent extended data, and a sensitivity analysis of strike prices to call option prices.