Optimal Pricing and Hedging of SOFR Derivatives

Abstract

Thousands of SOFR derivatives are available in exchanges and OTC, but the market remains illiquid and incomplete. Such a market is beyond the scope of classic risk-neutral approaches that imply linear pricing rules and, at best, approximate hedging strategies whose hedging error may be difficult to quantify. This paper develops an indifference pricing model which is consistent with observed derivative quotes, the agent's financial position and views about the uncertain future as well as risk preferences as described by a convex risk measure. In addition to prices and hedging strategies, the model gives an explicit description of the hedging error and the associated risk. The approach is illustrated numerically using hundreds of CME-listed derivatives to price and hedge unreplicable OTC SOFR derivatives. The indifference prices are computed in less than a minute on a regular PC. We find that the optimal hedging portfolios tend to be sparse but still provide good approximations of the derivative payouts.