Spike Modeling for Interest Rate Derivatives with an Application to SOFR Caplets

Abstract

With the forthcoming introduction of SOFR benchmark rates in the US, market participants will need to adjust their interest rate option models to accommodate a variety of idiosyncrasies of the SOFR rate. The materiality of these changes for quoted options level is currently unknown, and will depend on market sentiment (as expressed in market risk premia, say), regulatory policies, and the rate fixing conventions ultimately available in the market. While we wait for liquidity in SOFR options to build, this paper pre-emptively considers two important characteristics of SOFR derivatives: the backward-looking settlement style of SOFR floating rate payments; and the “jagged” nature of SOFR evolution through time. The latter originates with liquidity conditions in the repo financing markets from which SOFR is constructed, where temporary demand-supply imbalances can result in the formation of short-term spikes of substantial magnitude. We construct a variety of mechanisms that allows us to build rich stochastic models for both “surprising” and anticipated (e.g., year-end) spikes, and demonstrate how to modify existing (smooth) term structure models to capture them. To accommodate high-efficiency pricing of vanilla derivatives in top-down models, we also develop several convenient numerical techniques that allow for effcient pricing of these structures. For instance, a novel scheme merges existing spike-free pricing formulas with a given spike characteristic function in a custom low-dimensional quadrature routine, enabling us to spike-enable standard valuation models (such as SABR) at minimal computational effort. Using SOFR-style caplets for illustration, we numerically demonstrate that the effect of spikes on implied caplet volatility levels and skews can be substantial, even at modest levels of risk premia in the spike model parameters. Besides being useful for the pricing of SOFR derivatives, our paper more broadly establishes a complete mathematical framework for rate spikes, applicable to pricing, scenario generation, and risk management in any rates market where spike phenomena exist.