The impact of compounding on bond pricing with alternative reference rates

Dario Cziráky and Ana Ponikvar

Abstract

Alternative reference rates (ARRs) such as the Secured Overnight Financing Rate and the Sterling Overnight Interbank Average do not satisfy the assumptions of standard short-rate diffusion models, which are suitable for modeling interest rate processes with constant volatility without jumps. However, the overnight rate, which is characterized by stochastic volatility and jumps, would not often be used directly in pricing, and instead some sort of compounding will be done to arrive at the commonly used tenors (eg, one week to six months for most standard products). It is often argued that once the ARRs are compounded the resulting rate will become smoother with less pronounced jumps, and hence the currently implemented diffusion models might still be suitable after the model parameters are recalibrated to the newly constructed term rates, ie, compounded overnight ARRs. We looked at the impact of compounding on zero-coupon bond prices by considering the short rate when it follows a Gaussian diffusion process or a stochastic volatility jump-diffusion process. We find that, despite highly volatile and jumpy behavior of the overnight ARRs, pricing with compounded rates from one week to one year using simple Gaussian short-rate models leads to negligible bias. However, it does increase slightly with the pricing tenor. This was found to be the case when we compounded Gaussian processes, but the results for stochastic volatility with jump processes were similar.