Analytic Pricing of SOFR Futures Contracts with Smile and Skew

Paper: arXiv 2401.15728

Authors: Aurelio Romero-Bermúdez, Colin Turfus

Abstract

We introduce a perturbative formalism to solve the backward-looking futures pricing problem. The formalism is based on a time-ordered exponential series which allows to derive the functional form of the integral kernel associated to the backward-Kolmogorov diffusion PDE. We present an analytic pricing formula for SOFR futures contracts under an extension of the Hull-White model which incorporates not only the intrinsic convexity adjustments captured by Mercurio [2018], but also the skew and smile observed in options markets as done in Turfus and Romero-Bermúdez [2023].

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated mathematical framework using a perturbative formalism and time-ordered exponential series to address SOFR futures pricing with smile and skew. However, as a purely theoretical derivation expanding on Hull-White extensions, it lacks empirical validation, backtesting, or market data fitting.

Research Flowchart

  flowchart TD
    A["Research Goal: Price SOFR Futures with Convexity, Smile, and Skew"] --> B["Inputs: Hull-White Model + Options Market Smile/Skew"]
    B --> C["Formulate Backward-Kolmogorov Diffusion PDE"]
    C --> D["Apply Perturbative Formalism via Time-Ordered Exponential Series"]
    D --> E["Derive Integral Kernel Functional Form"]
    E --> F["Outcome: Analytic Pricing Formula for SOFR Futures"]