Paper: arXiv 2508.02691

Authors: Teemu Pennanen, Waleed Taoum

Abstract

SOFR derivatives market remains illiquid and incomplete so it is not amenable to classical risk-neutral term structure models which are based on the assumption of perfect liquidity and completeness. This paper develops a statistical SOFR term structure model that is well-suited for risk management and derivatives pricing within the incomplete markets paradigm. The model incorporates relevant macroeconomic factors that drive central bank policy rates which, in turn, cause jumps often observed in the SOFR rates. The model is easy to calibrate to historical data, current market quotes, and the user’s views concerning the future development of the relevant macroeconomic factors. The model is well suited for large-scale simulations often required in risk management, portfolio optimization and indifference pricing of interest rate derivatives.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated statistical model with stochastic differential equations and macroeconomic factor integration, which requires advanced mathematical understanding. However, it lacks implementation details like code or backtests, focusing instead on theoretical calibration and simulation setups without empirical validation on real market data.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Develop statistical SOFR term structure model<br>for incomplete markets"] --> B{"Key Methodology"}
  B --> C["Incorporate macroeconomic factors<br>driving policy rates & jumps"]
  B --> D["Statistical modeling within<br>incomplete markets paradigm"]
  C --> E["Data & Inputs<br>Historical data, market quotes,<br>macroeconomic views"]
  D --> E
  E --> F["Computational Process<br>Calibration &<br>large-scale simulations"]
  F --> G["Key Outcomes<br>Risk management & derivatives pricing<br>for illiquid SOFR market"]

Cited References (219)

  1. Convex Stochastic Optimization (2024)
  2. Stochastic modeling of assets and liabilities with mortality risk (2021)
  3. Cashflow-driven investment beyond expectations
  4. Stochastic models of control and economic dynamics (1987)
  5. PRICING INDEX OPTIONS BY STATIC HEDGING UNDER FINITE LIQUIDITY (2018) — link
  6. Risk measures and efficient use of capital (2009)
  7. On El Karoui’s general theory of optimal stopping (2018) — link
  8. A DIFFUSION MODEL FOR ELECTRICITY PRICES (2002) — link
and 211 more
  1. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (2001)
  2. Reinforcement Learning and Optimal Control (2019)
  3. Indifference price with general semimartingales (2011)
  4. Duality and optimality conditions in stochastic optimization and mathematical finance (2018)
  5. Hedging of Defaultable Claims (2004)
  6. Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk (2007) — link
  7. An introductory approach to duality in optimal stochastic control (1978)
  8. Theory of constant proportion portfolio insurance (1992)
  9. Topological Vector Spaces and Their Applications (2017) — link
  10. Convex Optimization (2004)
  11. Dynamic portfolio selection by augmenting the asset space (Forthcoming)
  12. Prices of state-contingent claims implicit in option prices (1978)
  13. Indifference pricing: theory and applications (2009)
  14. Towards a theory of volatility trading (1998)
  15. Price formation in double auction markets (1996)
  16. Pricing options in an extended Black–Scholes economy with illiquidity: Theory and empirical evidence (2006)
  17. Monte Carlo methods for multi-stage stochastic programs (2003)
  18. A deterministic approach to stochastic optimal control with application to anticipative control (1992)
  19. Portfolio selection with transaction costs (1990)
  20. Hedging bounded claims with bounded outcomes (2006)
  21. Probabilities and potential (1978)
  22. Probabilities and potential. B (1982)
  23. A survey of electricity spot and futures price models for risk management applications (2021) — link
  24. Optimal replication of options with transactions costs and trading restrictions (1993)
  25. CASH SUBADDITIVE RISK MEASURES AND INTEREST RATE AMBIGUITY (2009)
  26. PORTFOLIOS OF AMERICAN OPTIONS UNDER GENERAL PREFERENCES: RESULTS AND COUNTEREXAMPLES (2014)
  27. Optimal replication of contingent claims under transaction costs (1989)
  28. OPTIMAL INVESTMENT WITH RANDOM ENDOWMENTS IN INCOMPLETE MARKETS (2004)
  29. ON UTILITY-BASED PRICING OF CONTINGENT CLAIMS IN INCOMPLETE MARKETS (2005)
  30. OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS (2008)
  31. An Adaptive Importance Sampling Technique (2006)
  32. Hedging of portfolio-valued claims under convex transaction costs and portfolio constraints (2009)
  33. Notes On The Theory Of Choice (1988)
  34. Validation analysis of mirror descent stochastic approximation method
  35. Principles of Financial Economics (2001)
  36. Integration with Respect to Finitely Additive Measures (1991)
  37. Asset pricing theory for two price economies (2014)
  38. The MOSEK optimization toolbox for MATLAB manual. Version 7.1 (Revision 28) (2015) — link
  39. Measuring Risk Beyond the Cash-additive Paradigm (2015)
  40. Topology (2000)
  41. Confidence level solutions for stochastic programming (2000)
  42. Incomplete markets (2019)
  43. A splitting method for stochastic programs (2006) — link
  44. Convex Integral Functionals of Processes of Bounded Variation (2018)
  45. Convex duality in optimal investment and contingent claim valuation in illiquid markets (2018) — link
  46. Topological duals of locally convex function spaces (2022)
  47. Optimal stopping without Snell envelopes (to appear)
  48. Dynamic programming in convex stochastic optimization (2022)
  49. Duality in convex stochastic optimization (2022)
  50. Dual solutions in convex stochastic optimization (2022)
  51. Existence of solutions in non-convex dynamic programming and optimal investment (2016) — link
  52. Multi-stage stochastic optimization applied to energy planning (1991) — link
  53. Arbitragefreiheit in \protect F inanzm "a rkten mit \protect T ransaktionskosten (2001)
  54. Introduction to Mathematical Finance: Discrete Time Models (1997)
  55. Measuring Risk for Income Streams (2005) — link
  56. The natural Banach space for version independent risk measures (2013) — link
  57. Dual problems of L agrange for arcs of bounded variation (1976)
  58. Pathwise Stochastic Optimal Control (2007) — link
  59. Lifetime Portfolio Selection By Dynamic Stochastic Programming (1969)
  60. Investments (1999)
  61. Market models beyond the standard setup (2015)
  62. When are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals? (1997)
  63. Optimization for Machine Learning (2011)
  64. Convex Optimization of Power Systems (2015)
  65. Continuous-Time Dynkin Games with Mixed Strategies (2002) — link
  66. Risk measure pricing and hedging in incomplete markets (2006)
  67. Macroeconomics and reality (1980)
  68. Money, real interest rates, and output: A reinterpretation of postwar US data (1983)
  69. The Federal Funds Rate and the Channels of Monetary Transnission (1990) — link
  70. Money, income, prices, and interest rates (1992)
  71. Systematic monetary policy and the effects of oil price shocks (1997)
  72. Estimation Results| RDP 1999-11: A Structural Vector Autoregression Model of Monetary Policy in Australia (1999)
  73. Board Of Governors Of The Federal Reserve System (2024)
  74. CME Rulebook - Chapter 460 - Three-Month SOFR Futures (2024)
  75. CME Rulebook - Chapter 461 - One-Month SOFR Futures (2024)
  76. CME Rulebook - Chapter 901 - Interest Rate Swaps Contract Terms (2024)
  77. CME Rulebook - Chapter 902 - Interest Rate Swaption Contract Terms (2024)
  78. CME Rulebook - Chapter 900 - Interest Rate Products (2024)
  79. OTC SOFR Swaps Clearing (2018)
  80. The economics of money, banking, and financial markets (2007)
  81. Introduction to convex optimization in financial markets (2012)
  82. Optimal investment and contingent claim valuation in illiquid markets (2014)
  83. Convex duality in optimal investment and contingent claim valuation in illiquid markets (2018)
  84. Incomplete markets, King’s College London , University of London (2020)
  85. Numerical and Computational Methods for Mathematical Finance, King’s College London , University of London (2020)
  86. Pricing index options by static hedging under finite liquidity (2018)
  87. Monte Carlo methods in finance (2002)
  88. Essentials of Monte Carlo simulation: Statistical methods for building simulation models (2012)
  89. Student’s t-Distribution and Related Stochastic Processes (2013)
  90. Simulation and Optimization in Finance: Modeling with MATLAB,@ RISK, or VBA (2010)
  91. Mean-variance analysis in portfolio choice and capital markets (2000)
  92. Convex analysis (1970)
  93. Variational analysis (2009)
  94. The pricing of options and corporate liabilities (1973)
  95. Mathematical methods in risk theory (2007)
  96. Indifference pricing: theory and applications (2008)
  97. Optimal replication of contingent claims under transaction costs (1989)
  98. Theory of games and economic behavior (commemorative edition) (2007)
  99. Stochastic finance: an introduction in discrete time (2011)
  100. Empirical evidence on Student-t log-returns of diversified world stock indices (2008)
  101. The MOSEK optimization toolbox for MATLAB manual. Version 8.1., 2017
  102. A tutorial on geometric programming (2007)
  103. Convex optimization (2004)
  104. Numerical methods and optimization in finance (2019)
  105. Mastering Python for Finance (2015)
  106. Calibrated option bounds (2005)
  107. Numerical methods for engineers (2010)
  108. Applied numerical methods (1969)
  109. MATLAB manual (2020)
  110. A modified regula falsi method for computing the root of an equation (1971)
  111. Probability: theory and examples (2019)
  112. Generalized Gaussian quadrature rules for systems of arbitrary functions (1996)
  113. Universal option valuation using quadrature methods (2003)
  114. The generalized Weierstrass approximation theorem (1948)
  115. Legendre-Gauss Quadrature Weights and Nodes (2020)
  116. Complete markets with discontinuous security price (1999)
  117. Frequently asked questions in option pricing theory (2005)
  118. The second fundamental theorem of asset pricing (1999)
  119. Non-arbitrage and the fundamental theorem of asset pricing: Summary of main results (1997)
  120. A partial introduction to financial asset pricing theory (2001)
  121. General arbitrage pricing model: I–probability approach (2007)
  122. Fundamental theorems of asset pricing for good deal bounds (2004)
  123. The second fundamental theorem of asset pricing: A new approach (1999)
  124. Hedging contingent claims on semimartingales (1999)
  125. Realized Volatility, Working Paper 2008-14 (2008)
  126. Spot convenience yield models for the energy markets (2004)
  127. ‘Maximal’Convenience Yield Model Implied by Commodity Futures (2001)
  128. Options, futures and other derivatives/John C. Hull. (2009)
  129. Towards a theory of volatility trading (2001)
  130. Indifference pricing of insurance contracts in a product space model: applications (2003)
  131. Utility indifference valuation for non-smooth payoffs with an application to power derivatives (2016)
  132. Methods of mathematical finance (1998)
  133. Pricing and hedging in incomplete markets (2001)
  134. A super-martingale property of the optimal portfolio process (2003)
  135. Optimal consumption from investment and random endowment in incomplete semimartingale markets (2003)
  136. Handbooks in operations research and management science: simulation (2006)
  137. A guided tour through quadratic hedging approaches. E. Jouini, J. Cvitanic, M. Musiela, eds., Option Pricing, Interest Rates and Risk Management (2001)
  138. Pricing via utility maximization and entropy (2000)
  139. Exponential hedging and entropic penalties (2002)
  140. Galerkin methods in dynamic stochastic programming (2010)
  141. Risk aversion in the small and in the large (1978)
  142. Conjugate duality and optimization (1974)
  143. Progress Report : The Transition from U.S. Dollar LIBOR , The Alternative Reference Rates Committee (2021)
  144. Additional Information about Reference Rates Administered by the New York Fed (2022)
  145. An Updated User’s Guide to SOFR , The Alternative Reference Rates Committee (2021)
  146. CME Group Announces First OTC SOFR Swaps Cleared , CME Group (2018)
  147. CME Group to Launch SOFR Options on January 6, 2020, CME Group (2019)
  148. CME Rulebook , CME Group (2019)
  149. Indicative Forward - Looking SOFR Term Rates , FEDS Notes. (2019)
  150. Inferring Term Rates from SOFR Futures Prices (2019)
  151. Stochastic modeling of assets and liabilities with mortality risk (2021)
  152. An analysis of transformations (1964)
  153. Applied regression analysis (1998)
  154. CVXPY : A P ython-embedded modeling language for convex optimization (2016)
  155. A rewriting system for convex optimization problems (2018)
  156. Python reference manual (1995)
  157. Introductory Lectures on Convex Optimization - A Basic Course (2004)
  158. Gradient methods for minimizing composite functions (2013)
  159. Interior-point polynomial algorithms in convex programming (1994)
  160. Cashflow-driven investment beyond expectations (2024)
  161. Federal Funds Target Range - Upper Limit [DFEDTARU]
  162. Federal Funds Target Range - Lower Limit [DFEDTARL]
  163. Overnight Reverse Repurchase Agreements Award Rate: Treasury Securities Sold by the Federal Reserve in the Temporary Open Market Operations [RRPONTSYAWARD] (2024)
  164. Effective Federal Funds Rate [EFFR] (2024)
  165. Secured Overnight Financing Rate [SOFR] (2024)
  166. Discretion versus policy rules in practice (1993)
  167. A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables (2003)
  168. Understanding IMM Index and Dates (2024)
  169. Mosek optimization suite (2019)
  170. Reverse Repo Counterparties (2025)
  171. Standing Repo Facility Counterparties (2025)
  172. Primer: Money Market Funds and the Repo Market , U.S. Securities and Exchange Commission (2021)
  173. US Repo Fact Sheet (2021)
  174. The macroeconomy and the yield curve: a dynamic latent factor approach (2006)
  175. LIBOR market model under the real-world measure (2013)
  176. A simple multi-curve model for pricing SOFR futures and other derivatives (2018)
  177. Looking forward to backward-looking rates: a modeling framework for term rates replacing LIBOR (2019)
  178. SOFR term structure dynamics—discontinuous short rates and stochastic volatility forward rates (2024)
  179. Short rate dynamics: A fed funds and SOFR perspective (2021) — link
  180. Caplet pricing in affine models for alternative risk-free rates (2023)
  181. Term structure modeling with overnight rates beyond stochastic continuity (2024)
  182. Linear-price term structure models (2013)
  183. Hedging in a HJM model (2010)
  184. Valuation and hedging of contingent claims in the HJM model with deterministic volatilities (1996)
  185. Term Structure Modeling of SOFR: Evaluating the Importance of Scheduled Jumps (2024)
  186. Dynamic term structure models for SOFR futures (2021)
  187. Markov representation of the Heath-Jarrow-Morton model (2001)
  188. Consistent yield curve prediction (2016)
  189. Pricing and hedging of SOFR derivatives (2021)
  190. Spike modeling for interest rate derivatives with an application to SOFR caplets (2020)
  191. Bond yields and the Federal Reserve (2005)
  192. What drives jumps in the secured Overnight Financing Rate? Evidence from the arbitrage-free Nelson–Siegel model with jump diffusion (2024)
  193. A characterization of hedging portfolios for interest rate contingent claims (2004) — link
  194. Parsimonious modeling of yield curves (1987)
  195. The market model of interest rate dynamics (1997)
  196. Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation (1992)
  197. On incompleteness of bond markets with infinite number of random factors (2011) — link
  198. Forecasting the term structure of government bond yields (2006) — link
  199. Towards a general theory of bond markets (1997)
  200. Expected and Unexpected Jumps in the Overnight Rate: Consistent Management of the Libor Transition (2022) — link
  201. Pricing interest-rate-derivative securities (1990)
  202. An equilibrium characterization of the term structure (1977)
  203. Time series and cross-section information in affine term-structure models (2000)
  204. Zero-coupon yield curves: technical documentation (2005)
  205. New techniques to extract market expectations from financial instruments (1997)
  206. Estimating and interpreting forward interest rates: Sweden 1992-1994 (1994)
  207. The great moderation of the term structure of UK interest rates (2009)
  208. Forecasting the term structures of Treasury and corporate yields using dynamic Nelson-Siegel models (2011)
  209. An affine macro-finance term structure model for the euro area (2008)
  210. Forecasting the term structure of interest rates with dynamic constrained smoothing b-splines (2020)
  211. Market price of risk specifications for affine models: Theory and evidence (2007)

0 of 219 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.