Interest Rates

Statistical modeling of SOFR term structure ArXiv ID: 2508.02691 “View on arXiv” 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. ...

An Accurate Discretized Approach to Parameter Estimation in the CKLS Model via the CIR Framework ArXiv ID: 2507.10041 “View on arXiv” Authors: Sourojyoti Barick Abstract This paper provides insight into the estimation and asymptotic behavior of parameters in interest rate models, focusing primarily on the Cox-Ingersoll-Ross (CIR) process and its extension – the more general Chan-Karolyi-Longstaff-Sanders (CKLS) framework ($α\in[“0.5,1”]$). The CIR process is widely used in modeling interest rates which possess the mean reverting feature. An Extension of CIR model, CKLS model serves as a foundational case for analyzing more complex dynamics. We employ Euler-Maruyama discretization to transform the continuous-time stochastic differential equations (SDEs) of these models into a discretized form that facilitates efficient simulation and estimation of parameters using linear regression techniques. We established the strong consistency and asymptotic normality of the estimators for the drift and volatility parameters, providing a theoretical underpinning for the parameter estimation process. Additionally, we explore the boundary behavior of these models, particularly in the context of unattainability at zero and infinity, by examining the scale and speed density functions associated with generalized SDEs involving polynomial drift and diffusion terms. Furthermore, we derive sufficient conditions for the existence of a stationary distribution within the CKLS framework and the corresponding stationary density function; and discuss its dependence on model parameters for $α\in[“0.5,1”]$. ...

A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing ArXiv ID: 2408.02064 “View on arXiv” Authors: Unknown Abstract We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [“Phys. Rev. Lett. 55, 912 (1985)”] and Feynman and Kleinert [“Phys. Rev. A 34, 5080 (1986)”] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach makes it a viable alternative to fully-numerical schemes for a variety of applications in derivatives pricing. ...

The Mean Field Market Model Revisited ArXiv ID: 2402.10215 “View on arXiv” Authors: Unknown Abstract In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial feature of controlling the term rate’s variances over large time horizons. This maintains the market model’s practicability, since calibrations and simulations can be carried out efficiently without nested simulations. In addition, we show that our framework can be directly applied to model term rates derived from SOFR, ESTR or other nearly risk-free overnight short-term rates – a crucial feature since many IBOR rates are gradually being replaced. These results are complemented by a calibration study and some theoretical arguments which allow to estimate the probability of unrealistically high rates in the presented market models. ...

The Impact Of Interest Rates On Firms Financial Decisions ArXiv ID: 2311.14738 “View on arXiv” Authors: Unknown Abstract Financial decisions are the decisions that managers take with regard to the finances of a company. This article aims to examine and explain the effect of interest rates on economic and financial decisions such as investment, funding, and dividend in a firm. This research uses the correlation coefficient analysis methods and descriptive methods to illustrate the relationship between interest rates and financial decisions. The data used in this research was obtained from several government reports and leading economic sources. The results of this research show that interest rates have a negatively insignificant effect on investment and funding decisions, but positively moderate effect on dividend decisions. ...

Using Monte Carlo Methods for Retirement Simulations ArXiv ID: 2306.16563 “View on arXiv” Authors: Unknown Abstract Retirement prediction helps individuals and institutions make informed financial, lifestyle, and workforce decisions based on estimated retirement portfolios. This paper attempts to predict retirement using Monte Carlo simulations, allowing one to probabilistically account for a range of possibilities. The authors propose a model to predict the values of the investment accounts IRA and 401(k) through the simulation of inflation rates, interest rates, and other pertinent factors. They provide a user case study to discuss the implications of the proposed model. ...

The Age of Reason: Financial Decisions Over the Lifecycle ArXiv ID: ssrn-1293139 “View on arXiv” Authors: Unknown Abstract The sophistication of financial decisions varies with age: middle-aged adults borrow at lower interest rates and pay fewer fees compared to both younger and old Keywords: Household Debt, Interest Rates, Credit Markets, Life-Cycle Finance, Consumer Credit Complexity vs Empirical Score Math Complexity: 3.0/10 Empirical Rigor: 7.0/10 Quadrant: Street Traders Why: The paper uses standard econometric regression techniques to analyze large-scale financial datasets (mortgages, credit cards, etc.), which involves data processing and implementation, but the mathematical models are primarily descriptive statistics and linear regressions without heavy theoretical derivations. flowchart TD A["Research Goal:<br/>How does age influence<br/>sophistication of financial decisions?"] B["Methodology:<br/>Analysis of Household<br/>Credit Survey Data"] C["Data: Loan terms,<br/>interest rates, fees<br/>across age groups"] D["Computation:<br/>Regression & statistical<br/>comparison of outcomes"] E["Key Finding 1:<br/>Middle-aged adults<br/>secure lower interest rates"] F["Key Finding 2:<br/>Middle-aged adults<br/>pay fewer fees"] G["Conclusion:<br/>Financial decision<br/>sophistication peaks<br/>in middle age"] A --> B B --> C C --> D D --> E D --> F E --> G F --> G