Models used to generate the true stochastic interest rate generating process by using real market data
Over 1.8 million professionals use CFI to learn accounting, financial analysis, modeling and more. Start with a free account to explore 20+ always-free courses and hundreds of finance templates and cheat sheets.
Arbitrage Free Term Structure Models (also known as No-Arbitrage Models) are used to generate the true stochastic interest rate generating process by using real market data. Unlike equilibrium term structure models, which make certain assumptions about the true interest rate generating process to determine the correct theoretical term structure, arbitrage free term structure models use the actual term structure (known as the realized term structure) to estimate the true interest rate generating process.
Arbitrage free term structure models are less theoretical models and more exercises in data fitting. They are known as arbitrage-free because they work under the assumption that the market term structure is correct and that there are no opportunities for arbitrage.
Arbitrage Free Term Structure Model Parameters
Arbitrage free term structure models usually describe the interest rate process as a function of constant parameters. The accuracy of the data fitting exercise increases with the number of parameters and in general, the following result holds in the population:
y is the true description of the term structure
While working with sample data, an arbitrage free term structure model can be made to fit the data exactly by using as many constant parameters as data points. In practice, a small number of constant parameters are usually enough to provide a good approximation of the term structure. A subtle and often overlooked property of arbitrage free term structure models is that numerically solving the stochastic process generated by an arbitrage free model will always necessarily yield the term structure as output.
Mathematically, it implies that the data fitting exercise behind arbitrage free models is, in some sense, one-to-one mappings. The result, which some consider purely definitional, drastically reduces the time needed to solve the models using numerical optimization techniques.
The standard deviation of the short-term interest rate.
The term premium of the short-term interest rate.
CFI is the official provider of the global Financial Modeling & Valuation Analyst (FMVA)™ certification program, designed to help anyone become a world-class financial analyst. To keep learning and advancing your career, the additional CFI resources below will be useful:
Take your learning and productivity to the next level with our Premium Templates.
Upgrading to a paid membership gives you access to our extensive collection of plug-and-play Templates designed to power your performance—as well as CFI's full course catalog and accredited Certification Programs.
Already have a Self-Study or Full-Immersion membership? Log in
Access Exclusive Templates
Gain unlimited access to more than 250 productivity Templates, CFI's full course catalog and accredited Certification Programs, hundreds of resources, expert reviews and support, the chance to work with real-world finance and research tools, and more.