Models used to generate the true stochastic interest rate generating process by using real market data
Arbitrage Free Term Structure Models (also known as No-Arbitrage Models) are used to generate the true stochastic interest rate generating process by using realmarket dataDow Jones Industrial Average (DJIA)The Dow Jones Industrial Average (DJIA), also commonly referred to as the Dow Jones or simply the Dow, is one of the most popular and widely-recognized stock market indices. Unlikeequilibrium term structure modelsEquilibrium Term Structure ModelsEquilibrium Term Structure Models (also known as Affine Term Structure Models) are stochastic interest rate models used to estimate the correct theoretical, which make certain assumptions about the trueinterest rateInterest RateAn interest rate refers to the amount charged by a lender to a borrower for any form of debt given, generally expressed as a percentage of the principal. The asset borrowed can be in the form of cash, large assets such as vehicle or building, or just consumer goods.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 trueinterest rateInterest RateAn interest rate refers to the amount charged by a lender to a borrower for any form of debt given, generally expressed as a percentage of the principal. The asset borrowed can be in the form of cash, large assets such as vehicle or building, or just consumer goods.generating process.
Arbitrage free term structure models are less theoretical models and are 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 models usually describe the interest rate process as a function of constantparametersParameterA parameter is a useful component of statistical analysis. It refers to the characteristics that are used to define a given population. It is used to. The accuracy of the data fitting exercise increases with the number of parameters and in general, the following result holds in the population:
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 Ho-Lee Model was the first arbitrage free term structure model. It was introduced by Thomas Ho and Sang Bin Lee in their 1986 paper,Term Structure Movements and Pricing Interest Rate Contingent Claims.The Ho-Lee Model parameterizes the term structure using only two parameters:
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