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By M. Borowiecki, J.W. Kennedy, M.M. Syslo

ISBN-10: 3540126872

ISBN-13: 9783540126874

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Term structure models are specific applications of term structure theory. The joint stochastic process is driven by sources of uncertainty. For continuous processes, the sources of uncertainty are often specified as Wiener processes. If the evolution of the yield curve can be represented by Markovian state variables, these variables are called factors. A general theory of one-factor term structure models is given in the 1977 paper “An Equilibrium Characterization of the Term Structure” (Chapter 6).

This produces estimates of the discount function as a continuous function of time. For cubic or higher order splines, the forward rates are a smooth function. Since the model is linear in the discount function, ordinary least-squares regression techniques can be used. In addressing the effect of taxation, McCulloch [1975a] estimates the after-tax term structure of interest rates and the marginal income tax rate. Estimates of the tax rate were achieved by minimizing the standard error of the regression.

It was a completely nonanalytical approach, based on the relationship with the client and on experience. We proposed that the stock market in effect does all that—that it’s the aggregate judgment of hundreds of thousands of investors, with the bottom line of their evaluation expressed as the price at which they’re willing to buy and sell the stock. If we could succeed in extracting the information from the stock and converting it to the valuation of the credit, we’d capitalize on all this information.

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Graph Theory by M. Borowiecki, J.W. Kennedy, M.M. Syslo


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