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Vasicek's model was the first one to capture mean reversion, an essential characteristic of the interest rate that sets it apart from other financial prices.Thus, as opposed to stock prices for instance, interest rates cannot rise indefinitely.
The Wikipedia article on "Regression toward the Mean" gives a different definition of mean reversion in finance: "In finance, the term mean reversion has a different meaning. Jeremy Siegel uses it to describe a financial time series in which "returns can be very unstable in the short run but very stable in the long run."
Mean reversion is a financial term for the assumption that an asset's price will tend to converge to the average price over time. [1] [2] Using mean reversion as a timing strategy involves both the identification of the trading range for a security and the computation of the average price using quantitative methods.
It ensures mean reversion of the interest rate towards the long run value , with speed of adjustment governed by the strictly positive parameter . The standard deviation factor, σ r t {\displaystyle \sigma {\sqrt {r_{t}}}} , avoids the possibility of negative interest rates for all positive values of a {\displaystyle a} and b {\displaystyle b} .
With a fixed-rate product, such as a personal loan or savings account, the interest rate you sign up for is the interest rate you’ll either pay or earn for the life of the product.
John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative Analysis, Vol 28, No 2, (June 1993) pp. 235–254. John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) pp. 573–592.
The biggest difference: A fixed-rate mortgage carries the same interest rate for the life of the loan, while adjustable-rate mortgage’s interest changes at set intervals (after a fixed-rate ...
The future interest of C is not certain, thus it is "defeasible". Additionally, the interest cannot become smaller by the addition of more remainder owners, thus it is not "open". The identifying component is the possibility of being divested by D who owns an executory interest from the remainder if C becomes a lawyer. [7]