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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.
For example, for bond options [3] the underlying is a bond, but the source of uncertainty is the annualized interest rate (i.e. the short rate). Here, for each randomly generated yield curve we observe a different resultant bond price on the option's exercise date; this bond price is then the input for the determination of the option's payoff.
For both of these reasons, models such as Black–Derman–Toy (lognormal and mean reverting) and Hull–White (mean reverting with lognormal variant available) are often preferred. [ 1 ] : 385 The Kalotay–Williams–Fabozzi model is a lognormal analogue to the Ho–Lee model, although is less widely used than the latter two.
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. This is because at very high levels they would hamper economic activity, prompting a decrease in ...
The parameter corresponds to the speed of adjustment to the mean , and to volatility. The drift factor, a ( b − r t ) {\displaystyle a(b-r_{t})} , is exactly the same as in the Vasicek model. It ensures mean reversion of the interest rate towards the long run value b {\displaystyle b} , with speed of adjustment governed by the strictly ...
ARMA is appropriate when a system is a function of a series of unobserved shocks (the MA or moving average part) as well as its own behavior. For example, stock prices may be shocked by fundamental information as well as exhibiting technical trending and mean-reversion effects due to market participants. [citation needed]
In equation (2), g is the mean reversion rate (gravity), which pulls the variance to its long term mean , and is the volatility of the volatility σ(t). dz(t) is the standard Brownian motion, i.e. () =, is i.i.d., in particular is a random drawing from a standardized normal distribution n~(0,1).
This says that reversion to the mean has occurred when t1's radius (distance from mean) is less than t0's radius. For my earlier example with 39, 87, 49.5, mean reversion *HAS NOT OCCURRED*. It seems clear that "mean reversion" does not hold for a uniform distribution. Any previous outcomes regarding radii do not affect the next outcome.