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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.
The technique applied then, is (1) to generate a large number of possible, but random, price paths for the underlying (or underlyings) via simulation, and (2) to then calculate the associated exercise value (i.e. "payoff") of the option for each path. (3) These payoffs are then averaged and (4) discounted to today.
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 ...
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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 ...
Under general equilibrium theory prices are determined through market pricing by supply and demand. [6] Here asset prices jointly satisfy the requirement that the quantities of each asset supplied and the quantities demanded must be equal at that price - so called market clearing.
[The formula does not make clear over what the summation is done. P C = 1 n ⋅ ∑ p t p 0 {\displaystyle P_{C}={\frac {1}{n}}\cdot \sum {\frac {p_{t}}{p_{0}}}} On 17 August 2012 the BBC Radio 4 program More or Less [ 3 ] noted that the Carli index, used in part in the British retail price index , has a built-in bias towards recording ...