In the dynamic world of financial markets, prices assets can exhibit dramatic fluctuations, sometimes soaring to dizzying heights or plummeting alarming lows. However, amidst chaos, a fascinating phenomenon emerges: tendency for revert back their long-term average mean level. This concept known as reversion has intrigued traders, investors, and researchers decades. Understanding provides valuab...

Abstract This paper deals with the analysis of statistical properties profitability yielded by Private Equity from a fractionally integrated viewpoint. Using quarterly data 1981q2 to 2021q3, results support hypothesis stationarity and mean reversion in all cases; however, we observe differences degree persistence across regions, Europe being closest short memory while US shows highest long rang...

Received wisdom: industrial-country floating exchange rates contain unit roots. In three types of tests, however, the data support nominal-rate mean reversion. First, SUR tests on panels of Group-of-Ten nominal rates frequently reject the null of unit roots in favor of mean reversion for various samples over the current float, the first such results in the literature. Second, in out-of-sample f...

We carry out a Monte-Carlo simulation of a standard portfolio management strategy involving derivatives, to estimate the sensitivity of its downside risk to a change of mean-reversion of the underlyings. We find that the higher the intensity of mean-reversion, the lower the probability of reaching a pre-determined loss level. This phenomenon appears of large statistical significance for large e...

In this paper we examine a control variate estimator for quantity that can be expressed as the expectation of functional random process, is itself solution differential equation driven by fast mean-reverting ergodic forces. The same limit diffusion process approximates original when mean-reversion time goes to zero. To get an efficient estimator, propose coupling method build and process. We sh...