Statistics of Price Level Excursions (Normal, Student and Asymmetric Laplace Processes)

• Various statistics of future price level excursions are driving decision making of both sophisticated and amateur traders, although the latter are not necessarily aware of it. Such statistics are of paramount importance in intelligent placement of limit orders and monitoring their performance in time.• The random walk paradigm for independent logarithmic returns, i.e. with Brownian motion autocorrelation structure, is widely accepted in the literature and numerous applications. However, this well-known paradigm assumes that independent returns are Gaussian distributed – quite an unrealistic assumption. In reality, fat-tailed and symmetric probability density functions are substantially better for modeling distribution of returns. • In this research paper we present results for three different paradigms for returns distributions: Gaussian (no fat tails, symmetric), Student (fat tails, symmetric) and Asymmetric Laplace (fat tails, asymmetric) with the last one most relevant for real-life applications. • Statistics of price level excursions in the case of independent Gaussian distributed returns can be found in the literature. The same statistics are not available in the open literature for the cases when independent returns are Student or Asymmetric Laplace distributed. • Monte Carlo simulations for all relevant statistics of price level excursions are reported. In general, Monte Carlo simulations provide clear evidence that our underlying analytical results are correct. However, in extreme cases these simulations exhibit limitations of accuracy of Monte Carlo simulation