# Symmetric Power law or Pareto distribution

Also known as Pareto-distribution

P(X>x) = Kx^(-α)
where P(X>x) is the probability of exceeding a variable x
and α is the asymptotic power law exponent for x large enough


What would be its symmetric form for modelling the stock price change? Would it be just the same mirror on the other side?

Or would it be two different distributions glued together? (one for + side and another for - side of price change) because stocks tends to go up more than down. Like in picture below, probability for changing of current stock price of 100\$.

• Looks a little like Kou's double exponential jump diffusion (albeit with exponential driving the amplitude, not the pareto) – James Spencer-Lavan Dec 7 '19 at 11:12