• 1 Introduction
  • 2 First theoretical estimates
  • 2.1 Bachelier model
  • 2.2 Black-Scholes model
  • 3 Empirical estimation and the \large quotientpuzzle"
  • 3.1 Methods
  • 3.2 Data
  • 3.3 Empirical measurements of historical barrier quotients
  • 4 How to solve the puzzle?
  • 5 Barrier probabilities as a model benchmark
  • 5.1 Historical probability as a benchmark
  • 5.2 Independent probability as benchmark
  • 6 Conclusions
  • Acknowledgements
  • References