Masoliver, Jaume, 1951-Montero Torralbo, MiquelPorrà i Rovira, Josep Maria2018-01-252018-01-2520000378-4371https://hdl.handle.net/2445/119287High-frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well established by empirical evidence. Specifically, probability distributions have the following properties: (i) They are not Gaussian and their center is well adjusted by Lévy distributions. (ii) They are long-tailed but have finite moments of any order. (iii) They are self-similar on many time scales. Finally, (iv) at small time scales, price volatility follows a non-diffusive behavior. We extend Merton's ideas on speculative price formation and present a dynamical model resulting in a characteristic function that explains in a natural way all of the above features. The knowledge of such a distribution opens a new and useful way of quantifying financial risk. The results of the model agree - with high degree of accuracy - with empirical data taken from historical records of the Standard & Poor's 500 cash index.9 p.application/pdfeng(c) Elsevier B.V., 2000Distribució (Teoria de la probabilitat)Models matemàticsDistribution (Probability theory)Mathematical modelsinfo:eu-repo/semantics/article1529312018-01-25info:eu-repo/semantics/openAccess