Generalized Hyperbolic Distributions and Brazilian Data

Abstract

The aim of this paper is to discuss the use of the Generalized Hyperbolic Distributions to fit Brazilian assets returns. Selected subclasses are compared regarding goodness of fit statistics and distances. Empirical results show that these distributions fit data well. Then we show how to use these distributions in value at risk estimation and derivative price computation.

A new factor to explain implied volatility smirk

“…The Market Symmetry parameter (β) was estimated for two particular processes: the normal inverse Gaussian (NIG) and the generalized hyperbolic (GH) process, we made this choice since these models have shown a very good fit with financial returns, see Eberlein and Prause (2002) and Fajardo and Farias (2004). Also, two spans for the daily return (2 and 5 years) were considered.…”

Duality and Symmetry with Time-Changed Lévy Processes

“…For more examples and details on Lévy processes, see Cont and Tankov (2004). We also refer the reader to Fajardo and Mordecki (2006b) and Fajardo and Farias (2004) for applications of Lévy processes to Brazilian data.…”

On European and Asian option pricing in the generalized hyperbolic model

“…There are also many non-Gaussian market models, as the hyperbolic model ( [54] or Bingham & Kiesel [21]), the NIG model (e.g. see Barndorff-Nielsen [9], Karlis [75] or Rydberg [105]), the Meixner model (e.g.…”