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Practical computing for finite moment log-stable distributions to model financial risk

Abstract

This paper concentrates on the stable distributions which have maximum skewness to the left. The exponentials of such stable distributions are called finite moment log-stable distributions. They have the property that all moments are finite, and are of interest in financial options pricing as an alternative to log-normal distributions. Computation of density and distribution functions has been made faster by using interpolation formulae in two variables and made less error-prone by using computational objects to represent the distributions and performing computational procedures on those objects. Some computations using finite moment log-stable distributions for options pricing are illustrated. The most important qualitative difference from the Black–Scholes log-normal model for options pricing is that the log-stable model suggests that dynamic hedging will reduce portfolio risk by a much smaller amount than is suggested by the log-normal model. This suggests that finite moment log-stable distributions could be used to provide conservative assessments of portfolio risk.

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Correspondence to G. K. Robinson.

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Robinson, G.K. Practical computing for finite moment log-stable distributions to model financial risk. Stat Comput 25, 1233–1246 (2015). https://doi.org/10.1007/s11222-014-9478-9

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Keywords

  • Stable distributions
  • Interpolation
  • Computation
  • Option pricing
  • Hedging of risk