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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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
- Stable distributions
- Option pricing
- Hedging of risk