• DOI:10.2139/ssrn.4116959
• Corpus ID: 249806591

Levy Models Amenable to Efficient Calculations

@article{Boyarchenko2022LevyMA,
  title={Levy Models Amenable to Efficient Calculations},
  author={Svetlana Boyarchenko and Sergei Levendorskiui},
  journal={SSRN Electronic Journal},
  year={2022}
}

• S. Boyarchenko, Sergei Levendorskiui
• Published 5 July 2022
• Mathematics
• SSRN Electronic Journal

. In our previous publications (IJTAF 2019, Math. Finance 2020), we introduced a general class of SINH-regular processes and demonstrated that efficient numerical methods for the evaluation of the Wiener-Hopf factors and various probability distributions (prices of options of several types) in L´evy models can be developed using only a few general properties of the characteristic exponent ψ . Essentially all popular L´evy processes enjoy these properties. In the present paper, we define classes of Stieltjes-L´evy processes (SL-processes) as processes with completely monotone L´evy densities of positive and negative jumps, and signed Stieltjes-L´evy processes (sSL-processes) as processes with densities representable as differences of completely monotone densities. We demonstrate that 1) all crucial properties of ψ are consequences of the representation ψ ( ξ ) = ( a +2 ia ST G , where ST ( G ) is the Stieltjes transform of the (signed) Stieltjes measure G and a ± j ≥ 0; 2) essentially all popular processes other than Merton’s model and Meixner processes are SL-processes; 3) Meixner processes are sSL-processes; 4) under a natural symmetry condition, essentially all popular classes of L´evy processes are SL- or sSL-subordinated Brownian motion. Hyperbolic processes, Generalized Hyperbolic distributions, subordinated Brownian Motion