# 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} }

. 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…

## 5 Citations

### Efficient Evaluation of Expectations of Functions of a Lévy Process and Its Extremum

- MathematicsSSRN Electronic Journal
- 2022

. We prove simple general formulas for expectations of functions of a L´evy process and its running extremum. Under additional conditions, we derive analytical formulas using the Fourier/Laplace…

### Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema

- MathematicsSSRN Electronic Journal
- 2022

In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy models; the calculations are in the dual space, and the…

### Closed-form Option Pricing for Exponential Lévy Models: A Residue Approach

- MathematicsSSRN Electronic Journal
- 2021

Exponential Lévy processes provide a natural and tractable generalization of the classic Black-Scholes-Merton model which are capable of capturing observed market implied volatility skews. In the…

### Efficient evaluation of expectations of functions of a stable Lévy process and its extremum

- MathematicsSSRN Electronic Journal
- 2022

. Integral representations for expectations of functions of a stable L´evy process X and its supremum ¯ X are derived. As examples, cumulative probability distribution functions (cpdf) of X T , ¯ X T…

### Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring

- MathematicsSSRN Electronic Journal
- 2022

. We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse Z -transform,…

## References

SHOWING 1-10 OF 43 REFERENCES

### Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes

- Mathematics
- 2010

In this paper we introduce a ten-parameter family of L\'{e}vy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an…

### Efficient Laplace Inversion, Wiener-Hopf Factorization and Pricing Lookbacks

- Mathematics
- 2012

We construct fast and accurate methods for (a) approximate Laplace inversion, (b) approximate calculation of the Wiener-Hopf factors for wide classes of Levy processes with exponentially decaying…

### Meromorphic Lévy processes and their fluctuation identities.

- Mathematics
- 2010

The last couple of years has seen a remarkable number of new, explicit examples of the Wiener.Hopf factorization for Levy processes where previously there had been very few. We mention, in…

### SINH-ACCELERATION: EFFICIENT EVALUATION OF PROBABILITY DISTRIBUTIONS, OPTION PRICING, AND MONTE CARLO SIMULATIONS

- MathematicsInternational Journal of Theoretical and Applied Finance
- 2019

Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around [Formula: see text]. The Fourier transform…

### Barrier options and touch- and-out options under regular Lévy processes of exponential type

- Mathematics
- 2002

We derive explicit formulas for barrier options of European type and touchand-out options assuming that under a chosen equivalent martingale measure the stock returns follow a L evy process from a…

### Prices and Sensitivities of Barrier and First-Touch Digital Options in Levy-Driven Models

- Computer Science
- 2008

We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Levy process. The…

### Pitfalls of the Fourier Transform Method in Affine Models, and Remedies

- Mathematics
- 2013

ABSTRACT We study sources of potentially serious errors of popular numerical realizations of the Fourier method in affine models and explain that, in many cases, a calibration procedure based on such…

### Conformal Accelerations Method and Efficient Evaluation of Stable Distributions

- MathematicsActa Applicandae Mathematicae
- 2020

We suggest 3 families of conformal deformations and changes of variables for evaluation of integrals arising in applications of the Fourier analysis to fractional partial differential equations and…

### PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES

- Mathematics
- 2004

We consider the American put with finite time horizonT, assuming that, under an EMM chosen by the market, the stock returns follow a regular Levy process of exponential type. We formulate the free…

### Perpetual American options under Levy processes

- MathematicsProceedings of the 41st IEEE Conference on Decision and Control, 2002.
- 2002

We consider perpetual American options assuming, that under a chosen equivalent martingale measure the shock returns follow a Levy process. For put and call options, their analogs for more general…