Option Pricing for Truncated Lévy Processes

Boyarchenko, Svetlana; Levendorskiı̌, Sergei

doi:10.1142/s0219024900000541

Cited by 265 publications

(153 citation statements)

References 8 publications

Supporting

Mentioning

151

Contrasting

Order By: Relevance

“…HP, NIG and NTS Lévy processes also enjoy this property. The extended Koponen family of truncated Lévy processes was first constructed by Boyarchenko and Levendorskiȋ (2000). This is a pure jump process with the Lévy density (cf.…”

Section: Lévy Modelsmentioning

confidence: 99%

Pricing discrete barrier options and credit default swaps under Lévy processes

Innocentis

Levendorskiı̌

2013

Quantitative Finance

View full text Add to dashboard Cite

We consider discretely monitored barrier options under Lévy models, including single and double barrier options and first-touch digitals, as well as CDS and defaultable bonds. At each step of backward induction, we use piece-wise polynomial interpolation and an efficient version of the Fourier transform technique, which allows for efficient error control. We derive accurate recommendations for the choice of parameters of the numerical scheme, and produce numerical examples showing that oversimplified prescriptions in other methods can result in large errors.

show abstract

Section: Lévy Modelsmentioning

confidence: 99%

Pricing discrete barrier options and credit default swaps under Lévy processes

Innocentis

Levendorskiı̌

2013

Quantitative Finance

View full text Add to dashboard Cite

show abstract

“…Examples 2.2. a) The main example is KoBoL (see S. Boyarchenko and Levendorskiȋ [15,16,17]) of order ν ∈ (0, 2), ν = 1, with the characteristic exponent (2.12) where c ± > 0, λ − < 0 < λ + . In this thesis, we will make explicit calculations in the almost symmetric case c + = c − = c, which is also known as CGMY model (see Carr et al [21]).…”

Section: Classes Of Processesmentioning

confidence: 99%

Pricing of Discretely Sampled Asian Options Under Levy Processes

Xie

2012

SSRN Journal

View full text Add to dashboard Cite

Abstract. We develop a new method for pricing options on discretely sampled arithmetic average in exponential Lévy models. The main idea is the reduction to a backward induction procedure for the difference W n between the Asian option with averaging over n sampling periods and the price of the European option with maturity one period. This allows for an efficient truncation of the state space. At each step of backward induction, W n is calculated accurately and fast using a piece-wise interpolation or splines, fast convolution and either flat iFT and (refined) iFFT or the parabolic iFT. Numerical results demonstrate the advantages of the method.

show abstract

“…Eskin (1973), Barndorff-Nielsen and Levendorskiǐ (2001) and Boyarchenko and Levendorskiǐ (2002b). Essentially, these two properties (the characteristic exponent is analytic in a strip, and (10) is valid in the strip) are used in Boyarchenko and Levendorskiǐ (1999, 2000, 2002a to introduce the class of RLPE in terms of the characteristic exponent; the other definition starts with the Lévy density.…”

Section: Regular Lévy Processes Of Exponential Typementioning

confidence: 99%

Fast and Accurate Pricing of Barrier Options Under Levy Processes

Kudryavtsev

Levendorskiı̌

2007

SSRN Journal

View full text Add to dashboard Cite

We suggest two new fast and accurate methods, Fast Wiener-Hopf method (FWH-method) and Iterative Wiener-Hopf method (IWH-method), for pricing barrier options for a wide class of Lévy processes. Both methods use the Wiener-Hopf factorization and Fast Fourier Transform algorithm. Using an accurate albeit relatively slow finite-difference algorithm developed in (FDS-method), we demonstrate the accuracy and fast convergence of the two methods for processes of finite variation. We explain that the convergence of the methods must be better for processes of infinite variation, and, as a certain supporting evidence, demonstrate with numerical examples that the results obtained by two methods are in extremely good agreement. Finally, we use FDS, FWH and IWH-methods to demonstrate that Cont and Volchkova method (CV-method), which is based on the approximation of small jumps by an additional diffusion, may lead to sizable relative errors, especially near the barrier and strike. The reason is that CV-method presumes that the option price is of class C 2 up to the barrier, whereas for processes without Gaussian component, it is typically not of class C 1 at the barrier. (2006) (FDS-method), on démontre la précision et la convergence rapide des deux méthodes pour des processusà variation finie. On explique que la convergence des méthodes doitêtre meilleure pour des processusà variation infinie et on montre sur des exemples numériques la cohérence des résultats obtenus par les deux méthodes. Finalement on utilise les méthodes FDS, FWH and IWHmethods pour montrer que la méthode de Cont and Volchkova (CV-method), qui est basée sur l'approximation des petits sauts par une diffusion additionnelle peut entrainer des erreurs relativement importantes notamment près de la barrière et du strike. Cela s'explique par le fait que cette méthode présuppose que le prix de l'option est de classe C 2 jusqu'à la barrière, alors que pour des processus sans composante gaussienne, il n'est en général pas de classe C 1à la barrière.

show abstract

Option Pricing for Truncated Lévy Processes

Cited by 265 publications

References 8 publications

Pricing discrete barrier options and credit default swaps under Lévy processes

Pricing discrete barrier options and credit default swaps under Lévy processes

Pricing of Discretely Sampled Asian Options Under Levy Processes

Fast and Accurate Pricing of Barrier Options Under Levy Processes

Contact Info

Product

Resources

About