Numerical Study of Small-Jump Regularization on Exotic Contracts in Levy Markets

Powers, Lisa J.

doi:10.2139/ssrn.1354661

Cited by 1 publication

(3 citation statements)

References 23 publications

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“…For full details, see ( [21], Appendices). For n D 500 and N D 5; 000, we examine the prices obtained for parameter set III (Y D 0:6) as " is varied in the range 2 4 ; : : : ; 2 30 , and the same settings with Y D 1:4.…”

Section: Monte Carlo Resultsmentioning

confidence: 99%

“…whereas if " > 0, and the diffusion approximation used, different drift terms are used (see [21], Appendix for full details). For brief details of the algorithm from [20], see 5.…”

Section: Simulation Of the Underlying Process Under The Martingale Mementioning

confidence: 99%

“…These calculations are presented in detail in [21]. These calculations are presented in detail in [21].…”

Section: Variational Formulationmentioning

confidence: 99%

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Pricing American Options in an Infinite Activity Lévy Market: Monte Carlo and Deterministic Approaches Using a Diffusion Approximation

Powers

Nešlehová

Stephens

2012

Springer Proceedings in Mathematics

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Computational methods for pricing exotic options when the underlying is driven by a Lévy process are prone to numerical inaccuracy when the driving price process has infinite activity. Such inaccuracies are particularly severe for pricing of American options. In this chapter, we examine the impact of utilizing a diffusion approximation to the contribution of the small jumps in the infinite activity process. We compare the use of deterministic and stochastic (Monte Carlo) methods, and focus on designing strategies tailored to the specific difficulties of pricing American options. We demonstrate that although the implementation of Monte Carlo pricing methods for common Lévy models is reasonably straightforward, and yields estimators with relatively small bias, deterministic methods for exact pricing are equally successful but can be implemented with rather lower computational overhead. Although the generality of Monte Carlo pricing methods may still be an attraction, it seems that for models commonly used in the literature, deterministic numerical approaches are competitive alternatives.

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Section: Monte Carlo Resultsmentioning

confidence: 99%

“…whereas if " > 0, and the diffusion approximation used, different drift terms are used (see [21], Appendix for full details). For brief details of the algorithm from [20], see 5.…”

Section: Simulation Of the Underlying Process Under The Martingale Mementioning

confidence: 99%

See 1 more Smart Citation

Pricing American Options in an Infinite Activity Lévy Market: Monte Carlo and Deterministic Approaches Using a Diffusion Approximation

Powers

Nešlehová

Stephens

2012

Springer Proceedings in Mathematics

View full text Add to dashboard Cite

show abstract

Numerical Study of Small-Jump Regularization on Exotic Contracts in Levy Markets

Cited by 1 publication

References 23 publications

Pricing American Options in an Infinite Activity Lévy Market: Monte Carlo and Deterministic Approaches Using a Diffusion Approximation

Pricing American Options in an Infinite Activity Lévy Market: Monte Carlo and Deterministic Approaches Using a Diffusion Approximation

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