<scp>L</scp>évy Processes in Asset Pricing

Kou, Steven

doi:10.1002/9780470061596.risk0384

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Similarities Between Today and The 1960s1

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2013

2022

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Cited by 2 publications

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“…Mitzenmacher (2004) reminds us of how close these laws are to the so-called exponential laws, and that the two types of law can be distinguished only by means of a large volume of data. The advent of intraday data has made it possible to build sufficiently broad samples to provide firm proof of Mandelbrot’s idea that the evolution of financial markets could be characterized using stable Lévy processes such as those used by econophysicists (Kou 2008).…”

Section: Similarities Between Today and The 1960smentioning

confidence: 99%

Econophysics: A New Challenge for Financial Economics?

Jovanovic¹,

Schınckus²

2013

J Hist Econ Thought

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Section: Similarities Between Today and The 1960smentioning

confidence: 99%

Econophysics: A New Challenge for Financial Economics?

Jovanovic¹,

Schınckus²

2013

J Hist Econ Thought

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Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation

Cázares

Mijatović

2022

Finance Stoch

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We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel simulation algorithm for the joint law of the state, supremum and time the supremum is attained of the Gaussian approximation for a general Lévy process. We bound the bias for various locally Lipschitz and discontinuous payoffs arising in applications and analyse the computational complexities of the corresponding Monte Carlo and multilevel Monte Carlo estimators. Monte Carlo methods for Lévy processes (using Gaussian approximation) have been analysed for Lipschitz payoffs, in which case the computational complexity of our algorithm is up to two orders of magnitude smaller when the jump activity is high. At the core of our approach are bounds on certain Wasserstein distances, obtained via the novel stick-breaking Gaussian (SBG) coupling between a Lévy process and its Gaussian approximation. Numerical performance, based on the implementation in Cázares and Mijatović (SBG approximation. GitHub repository. Available online at https://github.com/jorgeignaciogc/SBG.jl (2020)), exhibits a good agreement with our theoretical bounds. Numerical evidence suggests that our algorithm remains stable and accurate when estimating Greeks for barrier options and outperforms the “obvious” algorithm for finite-jump-activity Lévy processes.

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Lévy Processes in Asset Pricing

Cited by 2 publications

References 29 publications

Econophysics: A New Challenge for Financial Economics?

Econophysics: A New Challenge for Financial Economics?

Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation

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