Robust Barrier Option Pricing by Frame Projection Under Exponential Levy Dynamics

38 Pages Posted: 23 Dec 2014 Last revised: 14 Sep 2017

See all articles by Justin Kirkby

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Date Written: December 22, 2014

Abstract

We present an efficient method for robustly pricing discretely monitored barrier and occupation time derivatives under exponential Levy models. This includes ordinary barrier options, as well as (resetting) Parisian options, delayed barrier options (also known as cumulative Parisian or Parasian options), fader options, and step options (soft-barriers), all with single and double barriers, which have yet to be priced with more general Levy processes, including KoBoL (CGMY), Merton's jump diffusion and NIG. The method's efficiency is derived in part from the use of frame projected transition densities, which transform the problem into the Fourier domain, and accelerate the convergence of intermediate expectations. Moreover, these expectations are approximated by Toeplitz matrix-vector multiplications, resulting in a fast implementation. We devise an augmentation approach that contributes to the method's robustness, adding protection against mis-specifying a proper truncation support of the transition density. Theoretical convergence is verified by a series of numerical experiments which demonstrate the method's efficiency and accuracy.

Keywords: Parisian options, Barrier options, delayed barrier options, cumulative Parisian options, Parasian, efficient, Toeplitz, knock-out option, fast Fourier transform, FFT, exotic options, Levy processes, valuation, COS method, basis projection, characteristic function

JEL Classification: G13, C63

Suggested Citation

Kirkby, Justin, Robust Barrier Option Pricing by Frame Projection Under Exponential Levy Dynamics (December 22, 2014). Applied Mathematical Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2541980 or http://dx.doi.org/10.2139/ssrn.2541980

Justin Kirkby (Contact Author)

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

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