Lookback options and diffusion hitting times: A spectral expansion approach

Vadim Linetsky

doi:10.1007/s00780-003-0120-5

Lookback options and diffusion hitting times: A spectral expansion approach

Vadim Linetsky^*

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

61 Scopus citations

Abstract

Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the option's lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an analytical characterization of lookback option prices in terms of spectral expansions. In particular, analytical solutions for lookback options under the constant elasticity of variance (CEV) diffusion are obtained.

Original language	English (US)
Pages (from-to)	373-398
Number of pages	26
Journal	Finance and Stochastics
Volume	8
Issue number	3
DOIs	https://doi.org/10.1007/s00780-003-0120-5
State	Published - Aug 2004

Keywords

Bessel process
CEV model
Diffusion maximum and minimum
Hitting times
Lookback options
Spectral expansions

ASJC Scopus subject areas

Statistics and Probability
Finance
Statistics, Probability and Uncertainty

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10.1007/s00780-003-0120-5

Cite this

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AB - Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the option's lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an analytical characterization of lookback option prices in terms of spectral expansions. In particular, analytical solutions for lookback options under the constant elasticity of variance (CEV) diffusion are obtained.

KW - Bessel process

KW - CEV model

KW - Diffusion maximum and minimum

KW - Hitting times

KW - Lookback options

KW - Spectral expansions

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ER -

Lookback options and diffusion hitting times: A spectral expansion approach

Abstract

Keywords

ASJC Scopus subject areas

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