A direct solution method for pricing options involving the maximum process

Masahiko Egami () and Tadao Oryu ()
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Masahiko Egami: Kyoto University
Tadao Oryu: Tokyo Metropolitan University

Finance and Stochastics, 2017, vol. 21, issue 4, No 3, 967-993

Abstract: Abstract One often encounters options involving not only the stock price, but also its running maximum. We provide, in a fairly general setting, explicit solutions for optimal stopping problems concerned with a diffusion process and its running maximum. Our approach is to use excursion theory for Markov processes and rewrite the original two-dimensional problem as an infinite number of one-dimensional ones. Our method is rather direct without presupposing the existence of an optimal threshold or imposing a smooth-fit condition. We present a systematic solution method by illustrating it through classical and new examples.

Keywords: 60G40; 60J75; American options with maximum process; Optimal stopping; Excursion theory; Diffusions (search for similar items in EconPapers)
JEL-codes: C61 C65 G13 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00780-017-0343-5

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