Pricing Perpetual American Put Options with Asset-Dependent Discounting

Jonas Al-Hadad and Zbigniew Palmowski
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Jonas Al-Hadad: Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, ul. Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
Zbigniew Palmowski: Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, ul. Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

JRFM, 2021, vol. 14, issue 3, 1-19

Abstract: The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as V A Put ? ( s ) = sup ? ? T E s [ e ? ? 0 ? ? ( S w ) d w ( K ? S ? ) + ] , where T is a family of stopping times, ? is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process S t is a geometric Lévy process with negative exponential jumps, i.e., S t = s e ? t + ? B t ? ? i = 1 N t Y i . The asset-dependent discounting is reflected in the ? function, so this approach is a generalisation of the classic case when ? is constant. It turns out that under certain conditions on the ? function, the value function V A Put ? ( s ) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ? such that V A Put ? ( s ) takes a simplified form.

Keywords: option pricing; American option; Lévy process (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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