A systematic approach for valuing European-style installment options with continuous payment plan

Pierangelo Ciurlia

No 115, Departmental Working Papers of Economics - University 'Roma Tre' from Department of Economics - University Roma Tre

Abstract: In this paper we present an integral equation approach for the valuation of European-style installment derivatives when the premium payments, made continuously throughout the contract’s life, are assumed to be a function of the asset price and time variables. The contribution of this study is threefold. First, we show that in the Black-Scholes framework the option pricing problem can be formulated as a free boundary problem under very general conditions on payo structure and installment payment plan. Second, by applying a Fourier transform-based solution technique, we derive a recursive integral equation for the free boundary along with a general integral representation for the option initial premium. Third, within this systematic treatment of the European installment options, we propose a unified and easily applicable method to deal with a broad range of monotonic payo functions and continuous payment plans depending on the time variable only. Finally, by using the illustrative example of European vanilla installment call options, an explicit valuation formula is obtained for the class of linear time-varying installment payment functions.

Keywords: Installment options; free boundary problem; Fourier transform; integral representations (search for similar items in EconPapers)
JEL-codes: D81 G13 (search for similar items in EconPapers)
Pages: 24
Date: 2010-04
References: Add references at CitEc
Citations:

Downloads: (external link)
http://host.uniroma3.it/dipartimenti/economia/pdf/WP115.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rtr:wpaper:0115

Access Statistics for this paper

More papers in Departmental Working Papers of Economics - University 'Roma Tre' from Department of Economics - University Roma Tre Via Silvio d'Amico 77, - 00145 Rome Italy. Contact information at EDIRC.
Bibliographic data for series maintained by Telephone for information ().