On a general class of free boundary problems for European-style installment options with continuous payment plan
type: Item
instance of: scholarly article
title: On a general class of free boundary problems for European-style installment options with continuous payment plan
zbMATH Open document ID: 1233.91260
author: Pierangelo Ciurlia
published in: Communications on Pure and Applied Analysis
publication date: 2011-12-19T00:00:00Z
review text: The aim of this paper is to provide an integral equation approach to pricing European-style installment options with continuous payment plan and general monotonic payoff function. The holder's ability to halt installment payments by dropping the option contract leads to a free boundary separating the region where it is advantageous to hold from that in which early stopping is optimal. In order to obtain a solution to this free boundary problem the author uses the incomplete Fourier transform. By inverting the solution of the transformed problem a recursive integral equation for the free boundary along with an analytic representation of the option price are derived. Based on these results it is proposed a unified framework to deal with monotonic payoff functions and continuous payment plans. Applications to the valuation of European vanilla continuous installment call options are presented and an explicit pricing formula is obtained for time-varying payment schedules.
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 5989657
zbMATH Keywords: European installment options
zbMATH Keywords: free boundary problems
zbMATH Keywords: continuous payment plan
zbMATH Keywords: incomplete Fourier transform
zbMATH Keywords: recursive integral equation
MaRDI profile type: Publication
full work available at URL: cpaa.2011.10.1205
OpenAlex ID: W1980819154
DOI: 10.3934/CPAA.2011.10.1205
description: scientific article; zbMATH DE number 5989657