A systematic approach for valuing European-style installment options with continuous payment plan
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.
|Date of creation:||Apr 2010|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +39 06 57114612
Fax: +39 06 57114771
Web page: http://host.uniroma3.it/dipartimenti/economia/it/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:rtr:wpaper:0115. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Telephone for information)
If references are entirely missing, you can add them using this form.