Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function

Maria do Rosário Grossinho, Yaser Faghan Kord and Daniel Sevcovic

No 2017/19, Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa

Abstract: We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price.It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.

Keywords: Option pricing; nonlinear Black-Scholes equation; perpetual American put option; early exercise boundary (search for similar items in EconPapers)
Date: 2017-12
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_019_2017.pdf (application/pdf)

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:ise:remwps:wp0192017

Access Statistics for this paper

More papers in Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa ISEG - Lisbon School of Economics and Management, REM, R. Miguel Lupi, 20, LISBON, PORTUGAL.
Bibliographic data for series maintained by Sandra Araújo ().