 A new closed-form solution as an extension of the Black-Scholes formula allowing smile curve plottingYacin Jerbi Quantitative Finance, 2015, vol. 15, issue 12, 2041-2052 Abstract: In this paper, as a generalization of the Black-Scholes (BS) model, we elaborate a new closed-form solution for a uni-dimensional European option pricing model called the J -model. This closed-form solution is based on a new stochastic process, called the J -process, which is an extension of the Wiener process satisfying the martingale property. The J -process is based on a new statistical law called the J -law, which is an extension of the normal law. The J -law relies on four parameters in its general form. It has interesting asymmetry and tail properties, allowing it to fit the reality of financial markets with good accuracy, which is not the case for the normal law. Despite the use of one state variable, we find results similar to those of Heston dealing with the bi-dimensional stochastic volatility problem for pricing European calls. Inverting the BS formula, we plot the smile curve related to this closed-form solution. The J -model can also serve to determine the implied volatility by inverting the J -formula and can be used to price other kinds of options such as American options. Date: 2015 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:15:y:2015:i:12:p:2041-2052 Ordering information: This journal article can be ordered from DOI: 10.1080/14697688.2012.762458 Access Statistics for this article Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral More articles in Quantitative Finance from Taylor & Francis Journals |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.