EconPapers    
Economics at your fingertips  
 

Conserving Capital by Adjusting Deltas for Gamma in the Presence of Skewness

Dilip B. Madan ()
Additional contact information
Dilip B. Madan: Robert H. Smith School of Business, University of Maryland, College Park, MD. 20742, USA

Journal of Risk and Financial Management, 2010, vol. 3, issue 1, 1-25

Abstract: An argument for adjusting Black Scholes implied call deltas downwards for a gamma exposure in a left skewed market is presented. It is shown that when the objective for the hedge is the conservation of capital ignoring the gamma for the delta position is expensive. The gamma adjustment factor in the static case is just a function of the risk neutral distribution. In the dynamic case one may precompute at the date of trade initiation a matrix of delta levels as a function of the underlying for the life of the trade and subsequently one just has to look up the matrix for the hedge. Also constructed are matrices for the capital reserve, the pro¯t, leverage and rate of return remaining in the trade as a function of the spot at a future date in the life of the trade. The concepts of pro¯t, capital, leverage and return are as described in Carr, Madan and Vicente Alvarez (2010). The dynamic computations constitute an application of the theory of nonlinear expectations as described in Cohen and Elliott (2010).

Keywords: Bid and ask prices; concave distortions; non linear expectations; variance gamma model; non-uniform grids (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (2) Track citations by RSS feed

Downloads: (external link)
https://www.mdpi.com/1911-8074/3/1/1/pdf (application/pdf)
https://www.mdpi.com/1911-8074/3/1/1/ (text/html)

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:gam:jjrfmx:v:3:y:2010:i:1:p:1-25:d:28367

Access Statistics for this article

Journal of Risk and Financial Management is currently edited by Prof. Dr. Michael McAleer

More articles in Journal of Risk and Financial Management from MDPI, Open Access Journal
Bibliographic data for series maintained by XML Conversion Team ().

 
Page updated 2018-10-02
Handle: RePEc:gam:jjrfmx:v:3:y:2010:i:1:p:1-25:d:28367