On the pricing and hedging of options for highly volatile periods
AbstractOption pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time. We consider a market suffering from a financial crisis. We provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during financial crisis more precise.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 45272.
Date of creation: 20 Mar 2013
Date of revision:
Asset Pricing and Hedging; Options; Financial Crisis; Black and Scholes formula.;
Other versions of this item:
- Youssef El-Khatib & Abdulnasser Hatemi-J, 2013. "On the pricing and hedging of options for highly volatile periods," Papers 1304.4688, arXiv.org.
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- G01 - Financial Economics - - General - - - Financial Crises
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
- Savit, R., 1989. "Nonlinearities And Chaotic Effects In Options Prices," Papers 184, Columbia - Center for Futures Markets.
- Dibeh, Ghassan & Harmanani, Haidar M., 2007. "Option pricing during post-crash relaxation times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 357-365.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Fabrizio Lillo & Rosario N. Mantegna, 2001. "Power law relaxation in a complex system: Omori law after a financial market crash," Papers cond-mat/0111257, arXiv.org, revised Jun 2003.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.