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.
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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
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- 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.
- 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.
- 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.
- Savit, R., 1989. "Nonlinearities And Chaotic Effects In Options Prices," Papers 184, Columbia - Center for Futures Markets.
- 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.
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