Long memory options: LM evidence and simulations
This paper demonstrates the impact of the observed financial market persistence or long term memory on European option valuation by simple simulation. Many empirical researchers have observed the non-Fickian degrees of persistence or long memory in the financial markets different from the Fickian neutral independence (i.i.d.) of the returns innovations assumption of Black-Scholes' geometric Brownian motion assumption. Moreover, Elliott and van der Hoek (2003) provide a theoretical framework for incorporating these findings into the Black- Scholes risk-neutral valuation framework. This paper provides the first graphical demonstration why and how such long term memory phenomena change European option values and provides thereby a basis for informed long term memory arbitrage. By using a simple mono-fractal Fractional Brownian motion, it is easy to incorporate the various degrees of persistence into the Black-Scholes pricing formula. Long memory options are of considerable importance in corporate remuneration packages, since stock options are written on a company's own shares for long expiration periods. It makes a significant difference in the valuation when an option is 'blue' or when it is 'red.' For a proper valuation of such stock options, the degrees of persistence of the companies' share markets must be precisely measured and properly incorporated in the warrant valuation, otherwise substantial pricing errors may result.
(This abstract was borrowed from another version of this item.)
References listed on IDEAS
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.:
- Cheung, Yin-Wong & Lai, Kon S., 2001. "Long memory and nonlinear mean reversion in Japanese yen-based real exchange rates," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 115-132, February.
- Cornelis A. Los & Jeyanthi Karuppiah, 2004.
"Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997,"
- Karuppiah, Jeyanthi & Los, Cornelis A., 2005. "Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 211-246.
- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
- Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999.
"A Multifractal Model of Assets Returns,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-072, New York University, Leonard N. Stern School of Business-.
- Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997.
"Scaling in stock market data: stable laws and beyond,"
Science & Finance (CFM) working paper archive
9705087, Science & Finance, Capital Fund Management.
- Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Papers cond-mat/9705087, arXiv.org.
- Opong, Kwaku K. & Mulholland, Gwyneth & Fox, Alan F. & Farahmand, Kambiz, 1999. "The behaviour of some UK equity indices: An application of Hurst and BDS tests1," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 267-282, September.
- Cheung, Yin-Wong & Lai, Kon S., 1995. "A search for long memory in international stock market returns," Journal of International Money and Finance, Elsevier, vol. 14(4), pages 597-615, August.
- John Barkoulas & Christopher F. Baum, 1996.
"Fractional Dynamics in Japanese Financial Time Series,"
Boston College Working Papers in Economics
334., Boston College Department of Economics.
- Barkoulas, John T. & Baum, Christopher F., 1998. "Fractional dynamics in Japanese financial time series," Pacific-Basin Finance Journal, Elsevier, vol. 6(1-2), pages 115-124, May.
- Morana, Claudio & Beltratti, Andrea, 2004. "Structural change and long-range dependence in volatility of exchange rates: either, neither or both?," Journal of Empirical Finance, Elsevier, vol. 11(5), pages 629-658, December.
- Mulligan, Robert F., 2004. "Fractal analysis of highly volatile markets: an application to technology equities," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(1), pages 155-179, February.
- Cheng F. Lee & Gong-meng Chen & Oliver M. Rui, 2001.
"Stock Returns And Volatility On China'S Stock Markets,"
Journal of Financial Research,
Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 523-543, December.
- Lee, Cheng F & Chen, Gong-meng & Rui, Oliver M, 2001. "Stock Returns and Volatility on China's Stock Markets," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 523-43, Winter.
- Jonathan Batten & Craig Ellis, 2001. "Scaling Foreign Exchange Volatility," Accounting, Finance, Financial Planning and Insurance Series 2001_01, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
- Marco Corazza & A. G. Malliaris, 2002. "Multi-Fractality in Foreign Currency Markets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 65-98, June.
- L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
- Lillo Fabrizio & Farmer J. Doyne, 2004.
"The Long Memory of the Efficient Market,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 8(3), pages 1-35, September.
- Nyo Nyo A. Kyaw & Cornelis A. Los & Sijing Zong, 2004.
"Persistence Characteristics of Latin American Financial Markets,"
- Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.
- Sijing Zong & Cornelis A. Los & Nyonyo Kyaw, 2004. "Persistence Characteristics of Latin American Financial Markets," Finance 0411013, EconWPA.
- Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
- Mulligan, Robert F. & Lombardo, Gary A., 2004. "Maritime businesses: volatile stock prices and market valuation inefficiencies," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 321-336, May.
- P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 3(2), pages 139-140, July.
- Matteo, T. Di & Aste, T. & Dacorogna, Michel M., 2005.
"Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development,"
Journal of Banking & Finance,
Elsevier, vol. 29(4), pages 827-851, April.
- T. Di Matteo & T. Aste & M. M. Dacorogna, 2004. "Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development," Papers cond-mat/0403681, arXiv.org.
- T. Di Matteo & T. Aste & Michel M. Dacorogna, 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Econometrics 0503004, EconWPA.
- Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
- Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Grau-Carles, Pilar, 2000. "Empirical evidence of long-range correlations in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 396-404.
- Gil-Alana, Luis A., 2004. "Modelling the U.S. interest rate in terms of I(d) statistical models," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(4), pages 475-486, September.
- Harvey, Campbell R & Whaley, Robert E, 1991. " S&P 100 Index Option Volatility," Journal of Finance, American Finance Association, vol. 46(4), pages 1251-61, September.
- Henry, Olan T. & Olekalns, Nilss, 2002. "Does the Australian dollar real exchange rate display mean reversion," Journal of International Money and Finance, Elsevier, vol. 21(5), pages 651-666, October.
- Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
- Batten, Jonathan & Ellis, Craig & Mellor, Robert, 1999. "Scaling laws in variance as a measure of long-term dependence," International Review of Financial Analysis, Elsevier, vol. 8(2), pages 123-138, June.
- Xu, Xinzhong & Taylor, Stephen J., 1994. "The Term Structure of Volatility Implied by Foreign Exchange Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 57-74, March.
- Andrew W. Lo, 1989.
"Long-term Memory in Stock Market Prices,"
NBER Working Papers
2984, National Bureau of Economic Research, Inc.
- Pierre Cizeau & Yanhui Liu & Martin Meyer & C. -K. Peng & H. Eugene Stanley, 1997. "Volatility distribution in the S&P500 Stock Index," Papers cond-mat/9708143, arXiv.org.
- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- Batten, Jonathan & Ellis, Craig & Hogan, Warren, 2002. "Scaling the volatility of credit spreads: Evidence from Australian dollar eurobonds," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 331-344.
- 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.
- Hauser, Michael A & Kunst, Robert M, 1998. " Fractionally Integrated Models with ARCH Errors: With an Application to the Swiss One-Month Euromarket Interest Rate," Review of Quantitative Finance and Accounting, Springer, vol. 10(1), pages 95-113, January.
- Jacobsen, Ben, 1996. "Long term dependence in stock returns," Journal of Empirical Finance, Elsevier, vol. 3(4), pages 393-417, December.
- Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
When requesting a correction, please mention this item's handle: RePEc:eee:riibaf:v:21:y:2007:i:2:p:260-280. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.