This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

General Black-Scholes models accounting for increased market volatility from hedging strategies

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
K. Ronnie Sircar, George Papanicolaou
Abstract

Increases in market volatility of asset prices have been observed and analysed in recent years and their cause has generally been attributed to the popularity of portfolio insurance strategies for derivative securities. The basis of derivative pricing is the Black-Scholes model and its use is so extensive that it is likely to influence the market itself. In particular it has been suggested that this is a factor in the rise in volatilities. A class of pricing models is presented that accounts for the feedback effect from the Black-Scholes dynamic hedging strategies on the price of the asset, and from there back onto the price of the derivative. These models do predict increased implied volatilities with minimal assumptions beyond those of the Black-Scholes theory. They are characterized by a nonlinear partial differential equation that reduces to the Black-Scholes equation when the feedback is removed. We begin with a model economy consisting of two distinct groups of traders: reference traders who are the majority investing in the asset expecting gain, and programme traders who trade the asset following a Black-Scholes type dynamic hedging strategy, which is not known a priori, in order to insure against the risk of a derivative security. The interaction of these groups leads to a stochastic process for the price of the asset which depends on the hedging strategy of the programme traders. Then following a Black-Scholes argument, we derive nonlinear partial differential equations for the derivative price and the hedging strategy. Consistency with the traditional Black-Scholes model characterizes the class of feedback models that we analyse in detail. We study the nonlinear partial differential equation for the price of the derivative by perturbation methods when the programme traders are a small fraction of the economy, by numerical methods, which are easy to use and can be implemented efficiently, and by analytical methods. The results clearly support the observed increasing volatility phenomenon and provide a quantitative explanation for it.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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.

File URL: http://taylorandfrancis.metapress.com/link.asp?target=contribution&id=UG48M31124BWPWT6
File Format: text/html
File Function:
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Publisher Info
Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 5 (1998)
Issue (Month): 1 (March)
Pages: 45-82
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:taf:apmtfi:v:5:y:1998:i:1:p:45-82

Contact details of provider:
Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=100141

Order Information:
Web: http://www.tandf.co.uk/journals/subscription.html

For technical questions regarding this item, or to correct its listing, contact: (Christopher F. Baum).

Related research
Keywords: Black-scholes Model; Dynamic Hedging; Feedback Effects; Option Pricing; Volatility;

Other versions 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.:
  1. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  2. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December. [Downloadable!] (restricted)
    Other versions:
  3. Sanford J. Grossman, 1989. "An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies," NBER Working Papers 2357, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 259-275, September. [Downloadable!]
  5. Frey, Rüdiger & Alexander Stremme, 1995. "Market Volatility and Feedback Effects from Dynamic Hedging," Discussion Paper Serie B 310, University of Bonn, Germany. [Downloadable!]
  6. Brennan, Michael J & Schwartz, Eduardo S, 1989. "Portfolio Insurance and Financial Market Equilibrium," Journal of Business, University of Chicago Press, vol. 62(4), pages 455-72, October. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Gregory Duffee & Paul Kupiec & Patricia White, 1990. "A primer on program trading and stock price volatility: a survey of the issues and the evidence," Finance and Economics Discussion Series 109, Board of Governors of the Federal Reserve System (U.S.).
  9. Frey, Rüdiger, 1996. "The Pricing and Hedging of Options in Finitely Elastic Markets," Discussion Paper Serie B 372, University of Bonn, Germany. [Downloadable!]
  10. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June. [Downloadable!]
Full references

Cited by:
(explanations, 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.)

  1. Christian Bauer & Bernhard Herz, 2007. "The Credibility of CIS Exchange Rate Policies-a technical trader's view," Macroeconomics, Department of Economics, Economics I, Bayreuth University, vol. 0, pages 50-66. [Downloadable!]
  2. Christian Bauer & Bernhard Herz, 2005. "How credible are the exchange rate regimes of the EU accession countries? Empirical evidence from market sentiments," Macroeconomics, Department of Economics, Economics I, Bayreuth University, vol. 43(3), pages 55-77. [Downloadable!]
  3. Bertram Düring & Michel Fournié & Ansgar Jüngel, 2001. "High order compact finite difference schemes for a nonlinear Black-Scholes equation," CoFE Discussion Paper 01-07, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  4. Christian Bauer & Bernhard Herz, . "Monetary and Exchange Rate Stability in South East Asia," Macroeconomics, Department of Economics, Economics I, Bayreuth University. [Downloadable!]
  5. Celso Brunetti & Alessio Caldarera, 2006. "Asset Prices and asset Correlations in Illiquid Markets," Computing in Economics and Finance 2006 331, Society for Computational Economics. [Downloadable!]
    Other versions:
  6. Christian Bauer & Bernhard Herz, 2006. "Monetary and Exchange Rate Stability at the EU Mediterranean Borders," Macroeconomics, Department of Economics, Economics I, Bayreuth University, vol. 57(Paris (4)), pages 899-917. [Downloadable!]
  7. K. Ronnie Sircar, George C. Papanicolaou, 1999. "Stochastic volatility, smile & asymptotics," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(2), pages 107-145, June. [Downloadable!] (restricted)
  8. David Bakstein & Sam Howison, 2002. "A Risk-Neutral Parametric Liquidity Model for Derivatives," OFRC Working Papers Series 2002mf02, Oxford Financial Research Centre. [Downloadable!]
Statistics
Access and download statistics

Did you know? A few items listed on IDEAS are over 2000 years old!

This page was last updated on 2009-12-10.


This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.