• Marek Ďurica University of Žilina, Faculty of Operation and Economics of Transport and Communications, Department of Quantitative Methods and Economic Informatics
Keywords: Chooser, option, delta, gamma, hedging


Correctly used financial derivatives can help investors increase their expected returns and minimize their exposure to risk. To ensure the specific needs of investors, a large number of different types of non-standard exotic options is used. Chooser option is one of them. It is an option that gives its holder the right to choose at some predetermined future time whether the option will be a standard call or put with predetermined strike price and maturity time. Although the chooser options are more expensive than standard European-style options, in many cases they are a more suitable instrument for investors in hedging their portfolio value. For an effective use of the chooser option as a hedging instrument, it is necessary to check the values of the Greek parameters delta and gamma for the options. Especially, if the value of the parameter gamma is too large, hedging of the portfolio value using only parameter delta is insufficient and brings high transaction costs because the portfolio has to be reviewed relatively often. Therefore, in this article, a modification of delta-hedging as well as using the value of parameter gamma is suggested. Error of the delta modification is analyzed and compared with the error of widely used parameter delta. Typical patterns for the modified hedging parameter variation with various time to choose time for chooser options are also presented in this article.


Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654.

Boyle, P. P. (1977). Options: A Monte Carlo Approach. Journal of Financial Economics, 4, 323-338.

Boyle, P. P., Broadie. M., & Glassermann, P. (1997). Monte Carlo Methods for Security Pricing. Journal of Economic Dynamics and Control, 21, 1267-1322.

Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option Pricing: A Simplified Approach. Journal of Financial Economics, 7, 229-264.

De Weert, F. (2008). Exotic Options Trading. England: John Wiley & Sons.

Ďurica, M., & Švábová, L. (2013). An improvement of the delta-hedging of the futures options. International scientific conference FMFFI 2013 Full Paper Proceedings, 140-148.

Ďurica, M., & Švábová, L. (2014). Delta and Gamma for Chooser Options. International Scientific Conference AMSE 2014 Full Paper Proceedings, 75-84. doi: 10.15611/amse.2014.17.08

Faseruk, A., Deacon, C., & Strong, R. (2004). Suggested Refinements to Courses on Derivatives: Presentation of Valuation Equations, Pay Off Diagrams and Managerial Application for Second Generation Options. Journal of Financial Management and Analysis, 17(1), 62-76.

Hull, J. C., & White, A. (1990). Valuing Derivative Securities Using the Explicit Finite Difference Method. Journal of Financial and Quantitative Analysis, 25, 87–100.

Hull, J. C. (2012). Options, Futures, and Other Derivatives (8th ed.). Pearson Education, England.

Merton, R. C. (1973). Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science, 4(1), 141-183.

Rubinstein, M. (1991a). Pay now, choose later. Risk, 4(2), 44-47.

Rubinstein, M. (1991b). Options for the undecided. Risk, 4(4), 70-73.

Švábová, L. (2014). Option pricing using Finite Difference Method. International Scientific Conference BT 2014 Full Papers Proceedings.

Whaley, R. E. (2006). Derivatives, Markets, Valuation and Risk Management. New Jersey: John Wiley & Sons.