Abstract
In this paper we study the pricing and hedging of options whose payoff is a polynomial function of the underlying price at expiration; so-called ‘power options’. Working in the well-known Black and Scholes (1973) framework we derive closed-form formulas for the prices of general power calls and puts. Parabola options are studied as a special case. Power options can be hedged by statically combining ordinary options in such a way that their payoffs form a piecewise linear function which approximates the power option's payoff. Traditional delta hedging may subsequently be used to reduce any residual risk.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Black, F. and Scholes, M.S. (1973), ‘The Pricing of Options and Corporate Liabilities’,Journal of Political Economy,3, 637–654.
Cox, J.C. and Ross, S.A. (1976), ‘Valuation of Options for Alternative Stochastic Processes’,Journal of Financial Economics,3, 145–166.
Cox, J.C. and Rubinstein, M. (1985),Options Markets, Prentice Hall.
Kariya, T. (1993),Quantitative Methods for Portfolio Analysis, Kluwer Academic Publishers.
Kat, H.M. (1996), Delta Hedging of S&P 500 Options: Cash versus Futures Market Execution,Journal of Derivatives 3(3) 6–25.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heynen, R.C., Kat, H.M. Pricing and hedging power options. Financial Engineering and the Japanese Markets 3, 253–261 (1996). https://doi.org/10.1007/BF02425804
Issue Date:
DOI: https://doi.org/10.1007/BF02425804