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Pricing and hedging power options. (English) Zbl 1153.91507

Summary: 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 F. Black and M. Scholes framework [J. Polit. Econ. 81, 637–654 (1973; Zbl 1092.91524)] 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.

MSC:

91B28 Finance etc. (MSC2000)

Citations:

Zbl 1092.91524
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References:

[1] Black, F. and Scholes, M.S. (1973), ’The Pricing of Options and Corporate Liabilities’,Journal of Political Economy,3, 637–654. · Zbl 1092.91524
[2] Cox, J.C. and Ross, S.A. (1976), ’Valuation of Options for Alternative Stochastic Processes’,Journal of Financial Economics,3, 145–166.
[3] Cox, J.C. and Rubinstein, M. (1985),Options Markets, Prentice Hall.
[4] Kariya, T. (1993),Quantitative Methods for Portfolio Analysis, Kluwer Academic Publishers. · Zbl 0833.90015
[5] Kat, H.M. (1996), Delta Hedging of S&P 500 Options: Cash versus Futures Market Execution,Journal of Derivatives 3(3) 6–25.
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