Pricing and hedging power options |
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Authors: | Ronald C Heynen Harry M Kat |
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Institution: | (1) Independent Consultant, Breda, the Netherlands;(2) TMG Financial Products (Europe) Ltd, 6th Floor, River Plate House, 7-11 Finsbury Circus, EC2M 7EB London, UK |
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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. |
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Keywords: | exotic option pricing option hedging static hedging |
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