Pricing and Hedging Power Options
Financial Engineering and the Japanese Market, Vol. 3, No. 3, September 1996
Posted: 1 Jun 2001
In this article we study the pricing and hedging of options whose payoff is a polynomial function of the underlying reference index at expiration; so-called power options. Working in the Black-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 that approximates the power option's payoff. Traditional delta hedging may subsequently be used to reduce any residual risk.
JEL Classification: G13
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