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Given a stock with price , fixed dividend yield , and assumed fixed interest rate , the pricing formulas for power calls and puts with strike and time to expiry are

,

,

with and . Here is the cumulative distribution function for the standard normal distribution.

Snapshot 1: in the special case , power options reduce to regular European options

Snapshot 2: for , the payoff curve for call options becomes concave, and thus the option can have negative time value (i.e., current price < payoff)

Snapshot 3: for put options, the reverse is true: the payoff curve becomes concave for

Snapshot 4: for call options, the option value becomes very large as increases

E. G. Haug, The Complete Guide to Option Pricing Formulas, New York: McGraw–Hill, 2007.