An exotic option whose standard payoff (underlying price in excess of the exercise price) is raised to a specific power (such as 2, 3, 4, etc). Powered options, therefore, have the potential of magnifying leverage substantially and may, thus, entail hefty losses for short positions therein.

A powered call option pays off:

**Powered call payoff = max [S – X, 0] ^{i}**

A powered put option pays off:

**Powered put payoff = max [X- S] ^{i}**

where: S is the underlying price, X is the strike price, and i denotes the power to which the payoff is raised: i = 2, 3, 4, etc.

For example, consider a power call option in which the underlying price is $100, the exercise price is $95, i=2, and the holder wants to exercise, then the payoff is:

Payoff= (100 – 95)^{2} = 25

If i= 3, then:

Payoff= (100 – 95)^{3} = 125

The power also has a magnifying effect on the option’s price. The following table illustrates values for powered call and put options, for different values of power (i) and volatility (σ), taking into account the following specifics: underlying price is $100, exercise price is $100, time to maturity is 6 months, risk-free rate is 10%, continuous dividend yield is 7%:

For a powered call option

Volatility |
Powered Call |
||

i= 1 | i= 2 | i= 3 | |

σ= 10% | 4.7524 | 53.4487 | 758.8427 |

σ= 20% | 7.3179 | 160.2955 | 4608.7213 |

σ= 30% | 9.9829 | 339.3731 | 15,624.1041 |

For a powered put option:

Volatility |
Powered Put |
||

i= 1 | i= 2 | i= 3 | |

σ= 10% | 1.3641 | 9.7680 | 89.6287 |

σ= 20% | 3.9296 | 57.8677 | 1,061.2120 |

σ= 30% | 6.5946 | 142.2726 | 3,745.1853 |

The powered option is similar, in concept, to the power option though each has its power mechanism.

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