Pricing Power Options in the Black-Scholes Model

option type

call

put

power n

2.

volatility (%)

25.

risk-free rate (%)

0.

time to expiry (years)

1.

current price

value at expiry

Power options are a class of exotic options in which the payoff at expiry is related to the

th

n

power of the stock price, where

n=1,2,…

. For a power option on a stock with price

S

t

having strike price

K

and time to expiry

T

, the payoff is

max(

n

S

T

-K,0)

for a call, and

max(K-

n

S

T

,0)

for a put. Within the Black–Scholes model, closed-form solutions exist for the price of power options. In this Demonstration, prices as a function of the various parameters are explored.