Expected value of a geometric Brownian motion raised to a power for S<K
created by:
Thijs van den Berg
(http://www.sitmo.com)
This equation calculates the expected value of a geometric Brownian motion raised to the power of p of the part of the geometric Brownian motion that is below K at time T. This equation is used in "Pricing and Hedging Power Options" by Ronald C. Heynen and Harry M. Kat.
List of symbols
B] The expectation of A under the condition of B
The value of an asset at time T
The value of an asset at time T raised to the power of p
K
Strike
Y
Yield of the asset. For stocks Y=interest rate, for futures Y=0
