LetX be an Ornstein-Uhlenbeck process with a long-run mean of zero; that is, dX = X dt

LetX be an Ornstein-Uhlenbeck process with a long-run mean of zero; that is, dX = −κX dt + σ dB for constants κ and σ. Set Y = X2. Show that dY = ˆκ(θˆ − Y)dt + ˆσ

√

Y dB for constants κˆ, θˆ and σˆ . Note: The squared Ornstein-Uhlenbeck process Y is a special case of the interest rate process in the Cox-Ingersoll-Ross model

(Section 18.3) and a special case of the variance process in the Heston model

(Section 17.4)—special because κˆ θˆ = ˆσ2/4.