I am implementing both the Fourier transform of the option price and the time value from Carr Madan's paper (http://portal.tugraz.at/portal/page...aluationUsingtheFastFourierTransform_1999.pdf)
I understand that the Fourier transform of the option price is for at-the-money strikes and becomes highly oscillatory for short maturities which is why Carr-Madan proposed the Fourier transform of the time value for out of the money.
My question is, do you use both methods to get a range of prices at different strikes and maturities? For example, don't use the option price for short maturities but what considered short. And only use time value to handle out of the money options (especially for short maturities)?
I understand that the Fourier transform of the option price is for at-the-money strikes and becomes highly oscillatory for short maturities which is why Carr-Madan proposed the Fourier transform of the time value for out of the money.
My question is, do you use both methods to get a range of prices at different strikes and maturities? For example, don't use the option price for short maturities but what considered short. And only use time value to handle out of the money options (especially for short maturities)?
