Question: In FFT, we define the range for log of strikes as km=+(m1)k=+(m1), form = 1, . . . ,N and some . There are many

In FFT, we define the range for log of strikes as km=β+(m−1)k=β+(m−1)λ, form = 1, . . . ,N and some β. There are many choices for β. One of which is to set β = ln S0 − λN
2 . This choice for β would cause at-the-money strike to fall in the middle of our range of strikes where S0 is today spot. For this choice of β, if we are interested in finding the premium for k = log(K) we would typically interpolate. (a) If we are interested in finding the premium for a specific strike, say k0 = log(K0)without any interpolation, what β would we choose? Find the index for this β. (b) What β would choose such that the first entry coincides to the premium for k0?

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