Variance-swap replication and discretisation

(a) Redo the proof of Proposition 9.9 with a general split point $S^*$ instead of $F$, and show that the extra terms are $\frac2T\left[\ln\frac{F}{S^*}-\left(\frac F{S^*}-1\right)\right]$. Deduce the correction term in (9.25). (b) Take $F=100$, $r=0$, $T=30/365$, flat implied vol 20%, and only five strikes 80, 90, 100, 110, 120. The OTM option prices are $Q=(0.0000589,\ 0.07059,\ 2.28715,\ 0.12047,\ 0.0012536)$ (put, put, average of call and put, call, call). Compute (9.25). Explain why it differs so much from $0.04$, and in which direction strike spacing and truncation bias the estimate.