Assume the observed call option prices $C(K_i,T_i)$ for $i = 1,\dots,N$ are disturbed by some unknown measurement noise $\epsilon$. What would an appropriate covariance structure be for $\epsilon$?
In literature I often see authors making the simplified assumption that $\epsilon_i$ are independent and identically distributed Gaussian with some scaling variance that could depend on for example the bid-ask spread. This seems very unreasonable since if one considers two options $C(K,T)$ and $C(K + \delta,T)$ then in the limit $\delta \to 0$ they should be perfectly correlated.
Has anyone read any literature that discusses these types of modelling choices in more detail?