I am working with some real time options tick data (mainly futures options and index options), and in many cases the quotes are single sided (as seen on bloomberg terminal). I will denote a quote as BID_PRICE/ASK_PRICE.
For instance, if a call with strike K does not have a quoted ask price like 100/, what I am currently trying to do is, via put-call parity, estimate the call ask price with the ask of an equivalent put (assuming the put quote is double sided) of the same strike K. Something like:
$$C_{unknown\space ask} = S_{0}+P_{known\space ask}-Ke^{-rT}$$
The same applies for a missing bid as well.
My questions are:
I am aware that this is an extremely crude pricing methodology to 'value' an option. Does the above workflow make sense and if not, are there better ways to estimate the bid/ask of an option quote in the event of a single sided book? How is this usually handled in practice? Any advice for the current workflow will also be much appreciated. The choice of put-call parity was of its ease of understanding/implementation and it is computationally cheap.
Which risk-free rate $r$ do I use? I've heard people say LIBOR, US treasury yields, OIS etc. From a practical perspective, which bloomberg name can I use to stream real time values of the rate?
Continuing on the topic of rates, would I need to perform some sort of a linear interpolation to 'match' the option tenor? For instance, if an option has 45 DTE, and lets say I am using US treasury yields. Would I need to get the 1m and 2m treasuries, linearly interpolate between them and back out a rate corresponding to 45 DTE?