Using Put-Call Parity to Estimate Missing Option Quotes
Summary
The document raises a practical problem in real-time options data: a call or put may have only one side quoted. It proposes inferring a missing side from the corresponding option of the same strike using put-call parity, and asks whether this is suitable for futures and index options. It also asks how to select a risk-free rate and whether to interpolate rates for the option’s maturity.
The text is a question rather than a resolved method: it supplies no answer, empirical comparison, or alternative quoting procedure. Any parity estimate would depend on consistent inputs and market conventions, including the underlying or futures price, discounting, maturity, and applicable carry or settlement terms. A parity-implied value should therefore be understood as a rough estimate rather than evidence of an executable bid or ask. The document leaves rate selection and maturity matching open.
Key ideas
- The proposed approach uses put-call parity to infer a missing option quote from the corresponding put or call.
- The question concerns single-sided real-time quotes in futures and index options.
- The author recognizes that parity-based estimates may be crude and asks about practical alternatives.
- Choosing a rate and matching it to the option tenor are unresolved issues in the document.
Tags
Full text
# Put call parity with real time tick data
# Put call parity with real time tick data
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?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.