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have 2 quick questions please help.

Constructing vol smile (OTM puts & OTM calls) from US equity market data. for Parabolas fit or other methods, the choice/method for ATM vol is non-trivial, since within the market data it is rarely the case that Underlying price == strike price (unlike Fx mkt where we have atm, bf, rr quotations) need help on 2 things.

  1. In data set underlying price does not equal strike so-> Is there a method to find the correct ATM implied volatility, since the market will certainly not pin the exact ATM strike during the daily computation of the smile.

  2. What is the common methodology to handle the gap between OTM Calls and OTM puts when connecting the curves to create the smile; continuously and accurately.

Many Thanks!

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  1. The standard way is to fit to a parametric curve and then sample the curve at the strike of interest.
  2. In order for call and put vols to match you need to have the correct forward. Finding the appropriate forward presents several challenges. For example, in the case of equity options market a) the underlier can be not in sync with the options' snapshot, b) the dividends may not be known, c) the borrow is unknown.
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  • $\begingroup$ I have quote data from several vendors. The quote providers, however conventionally quote IV according to BS/Bjerk/Whaley; how could I imply to correct forward to align the data reliably? Or more correctly phrased what is the method to find the implied total cost of carry (Div+borrow+r+error) to gather the correct forward to have accurate IV curves for calls and puts for american options with divs? Please point me to a good source or suggest a method if you are familiar with something reliable. $\endgroup$
    – JBerstein
    Oct 23, 2020 at 15:21

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