I am wondering how the industry decides the yield rate for a certain maturity when calculating the implied volatility for the SPX option. Is it just a simple linear interpolation from the two near dividend records? Or something else?
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up.Sign up to join this community
If your ultimate goal is backing out implied volatilities from SPX options for a certain maturity, you would determine the forward for that maturity as the fundamental quantity first. The yield rate is a derived quantity from the forward and the index spot containing the dividends and the funding component. Since dividends are not evenly spread over the year, interpolation of the yield rate is always problematic in my opinion.
If you happen to have both put and call prices available for a couple of strikes for a certain maturity you can determine the forward from put-call parity (since the listed SPX options are European). Or, in case you know the dividend records and the funding rate, you can try to calculate the forward from the index spot directly.
When you know the forward you simply need to solve Black76 equation for the implied volatility.