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I'm currently working on a project using S&P 500 index options(European) data. I haven't done any empirical experiments before, so I'm confused how to find the corresponding risk-free rate and the dividend rate.

  1. For risk-free rate, currently I'm using the 3-month Treasury yield curve rates. Here is the link: https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yieldYear&year=2017

    Some people mentioned we should use 1-year rate instead of 3-month rate. I'm not sure which one is more appropriate.

  2. The dividend rate is far more confusing. I googled and someone said the S&P 500 index includes dividends, which means we should set dividend rate to 0. But I also find links of the S&P 500 dividend yield: https://ycharts.com/indicators/sp_500_dividend_yield#:~:text=S%26P%20500%20Dividend%20Yield%20is,month%20and%201.92%25%20last%20year.

My question is: How do we find the appropriate risk-free rate and dividend rate for S&P 500 index options?

Thanks for your help.

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    $\begingroup$ It depends on the purpose of the calculation and the accuracy needed. For a quick first approximation you can certainly use the 3 month treasury rate and the S&P dividend yield, translated into continuous time equivalents. To be closer to how banks do it, you could use the OIS interest rate for the same maturity as the option. For best results, infer the rates that the options market is using by estimating the Forward price, i.e. find the strike level where a put costs the same as a call; this is a bit more complicated. OTH. $\endgroup$
    – nbbo2
    Commented Sep 21, 2020 at 11:52

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