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I can think of at least two rates with different physical meanings to use.

  1. rate on assessed balance.
  2. short rate of the underlying stock

I understand that BS model is a theory and practice getts messy,but at least in theory which is the one that makes sense to use?

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Usually the bank funding rate that corresponds to the length of the option - I.e., for a 3 month option probably the 3 month Fed Funds rate

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  • $\begingroup$ @user1559897 I don't know what interest rate you should use, but this answer tells you what the counterparty investment bank that you deal with (the option market maker) will be using. $\endgroup$ – Alex C May 23 '18 at 1:29
  • $\begingroup$ Yes, and if you want to check how fair their pricing is, that is the number to use. $\endgroup$ – eSurfsnake May 23 '18 at 1:34
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BS model uses risk-free rate to price option. The most popular way of deriving risk-free rate from treasury zero-coupon yield curve based on the expiration of the option.

For options expiring within a year, you can directly use the yield from the treasury bills(expiring within a year). For longer than a year, zero coupon rates (or spot rates) have to be derived from coupon bonds through bootstrapping.

This is the way of bootstrapping: https://en.wikipedia.org/wiki/Bootstrapping_(finance)

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  • $\begingroup$ This is incorrect. The rate should reflect the bank's funding cost for the hedge and this is not equal to the treasury rate. $\endgroup$ – Dom May 24 '18 at 4:59
  • $\begingroup$ I disagree. banks' funding rate involves credit risk, it's not riskfree. Please provide some paper/material to support your comment. Otherwise, please do not mislead other readers $\endgroup$ – Hui May 25 '18 at 3:57
  • $\begingroup$ Don't patronise me. I have 20 years of quant experience in US investment banks and I teach at a major business school. Here is a paper that discusses the issues. www-2.rotman.utoronto.ca/~hull/DownloadablePublications/… $\endgroup$ – Dom May 25 '18 at 8:29
  • $\begingroup$ Sorry Dom, I apologize I was overconfident about my thoughts as I know many companies do use fed fund rate(which doesn't necessarily mean they are right). I read through your paper and I agree with your comment $\endgroup$ – Hui May 26 '18 at 0:25
  • $\begingroup$ Fed funds rates are ok for collateralised derivatives trades as they are linked to where banks fund themselves by trading balances at the federal reserve and hence to where banks borrow. This is not the same as the rate at which governments borrow, $\endgroup$ – Dom May 29 '18 at 8:58

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