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In Black Scholes model r is defined as risk free interest rate. Could you please explain what is risk free? Is it same as interest rate on checking account?

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  • $\begingroup$ Risk free means just that. You are guaranteed to receive the money in the future no matter what happens. Granted, Black Scholes is only a model, a simplification of reality; so it doesn't correspond to anything in the real world precisely. But there are some financial instruments that are close enough to be treated as such. $\endgroup$ Dec 15, 2022 at 1:23

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Generally speaking, a risk-free rate refers to the yield you get on a government bond (read more here).

On a checking account there's a possibility that the bank would fail. Yes, it's FDIC insured, but up to \$250K.

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    $\begingroup$ +1 I would just add that it’s not just any government bond. It has to be bond of a country where default probability is for all practical purposes 0 (Germany, Switzerland, USA etc) $\endgroup$
    – 1muflon1
    Jan 29, 2020 at 10:33
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Usually, no one uses government bonds when pricing derivates. Bloomberg for example does not even offer govy curves as a choice for the interest rate in all of their derivatives pricers (OVME, OVML, SWPM, DLIB etc.)

The RFR (for risk free rate) swap rates (SOFR for USD, ESTR for EUR for example) are used, and you have a choice for other swap curves like Euribor and Libor (legacy reasons) as well as other OIS swaps like the Fed funds swaps. It's also standard for clearing houses and exchanges like LCH and CME to use these RFR rates for discounting and Price Alignment Interest (PAI) calculations, which is the interest rate paid on the collateral that is held.

There is work on why treasuries are not a good proxy aside from the aforementioned point (usually based on convenience yield arguments). See for example Decomposing Swap Spreads by Feldhütter et al..

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