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Old Yesterday, 10:19 AM
Undecidedusernam Undecidedusernam is offline
Join Date: May 2017
Posts: 5
Default Stupid qns on Risk free rate vs Expected return


I am really confused about when to use risk free rate or expected rate of return in Blackscholes formula (in the d1 and d2 terms).
Can anyone please advise?
Is there a rule of thumb like if rate of return is provided then we should always use it?
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Old Today, 12:07 PM
disluckyperson disluckyperson is offline
Join Date: Jun 2018
Posts: 12

The Black-Scholes formula for option prices uses the risk neutral probability, which uses the risk-free rate. The same is with binomial trees for pricing option, you use the risk-free rate to derive the risk neutral probability. But this is all when pricing options.

If you want to know the expected payoff of the option at the end, or the probability of the option paying off, or the probability of a stock being above or below a certain price, you use the expected rate of return, either in the lognormal formula (which will then be just like the Black-Scholes formula for d1 and d2, just with expected rate of return replacing the risk-free rate), or in the binomial probability formula for binomial trees (but keep in mind for calculating u and d in the binomial trees, you still use the risk free rate).

Last edited by disluckyperson; Today at 03:00 PM..
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