Currently reading A. Damodaran‘s book Investment Valuation. In chapter 5 in order to value an option using black-scholes model he adjusts risk free rate using the following formula: $1-e^{-r}$ I. E. If given risk free rate is $3,6%$ it becomes $1-e^{(-0,036)} = 3,54\%$ Why is that? I wasn’t able to find any explanation on that
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$\begingroup$ Now that you accepted the answer, can you please add a simple comment to explain what the issue was ? Just to close it. $\endgroup$– DomFeb 4, 2021 at 22:44
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Black Scholes uses a continuously compounded rate $r$. To go from a $T$-year annually compounded rate $\hat{r}$ to a $T$-year continuously compounded $r$ you use the formula
$e^{rT} = (1+\hat{r})^T$
So to solve for the Black-Scholes continuously compounded rate you take logs and simplify which gives
$r = \ln(1+\hat{r})$.
This is what Damodoran quotes on page 132 (chapter 5, page 12) on the second edition of his book (I found a free online version).
So if $\hat{r} = 0.036$ then $r=0.0353$. It's very close to the result you got, but not identical.
If you are converting in the opposite direction in order to solve for $\hat{r}$ the formula is
$\hat{r} = e^r - 1$
which is not the same either.
I don't know where the formula you get comes from. It's almost the correct formula - but the signs of the interest rates are incorrectly reversed.
