2
$\begingroup$

So I was reading here where they calculate the expected value of an option at present given the expected value of the option in a year by calculating

$$C_0 = C_1 e^{(-r)}$$

where r is the interest rate. But where does e come from here? Shouldn't present value just be calculated using

$$C_0 = C_1 / (1 + r)$$

What am I missing?

$\endgroup$
2
$\begingroup$

$e^{-rt}$ is the continuous discounting factor while $(1 + r)^{-t}$ is its discrete counterpart.

Identically/equivalently, there is the continuous manner of computing factors of variation, e.g. $1 + \ln \frac{x_{0+t}}{x_0}$, and its discrete counterpart $\frac{x_{0+t}}{x_0}$.

It all depends on whether you think you are dealing with a continuous quantity or not.

In asset pricing (or finance in general) the underlying notion is that of continuous (interest) compounding.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.