0
$\begingroup$

Let's say you enter into a contract today in which in time t, you receive the difference between the underlying stock price and 100. Denote the stock price as S. Why is today's value of such a contract equal to:

S - 100 * exp(-rt)

As opposed to:

(S - 100) * exp(-rt)

I see the former in texts a lot.

Thanks!

$\endgroup$
1
$\begingroup$

Keeping it simple, your payoff at time t is:

$S_t-100$

The present value of the stock is $S_0$, it’s current price; and the present value of 100 is its discounted value as you correctly explained in your question.

$\endgroup$
  • 1
    $\begingroup$ Thanks! That's key that S in these is implied to be S0, which is already discounted. This is super helpful! $\endgroup$ – confused Jul 24 at 19:07

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