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.



Keeping it simple, your payoff at time t is:


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.

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    $\begingroup$ 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 '19 at 19:07

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