# Why aren't the prices discounted when futures are marked-to-market? [closed]

I am a complete novice with a background in physics, currently self-studying derivatives. My primary reading resources are John Hull's book and "Introduction to the Economics and Mathematics of Financial Markets" by Jvaska Cvitanic.

I have a confusion regarding marking-to-market. Suppose $$A$$ takes a long position on a futures contract $$t = t_0$$ at time with expiry at $$T$$. The futures price at $$t_0$$ is given by $$F_T(t_0) = S_0 e^{r(T-t_0)}$$ where $$S_0$$ is the price of the underlying at $$t_0$$ and $$r$$ is the rate of risk-free return which we assume remains fixed.

If at $$t_1$$ the price of the underlying becomes $$S_1$$, the futures price at time $$t_1$$ with the same expiry is $$F_T(t_1) = S_1 e^{r(T-t_0)}$$. So, at $$t_1$$, the account of $$A$$ has to be adjusted with an amount $$F_T(t_1) - F_T(t_0)$$

My confusion is since the $$F_T(t_0)$$ and $$F_T(t_1)$$ are the futures prices and they are being adjusted at time $$t_1$$, why isn't the adjustment calculated as $$F_T(t_1)e^{-r(T-t_1)} - F_T(t_0)e^{-r(T-t_1)}$$?

Pardon me if this is very obvious, I am a complete novice.

• That the daily adjustement in the margin account is $F_T(t_1)−F_T(t_0)$ is just a basic rule of the futures exchange, it is how the game is played. You can imagine other more complicated rules but they are of no interest if they are not used in practice; it is like inventing new rules for chess. Oct 5, 2022 at 13:17
• So there's no underlying theoretical reason for that. It's just how it is done? Oct 5, 2022 at 13:21
• Just one more question. So if the price of the underlying moves from $S_0$ to $S_1$. Any losses or profits accrued from taking a position in a futures contract will also add an interest in addition to that of the P/L from holding the underlying itself for the same period? Oct 5, 2022 at 13:25