0
$\begingroup$

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.

Improve this question
$\endgroup$
3
  • $\begingroup$ 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. $\endgroup$
    – nbbo2
    Oct 5, 2022 at 13:17
  • $\begingroup$ So there's no underlying theoretical reason for that. It's just how it is done? $\endgroup$
    – Abhishek Banerjee
    Oct 5, 2022 at 13:21
  • $\begingroup$ 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? $\endgroup$
    – Abhishek Banerjee
    Oct 5, 2022 at 13:25

1 Answer 1

Reset to default
1
$\begingroup$

When considering the value of a futures contract it often helps to take a step back to fundamentals. What is the market value of your contract? It's almost a trick question because you can observe the price directly on the exchange (ignoring any bid/ask spreads).

The day-on-day difference in market value of your contract is exactly the difference in the market price of said contract, because this is the price at which you could sell it.

That being said, it's common to use a heuristic similar to yours, where one assumes that the futures price is a function of some spot price (which may not be well-defined to begin with, oftentimes the front month contracts are used as a starting point) together with a combination of risk free rates, storage costs, convenience yield, etc., to arrive at some fair futures price. It could also be done in reverse, i.e. finding some implied convenience yield for a given futures price, to be used in some model where your risk factors are defined in terms of spot prices + rates, rather than futures prices directly.

I hope this helps!

Improve this answer
$\endgroup$

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