Is there a forward contract on a forward contract?
Let us take a simple example: Persons $A$ and $B$ agree that $A$ sells $B$ some asset tomorrow at the fixed price $K_1$. This is a normal forward contract on the asset.
Let us then assume that persons $B$ and $C$ agree that $B$ sells $C$ the previously described forward contract tomorrow at the fixed price $K_2$.
This would mean that person $C$ pays the amount of $K_2$ to $B$ to receive the first forward contract, and then $C$ pays the amount of $K_1$ to $A$ to acquire the asset. To summarize:
- Person $C$ pays $K_1+K_2$ to acquire the asset,
- Person $A$ sells the asset and receives $K_1$,
- Person $B$ gains $K_2$.
But wouldn't this be arbitrage (meaning that person $B$ makes money out of nothing)?
Would this kind of agreement make sense? And more importantly, how this contract would be valued?
If we assume that the asset in this example is a non-dividend-paying stock $S$, then the fair value of $K_1$ would be the forward price $F_0=S_0 e^{rT}$, where $r$ is the risk-free interest rate and $T$ is the time to maturity.
With similar reasoning, the fair value of $K_2$ would be the forward price $F_0^\ast = x_0 e^{rT}$, where $x_0$ denotes the initial value of the underlying of this forward, i.e. $x_0$ denotes the initial value of the first forward, which is $0$. Thus $K_2=0$.
Is this reasoning valid? Can we conclude that a forward contract on another forward contract is just a regular forward contract on the asset?