# Is it possible to buy/sell a futures contract with a non-zero initial price?

At creation, the strike price $K$ of a futures contract is determined using the formula $$K = S_0 e^{rT}$$ where $S_0$ is the price of the underlying asset at time $t=0$, $r$ is the risk-free interest rate, and $T$ is the time to maturity of the contract. Setting the strike price of the contract in this way ensures that it has a non-zero initial value.

My question is, in a real-world situation, is it possible for a domestic trader to sell am unfair futures contract with strike price $K < S_0 e^{rT}$ in exchange for an initial premium payable at time $t=0$?

• A futures contract no because those are standardized and centrally-cleared. However 2 counterparties could in theory agree on a OTC forward contract by which the contractual strike is different from the theoretically fair strike in exchange for an initial premium which would equal the risk-neutral expected difference between the contractual strike and the underlying asset at maturity. – Daneel Olivaw Mar 28 '18 at 17:42
• Thank you. I'm guessing that, though in theory possible, that this would not be possible for your average domestic trader? I mean could I, a student with a laptop, enter into such contracts? – M Smith Mar 29 '18 at 10:52
• No I don't think you could enter into a forward agreement, these are bespoke and normally agreed between institutions (banks, insurance companies, etc.) – Daneel Olivaw Mar 29 '18 at 11:07

• Is it possible to do something equivalent to this then? For example, trading a futures contract at some intermediate time $0 < t < T$ will involve some exchange of cash? – M Smith Mar 28 '18 at 17:34