# 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

## 2 Answers

You can almost do it using futures options. For example , if a futures contract is trading at 97.00 you can simultaneously buy a 98.00 call and sell a 98.00 put expiring at the next available listed expiration date. Thus, you have promised to buy the futures contract for 98.00 on the expiration date. You will receive a payment of the present value of 1 point for doing this. However on the expiration date of the options you will pay back this 1 point because the options get exercised into futures contracts. A retail investor can actually do this in a margin account.

No. Arbitrage principles force those contracts to have zero cash-flows at inception. I have never heard of any type of future contracts that require cash-flows exchange at the inception. If there is any premium (for any reason such as liquidy, convenience yield) the discount rate will adjust. The only exception I know to this are CDS contracts which theoretically should have no cashflow exchange at inception as well. There are cases where cash exchanges hands when the contract is initiated but not exactly because there is a premium but because coupons are standardized.

You can read more about this issue in Augustin, Patrick, Subrahmanyam, M. G., Tang, D. Y. and Wang, Sarah Qian. (2014) . A quote from the book:

The coupons are standardized, usually 100 or 500 basis points, the difference being settled as an upfront payment between the protection seller and the protection buyer

• 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