Options Vs. Futures: Which on Average Will Have the Greater Payoff?
Creators: name: Silvester, Ryan 
Publisher: name: Utah State University
Year: 2012

description: The use and idea of futures contracts has been around for almost as long as humans have existed. Many of these contracts can be as simple as the shaking of someone’s hand with the agreement to trade an asset for an agreed upon price in the future. These contracts have often been used by farmers to ensure a needed price for an asset, or for a store owner to ensure a needed asset for a given price. The idea of a futures contract is to either buy or sell an asset later on at a specified price. In this paper I will look at both positions. First, wanting to buy an asset in the future is said to be long a futures contract, and to sell an asset in the future is said to be short a futures contract. The benefit of these contracts is that it gives the seller peace of mind to know that they will get paid a specified amount for an asset in the future; or the buyer will not have to pay more than the specified amount for an asset in the future. There can be disadvantages to these types of contracts as well. For example, if in the time between making the contract and the exchange of the asset the price moves in your favor, you will have lost out on the price move.
This brings up the idea of the options market. I will focus on the basic European call and put options. A European option means that the options can only be exercised at the expiration date of the options. A call option is used when one is looking to buy an asset in the future, with a desire to put a cap on the amount that will be paid for the asset. A put option is used when someone is looking to sell an asset in the future and wants to put a floor on how much will be received for the asset.
There are a couple differences between the options and futures contracts. First, with a futures contract no money is exchanged until the expiration of the contract; whereas with an options contract the person purchasing the contract will pay a fee for the contract up front, similar to an insurance premium. The second difference is with a futures contract, the agreed upon amount must be paid and received whether or not it is to your benefit; whereas with an options contract, the purchaser of the contract has the choice to look for a better price in the market, and if found, they can simply walk away from the contract. Thus, for an options contract, a premium is paid to be able to walk away from the contract.
These differences lead to different payoffs for each of the types of contracts. First, to compare the contracts that deal with purchasing an asset in the future, we will look at a call option and a long futures contract. The call option payoff formula is: payoff = Max( PT – K, 0) – Premuim; This will yield a payoff that looks like figure one, Where PT is the price of the asset at the end of the contract and K is the strike price. It starts negative, the amount of the premium, and continues to stay flat until it reaches the strike price then it increases upward. The long futures contract payoff formula is: payoff = PT – K; This will yields a payoff that looks like figure two. It starts negative, the set price, and then continues upward crossing through the zero payoff line at the set price and continues up. One can see that if compared, the call option will outperform the long future contract up until a point just before the strike price and then the future contract will outperform the call option. The call option outperforms the long futures contract by more in the beginning, than the amount that the long futures contract outperforms the call option in the end. Thus the long futures contract has a lot of ground to make up to come out even or on top.
Now, to look at the contracts that deal with selling of an asset, we look at a put option and a short futures contract. The put option payoff formula is: payoff = Max( K – PT, 0) – premium; this will yield a payoff that looks like figure three. It starts positive and decreases until it reaches the strike price at which it is negative, the amount of the premium, and then it continues flat. The short futures contract payoff is: payoff = K – PT; this will yield a payoff that looks like figure four. It starts positive, the amount of the set price, and continues down crossing the zero payoff line at the set price and then continues to decrease. One can see that if compared, the short futures contract will outperform the put option until a point just after the strike, at which the put option will then outperform the futures contract. The put option outperforms the short futures contract by more at the end, than the short futures contract outperforms the put option at the beginning, like the call option outperformed the long futures contract.
Now that I have laid out the different payoffs of these contracts, I want to know which of these contracts on average will outperform the other. In each of the two comparisons, either of the contracts has the possibility of outperforming the other, depending upon what the final price is. Using the examples from before, if I were a farmer trying to get the most out of my harvest which of these contracts should I use? Or, if I were a store owner trying to get the needed assets for my store at the cheapest price, which of these contracts should I use?
To answer these questions, I use Monte Carlo simulation to create data. I simulate a year’s worth of price changes, where price changes happen on every minute. I do this ten thousand times for each of my models. I then take the ending price and apply the payoff rule for each of the four contracts; a call option, a long future, a put option and a short future contract. I calculated the mean and the standard deviation of these payoffs to compare the difference between the contracts.