Reverse Parimutuel on Cryptocurrency Option Trading

Friedrich August von Hayek, a prominent Austrian economist and philosopher, winner of the 1974 Nobel Prize in Economics, once proposed a revolutionary concept of creating private money. In his book “The Denationalization of Money”, he spoke about the need to deprive the state of the monopoly of issuance of money.

The appearance of Bitcoin and other crypto currencies not only makes Hayek’s ideas more realistic, but also improves them, because as Hayek believed, banks should be issuing competitive currencies, and Bitcoin is produced by a decentralized system without a single controlling body.

Like any financial instrument for maintaining liquidity, hedging risks, etc., crypto-currencies require the existence of various derivative financial instruments (derivatives), such as futures and options. It can be said that the basic theory of options arose with the advent of the Black-Scholes equation in 1972 and has since been the main equation determining the price of options. In addition, the system of their circulation on the stock exchange has not changed. The system of a double auction, where both the buyer and the seller must be present.

However, large price fluctuations, inability to sell Bitcoin shorts (note: short selling — selling securities, goods or currencies that the trader at the time of sale does not own.), makes Bitcoin behavior similar to the behavior of weather options. As a result, there is a high premium of options, demand for large collateral and a large spread between the purchase price and the sale price.

Options on cryptocurrency

To solve this problem, we propose a new method, called reverse parimutuel, where sellers need not exist, and settlements are paid from a common pool. To understand our proposal, we must first consider the difference between the conventional options market for currencies and stocks, and options markets like Bitcoin, weather, etc.

The Call option is the right to buy, and the Put option is the right to sell an asset by a certain date in the future at a predetermined price (strike).

The price of the option is the premium that the buyer is willing to pay. The main problem is to determine the price of the option — the premium. What premium should the option seller receive? The amount of the premium is determined by the possibility of hedging between the options contract and the underlying asset to which this option was issued.


Imagine an ant that crawls along a tree. At the moment, it is at a height of 100cm, and is going to crawl higher, but it does so by chance, going up and down. Imagine that we have a one period of model and after a time t, with a probability of p = 0.6 the ant will be at a height of 110cm or with a probability of p = 0.4 at a height of 90cm. Let’s say we want to place a wager for such an event to occur and for the game we chose a call and a put options with a strike price of 100. How much will these two options cost in this one period of model? This, it would seem, is easy to calculate:

Call = (10 х 0.6 + 0 x 0.4) = 6
Put = (0 x 0.6 + 10 x 0.4) = 4

However, if we consider the same one period of model, but where the asset is not the height of the tree, but a stock worth $100, which can be bought or sold short, then the option price under the same conditions (for simplicity, the bank interest is 0), Call price and Put would be completely different:

Call = (10 x 0.5 + 0 x 0.5) = 5
Put = (0 x 0.5 + 10 x 0.5) = 5

We see that in this case, the options are equal and this is the main property of option pricing when there is an existence of the hedging asset. So, if the price of the call was 6 and the put was 4, then we can sell the call, short the stock for $100 and buy the put, getting 100% profit without any risk. However, in the real-world market there is an unbreakable rule — it is impossible to receive a guaranteed profit without risk. Therefore, the price of options is determined in accordance with this basic rule.

We looked at the difference between a complete and an incomplete market. In the first example with a tree and an ant, the market is called incomplete, and in the second complete. It is important to understand that even if there is an hedging asset, such as a stock, the market can still be incomplete. For example, before release of important news, such as a profit report [1], the stock makes a jump in price and it is impossible to implement dynamic hedging.

There are quite a few examples of incomplete markets — weather options, economic reports, such as unemployment data, inflation, etc.


In this article we are interested in Bitcoin and other crypto-currencies. The Crypto-currency market is a typical example of an incomplete market, with all its features, such as unpredictable sharp fluctuations and an inability to hedge the depreciation of the currency due to an inability to sell short. This is the main reason there are high premiums for options on Bitcoin, high spreads between the price of buying and selling and a huge guarantee of security that brokerage companies and exchanges require.

One solution to this problem is the application of the reverse parimutuel method, where there is no need for the participation of sellers — buyers are enough.

A simple parimutuel betting — when bets on certain outcomes of events are placed in a pool, and the winning bets are calculated by distributing this pool amongst the winning stakes. The parimutuel system is used in sports games, horse races, car races, etc.

An important advantage of such a system is that it does not require sellers, and the winners receive their winnings from a common pool. The use of this system in options trading faces a problem of a fixed pre-determined payment in the event of an option contract win. In the parimutuel system, it is impossible to determine the final payment before the auction closes. In cases with options, investors, and especially hedgers and arbitrageurs need to know in advance what the payment for this option will be, in the event of a win. Otherwise, it is impossible to protect futures, shares, or currency, from unexpected growth or fall.

Therefore, we named our method using the parimutuel system, where a pre-determined amount is paid out, a reverse parimutuel system. Reverse parimutuel, differs from the standard parimutuel, in that final payments are determined before the close of the auction. While in the parimutuel model, we have a fixed cost and an unknown amount of reward, in the reverse parimutuel model, we do not have a fixed cost (market or limit order), but we know the price of the reward in advance.

Reverse parimutuel examples

Imagine that we have any financial instrument, for example, with a price of $20 and we divide the price range into sections with steps of $1 from $15 to $25. $15 to $16 is one section, $16 to $17 is another section, and so on. Then the numerical sequence is as follows:

15 16 17 18 19 20 21 22 23 24 25

Just like in parimutuel betting where one can bet on a horse or a few horses, here one can bet on any number of sections (or basic states), we called them ranges. By analogy, with the plate, the participants will throw in their bets on particular plates. For our example, this is what the data looks like when 20 units are placed on plate 17–18, and 17 units are placed on plate 21–22:

15 16 17 18 19 20 21 22 23 24 25
20 17

Using this principle, we can create a binary option. A binary option is a contract in which a participant pays a premium and receives either a 1 for a win or a 0 for a loss. This is what one binary option Call looks like, with a strike price of 20:

15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1
But in the reverse parimutuel, the premium is much lower than the payout.

As you can see, if the stock closed above 20, then the option payment in each state above 20 will be equal to 1. This is how it should be in the case of binary options. The Put option with strike price of 18 will look like this:

15 16 17 18 19 20 21 22 23 24 25
1 1 1 1

Now the participant can create a standard option (vanilla option), just change the weight of the bets in each basic state: For example, one Call with a strike price of 21 will look like this:

15 16 17 18 19 20 21 22 23 24 25
1 2 3 4

Payment on expiration date (execution), if the stock closes at $24, will be $3, and if it closes at $25, will be $4. This is how it should be in case of a vanilla Call. Accordingly, one Put with strike price of 17 will look like this:

15 16 17 18 19 20 21 22 23 24 25
3 2 1
The advantage of such a system is that a participant can make any options that he considers interesting.

Usually, replicating exotic options from simple ones is not such a simple task and is not always possible [2]. But with our basic states, this is not difficult at all. Just as any material can be created from atoms, so any option can be created from elementary basic states.

For example, consider an exotic option up-and-out call. Such an option belongs to the barrier class. Profit is gained when the price of an asset is higher than the strike price, but lower than a specified barrier. The cost of an up-and-out option is lower than normal and it is necessary when the participant believes that the asset price will not go above a certain level and there is no point in paying an additional premium for it. Here is an example of how you can make such an option with strike price of 20 and a barrier of 23 using our elementary states:

15 16 17 18 19 20 21 22 23 24 25
1 2 3

Here it is visible that at achievement of an active above 23 any payments will not follow, and more low, payments will occur, as at the usual option. Accordingly put put-and-out option with strike 20 and barrier 16 will look like this:

15 16 17 18 19 20 21 22 23 24 25
3 2 1

In cases where a participant expects a jump in the price of the underlying security, it makes no sense to use the nearest asset prices and you can apply another exotic option, called up-and-in. It is also cheaper than an ordinary option, but it starts acting as a normal option only when the specified barrier is reached. In case of a price jump, you can create a straddle consisting of such exotic call and put options.

Here’s an example of an up-and-in call with strike price of 20 and a barrier of 23 and a down-and-in put with strike price of 20 and a barrier of 17:

15 16 17 18 19 20 21 22 23 24 25
5 4 3 3 4 5

If the price reaches or exceeds the barrier on the settlement date, the owner of such an option will receive a payment in accordance with the payment of the ordinary option.

Using basic elementary states, you can create any barrier exotic option, such as a down-and-out, down-and-in, and so on.

Another interesting application of the reverse parimutuel system is the filling of elementary base states with nonlinear coefficients. For example, ultra funds have now become popular. Such funds create a portfolio that represents an exact copy of the curve of a specific index, just such that it moves two or three times more than the index. Especially, it becomes interesting for the participant who wants to get the maximum profit from this curve, especially if the asset is in a bubble state and during this time period one can get the maximum possible profit. In our case, the replication of the nonlinear state of the option can be replicated as follows, here is an example of a call and a put, both with a strike price of 20:

15 16 17 18 19 20 21 22 23 24 25
16 8 4 2 1 1 2 4 8 16

In existing financial markets, exotic and flex options have small liquidity and large premiums. In our case, all the premiums for all options (binary, vanilla, exotic) go to a common pool, which is fully self-financing and does not require the existence of sellers. The winners gain at the expense of the losers. A more detailed explanation and methodology of this process was considered by us in [3]

A reverse parimutuel auction can take place even within a couple of hours. After the auction the participants receive options with the ordered characteristics, after which they can trade in the standard market through the double auction system, for example, on the NASDAQ exchange. In this case, the seller will already be the owner of the option.

Order types

If a participant has placed a market order, then he is guaranteed the purchase of all contracts. If a participant has placed a limit order, then he is guaranteed to have all orders filled only if the price of his order is higher than the market price, otherwise the order can be partially filled or not at all.

Here it should be noted, the difference of a market order in the regular market and the advantage of reverse parimutuel. In a conventional market, placing a market order is dangerous, since it can be executed at an unfair price, for example, a market maker, can fill an order simply by raising the selling price without even making a deal for it and after filling your order, lower the price.

There are also instantaneous spikes (jumps in price) and that is when you get your order filled. In case of reverse parimutuel, such situations are impossible. In order for the price of the option to change, real orders must exist. Another main point is that at the end of the auction, everyone will pay the same price for the same option, regardless of when the order is placed. Therefore, if you want your order to definitely be executed, you will place a market order and not be afraid to overpay, because you will get a fair price that depends only on the number of people who placed an order for the same option.

The advantages of a reverse parimutuel market:

  • No option sellers are necessary, buyers are enough;
  • There is no spread between the price of buying and selling;
  • Guarantee of payments to all winning participants from a pool;
  • No collateral, margin, etc.;
  • It is possible to combine a variety of different options, in one auction;
  • Opportunity for participants to create their own options.

Over the years, crypto-currencies have proven their worth, and in the future, perhaps much of the world’s financial systems will be built on top of them. Now the time has come for derivatives on crypto-currencies to make the market even more stable and stronger.