Distribution of the Final payoff - sum of the two packs

I noticed that we have treated the distributions of the two packs separately and not looked at the distribution of the final level which is the sum of the 14 cards. So, the final distrubution has a mean of 164 and a standard deviation of 38.9. The histogram for a population of 10^6 looks like:-

Introduction of a structuring desk

John Arvanitis mentioned the idea of introducing a structuring desk (SD) that can offer packages of options to the IB and the HF but not pit members. The idea here would be to provide option types of various strikes - calls, puts, binaries plus combinations such as call spreads.

These would be over-the-counter trades which means they are private between the two counterparties and bilateral in nature so would not go through the exchange settlement process. Secondary pricing is provided on request by the SD in the form of a close-out price, settlement at the end of the deal would also be bilateral.

This introduces significant bilateral counterparty risk which is now non-transparent - which reflects the issues faced in 2008/9. This will require a form of waterfall that would enforce settlement with the exchange first before bilateral agreements are considered.

The only condition is that if the package is executed delta neutral (for example a 160 call might be priced at 26 points together with a short position in the traded contract at 164 at a ratio of 10:6) then the contract must settle through the exchange.

This is an interesting additional layer of complexity that has yet to be tested. The ability to price call options throughout the life of the game has yet to be developed. however I did manage to price a series of calls and puts at different strikes based on a simple average of the payoffs of a sample of 10^6 games. The results are as follows:-

Strike__ Call___ Put
100 ____65____ 1.0
110 ____55____ 1.5
120 ____46____ 2.5
130 ____38____ 4.0
140 ____30____ 6.5
150 ____23____ 9.5
160 ____18____ 14
170 ____13____ 19
180 ____9.0____ 25
190____ 6.0____ 32
200____ 3.5____ 40
210____ 2.5____ 48
220____ 1.0____ 57

More analysis on binaries and implied deltas to follow.

The role of the Market-Maker

The Market-maker is central to the smooth operation of the market and hence is key for making the game as realistic as possible.

The key aspect is that the MM has no incentive to make money, only to avoid losing a lot. Any money the MM makes goes to the Bar Bill that is expected to pay for the drinks after a long afternoon session. This is not a position to give to a junior member of the group.

Given that approx 60% of total volume goes through the MM, the key function is to move the market to the point of balance. It is therefore better to lose a little money by moving (for example) the spread beyond the original bid-ask and flushing out a couple of quick profits for the other dealers than to take a wrong direction view, in particular between trading sessions. The tails of the distribution in the second pack include numbers that can move the market by +/- 20 points.

Compensation for the MM only comes from the bid-ask spread which at a fixed 3 point spread so long as he can find a balanced market and get sufficient volume done.

Unlike the LT who can shout out Bid or Ask prices at any time, the MM also is required to make a two-way price at all times. This is tough to maintain but is an important component to maintain a functioning market. This is particularly true during the last trading session where the Hedge funds have to unwind all of their positions. sometimes with size that is multiple the 5 that the MM is good for.

To keep the noise level up, the MM should continue to shout out the market levels during the trading sessions.

One last aspect of the MM is to keep track of he open interest, less on the PL which should not be a distraction, but more on the net position. Target is always to be close to home when the closing bell calls. It is surprisingly difficult to maintain the bid-ask price, deal, create deal tickets and keep track of open position at the same time. Hence the pads!

Suggestions for Materials

The game should be played as paper-based as possible. The action of settling the trades should be done manually but the record-keeping can be via a spreadsheet. OK Materials:-

1) Cards for the two packs - ideally use cards similar in size and thickness to a business card - they need to be shuffled, dealt and not be transparent. Therefore you need 40 for the first pack and 100 for the second pack.

2) Trading cards. There should be a deal ticket for each buy and each sell, so again the size of a business card works well, enough to write the dealer, the counterpart, the buy or sell size and price. Card is better as the MM needs to stand in the pit with a pack and deal quickly. In a recent game we closed just over 100 deals, so you need north of 200 cards or ones that can be reused

The best way to deal in the pit is for one member of the IB to come to the pit members, ask for a price, deal, enter the details on their ticket, then take the pit members deal ticket and hand it over to the person who is running the settlement. Presenting both sides of the deal massively reduces settlement burden.

3) ID tags. Each group of HF, IB and Pit members should come up with a two letter identifier and display on a badge when dealing, this speeds up the settlement process.

4) Pads etc, very useful for each group to keep a tab on their outstanding positions. Ultimately the prime record of each deal lies with the settlement person. More on their role in following blogs.

5) Spreadsheet for settling trades, once entered the deal size and economics are binding.

6) Alarm for the MM to sound the end of each trading session (pen on a glass works!)

Distribution of the second pack

Using the example below, the histogram of the pack is some distance from looking like a normalised distribution.

Note the forced lack of a zero which was put in to make the game more interesting, but looks like the resultant distribution has shifted to the right a bit. Not sure it works. The distribution of the sum of the six cards chosen at random has a mean of zero (no surprise) and a standard deviation of 25.25. The histogram looks like based a sample of 100k.

Distribution of the first pack

The distribution for the sum of eight cards to be picked out of a list of cards numbered 1 to 40 has an average of 163.9 and standard deviation of 29.5. The histogram shows its distribution based on a sample of 100,000.

How to Trade

One thing to get used to when trading contracts in open market conditions is the role of the Bid-Ask spread. So when the market-maker states "I am 163 eight five up" this means he will buy or go long in size of upto 5 lots (£ per point) at a level of 163. The MM also states that he will sell or go short in size of upto 5 lots at a level of 168 - the big numbers of 16 are not repeated.

When the IB trade they "hit the bid" to sell at 163 (MM therefore buys at 163) and "lifts the offer" to buy at 168 (MM therefore sells at 168)

Suppose DK is the MM and PH is the IB and PH sells at 163 in 5 lots. Two tickets are therefore created by each counterparty. They look like the image to the side:-

The Second pack

The second pack is a set of 100 cards that have number that are 10 * normal(0,1) distributed. It is important to come up with a distribution that sum is zero so that it is neutral. The example below has the additional restriction that there are no zero cards, thought this is not really necessary.

15, 12, 8, -20, 15, -5, 4, 4, 8, -4, -5, 8, -11, -1, 16, 2, 7, -15, 5, 12, 21, -2, -10, -11, -14, 11, -7, -4, 11, -14, -3, 6, -5, -6, -25, -8, 20, -17, 19, 4, 3, 2, 21, -11, 1, -10, -15, 14, 4, 10, -5, -19, 1, -9, -13, 15, -6, -7, -4, 7, -8, 16, 11, -2, 16, 10, 5, 14, -16, -1, 7, -1, -19, -13, 8, 14, 4, 7, 7, -4, -3, -4, -9, -6, -15, 6, -7, -6, -1, 2, 9, -15, 9, -11, 4, -3, -5, 6, 10, -16

The distribution of the sum of six cards provides a zero mean and a standard deviation of around 25.

Overview of Bar Bill Trading

Bar Bill Trading Game

The purpose of the game is to simulate the functions of four participants in a financial trading market – market-makers (MM), Locals (LT) investment bankers (IB) and Mr Big hedge-fund clients (HF). The game works with one MM, two locals, four IB and two HF.
For 21 people, the split is 1 MM, two LT that create a trading Pit, 3 in each IBs to create four banks and have 3 in each of the 2 HF. At this stage, it is advisable for someone to organise an exchange to settle the trades and keep track of open positions and PL. If someone is tracking positions and PL, it must be kept confidential.
All groups are trading contract for differences (CFD) whose final level is based on the sum value of the 14 cards that are chosen from two packs of cards. The first pack of cards is numbered 1 to 40. Each IB receives two cards which only they can see. The MM and MB do not receive any cards and are therefore blind.
The second pack contains 100 cards that have been selected from a standard normal distribution multiplied by 10 – note they can be positive as well as negative. The MM chooses six cards and places them face down in the centre. These cards are blind to everyone and make up the 14 cards that will define the closing price.
All participants now trade CFDs on an underlying that is defined as the sum of the 14 cards which are revealed once all trading has ceased.
The roles for each participant are:-
· The MM makes a fixed three point spread at all times, his incentive is to avoid losing money and therefore his role is purely price discovery on where the market can operate at an equilibrium – as many buyers as sellers. Any money he makes goes towards the Bar Bill and any money lost comes out of his pocket.
· The LT join the MM to form the pit. They trade on their own account and are not required to show a two-way price if asked. They show prices inside the spread shown by the MM on where they can buy or sell. They can deal with IBs only if their price is better than the MM or when the MM prefers to split an order. The LT trade also with the MM but not the HF.
· The IB uses the proprietary information represented by the two cards and trades with the MM, LT and of course their all-important HF client. The IB shows private or sealed prices to the HF at a maximum of five point spread but in much greater size than is available from the MM.
· MB receives quotes from each IB during each session and trades in large size with them. The only condition is that at the end of the game, the HF’s position is flat.
Eight trading sessions:-
· The MM first makes a three point two-way market for the contract on which all IB have to trade upon, minimum trade size is £1 a point and maximum is £5.
· The MM will continue to make further markets until all trading activity has ceased. IBs are not required to trade on this further activity
· During the second phase, each IB shows a sealed quote to HF for £10 a point, the spread can be no wider than five points, trading priority is given to those who provide the narrowest quotes
· Once the HF has concluded his deals with the IB and all activity between IB and the Pit has stopped, the MM rings the bell and the trading session ends. At this point all trades are reconciled on price, trade size with the exchange.
· Just before the next trading session starts the MM turns over one of the six cards that are facing down. This simulates the dissemination of new information into the market.
· Once all cards are turned over, each IB takes a card from the IB sitting to his right. This simulates the action of traders moving jobs and taking their knowledge with them. At this stage, the IB must now show prices to each HF in order to liquidate their positions. This can be no more than 5 points away from the last bid-ask quote from the MM.
· The HF can choose not to liquidity with IB and instead deal with the Pit. The HF must now liquidate outstanding position with the Pit. The IBs are not required to reduce or close out their outstanding position.
· At the end, all 14 cards are overturned and the settlement price is calculated by taking the sum. All losses from IB, HF, LT and MM are paid out through a single settlement; all gains from MM are transferred to the Bar Bill pot.

Welcome to Bar Bill Trading

Bar Bill Trading is a simple game that simulates the functions in the financial markets. The key to the game are:-

1) Trade a contract for difference - make prices, trade, settle and closeout. This may seem simple but believe me not everyone finds it easy

2) Execute trading and pricing strategies based on asymetric information. Each of the participants has different proprietary informtion, different functions and hence different incentives

3) Trade contracts to make money, or to avoid heavy losses

The purpose of the blog is to introduce the game to current and future users, provide resources and to open up the blog to users in order to enhance the rules and structure of the game. There will also be a number of numerical analysis either done using Excel or Mathematica.

The game has gone through a couple of iterations and had a successful v 3.0 outing so I am now comfortable that we have the basics in place. As mentioned, there is always room for improvement so open feedback and dialogue will be welcome.

Thank you for taking an interest and best of luck. Who knows we might develop this into a league!