An Extended Petri Net Based Approach for Margin Requirements Model in the Crude Oil Futures Market

www.seipub.org/ff Frontiers in Finance Volume 1, 2015 doi: 10.14355/ff.2015.01.010

An Extended Petri Net Based Approach for Margin Requirements Model in the Crude Oil Futures Market Qing Zhou *1, Yixian Liu 1 School of Business Administration, China University of Petroleum‐Beijing, 18 Fuxue Road, Changping, Beijing, China *1

fengdan2013@hotmail.com

Abstract In the international oil market, the virtual demand could have a significant impact on the international oil price. The oil price formation mechanisms have gradually changed as oil futures prices are regarded as a basis from pricing by OPEC. The marginʹs influence on the fluctuation of price and market efficiency is still a controversial and urgent issue. In this paper we combine modelling ideas, and use Petri Net modelling techniques to establish a crude oil futures market trading model, then to develop the simulation program which is based on swarm platform. While by simulating the different margin ratio, the crude oil price fluctuations are analyzed. From the result of the simulation we should conclude that the lower the margin ratio is, the greater the fluctuation of oil prices is produced, and the more unstable markets will be.

Keywords Petri Net; Crude Oil Futures Market; Multi‐Agent Model; Complex Adaptive System

Introduction In recent years, the international crude oil price fluctuates highly. Volatility of oil prices has brought risks and challenges to the world economy, and has a significant economic impact on oil producers and consumers. As a commodity, the price of oil is firstly affected by supply and demand, meanwhile fluctuates up and down around the value of crude oil. But at the same time, the oil has special attributes such as the monopolization and scarcity from the inconsistency between source area and destination, the rigid demand and short‐term irreplaceability caused by sunk costs, irrefragable of oil, etc. This particularity determines the formation of oil prices will be affected by many other factors. It is difficult to accurately quantify all the factors which are intertwined with each other to form the complex oil price system.

Virtual demand’s influence on oil prices is becoming more and more important among many factors. Oil price’s formation mechanism has been gradually transformed to put oil futures prices as a basis from pricing by OPEC. On the crude oil futures market, speculators’ buying and selling of crude oil futures contract actually formes an additional demand and supply of virtual oil, which directly affects the oil price of future of oil trading in the real.

Chicago Mercantile Exchange announced that U.S. crude oil futures margin will increase by 25% on May 10, 2011.

Looking back into the past, CME has increased margin of crude oil futures for three times, including October 30, 2007, August 6, 2008, and March 6, 2011.

Some scholars believe that margin’s influence on the fluctuation of price and market efficiency is still a controversial and urgent issue. “Mr Zeigler, vestas, hart, mark, Gerhard Wu considered that the change of the deposit and deposit caused traders great cost.ʺ The results show that both the number of contracts that all traders hold and the number of speculators and hedgers have a negative correlation with margin.[1].

Agent-Based Financial Simulation Model Agent‐Based Computational Finance is the application of CAS theory in the financial field. Agent‐Based financial

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simulation research combines the micro traders and the macro properties of market organic which refers to the research about market participants behavior rules and patterns in Behavioral Finance, and regards the evolution of financial markets as a nonconstant and dynamic complex adaptive system to study.[2] ASM model regards the financial market as a complex adaptive system for the first time and it adds the concepts of bounded rationality, adaptation, nonlinear evolution . In addition, ASM model uses the method of computer simulation to study the microscopic explanation behind the financial market macroscopic phenomenon and initiates the Experimental Finance. [3] In the multi‐agent model of stock trading established by Hokky Situngkie and Yohanes Surya in 2004, the agent was divided into three categories and added chartist traders on the basis of the traders of principle and noise traders, this kind of agent trading is used to analyze the historical data of stock market and chart to predict the trend of stock price .[4] The financial market model based on multi‐agent built by Lux and Marchesi using the method of computer simulation shows the financial markets as a endogenous dynamic system have three kinds of random attributes.[5] Marco and others design agents are equipped with various of heterogeneous behaviors and study the trading of single stock. The simulation results also show the sharp peak and heavy tail phenomenon in income distribution and the clustering appearances of market volatility.[6] There are many research outcomes about the financial markets using simulation method based on agent. This paper refers to the Artificial Stock Market model of SFI, at the same time, according to the characteristics of the futures Market itself, and adds hedgers’ close position of delivery and spot trading and inventory behaviors on futures Market; the crude oil futures market operation model is established according to ideas of the complex adaptive system modelling and is combined with advanced Petri net modelling techniques. The model includes two categories, environmental (crude oil futures market) and traders agent, as shown in Fig. 1. We divided the trader agent into three types, including non‐commercial traders, business traders (spot suppliers) and commercial traders (spot contractors) according to the different nature of traders. Non‐commercial traders just participate in the futures market trading, but donʹt involve in the prompt goods delivery.

FIG. 1 TOP‐LAYER MODEL OF CRUDE OIL FUTURES MARKET

Execution Layer Model Non‐commercial traders executive model diagram is shown as figure 2. Non‐commercial traders work out trading decisions (TF1) according to the price information (PW1) and the current conditions of assets (including cash, margin account and the amount of futures) (PW2) after receiving the futures price information (PW1) on the market, and thus form the order (PW3) and issue it. Then non‐commercial traders hold off on margin (PW34) calls (TG11) according to contract information (PW32) from the trading market, margin calls instruction (PW33) and the conditions of assets (PW2). Close position is decided and the income and changes of assets are calculated (TG14) after receiving the close position instruction (PW40) of market.

Trading decisions (TF1) is a transition; the specific decision‐making process of replacement is shown as figure 3.

Non‐commercial traders calculate (TR1) the expected price (PW6) and decide on trading behavior (PW7) according

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to the futures price information (PW4), earnings information (PW5) and the rules (PR7). They can calculate(TG1) price (PW9) on the basis of expected price(PW6) , then calculate (TG2) futures trading volume (PW10) on the basis of the rules(PR1) according to the trading behavior (PW7), the expected price (PW6) and the current conditions of assets (PW8) and combine with price (PW9) to form (TG3) orders (PW11) and issue it.

FIG. 2 EXECUTION LAYER MODEL OF NON‐COMMERCIAL TRADERS

FIG. 3 TF1 TRADING DECISION OF NON‐COMMERCIAL TRADERS

Parameters and Variable Settings of Non‐commercial Trades (1) Attribute Variables: The attribute variables Settings of non‐commercial transactions are shown as table 1.

(2) Parameters: e previous expected price error; r1 ROC of the noise traders expected price; r2 ROC of speculators price based on the current futures price; ……

TABLE 1 ATTRIBUTE VARIABLE OF NON‐COMMERCIAL TRADES

Variable Tag

Appearance (in Palatino Linotype) Definition

Variable

Definition

Number of cash demander;

AVF1

Long‐term moving average futures price;

Day

Current date;

AVF2

Short‐term moving average futures price;

Day0

Contract date;

AVS1

Long‐term moving average cash price;

Day1

Time interval of rules changed by traders;

AVS2

Short‐term moving average cash price;

FD

Futures demand of non‐commercial traders;

QP

Quotation price;

……

……

……

……

Behavior Rule of Non‐commercial Traders Non‐commercial trader’s behaviors mainly contain order decision (TF1), margin calls (TG11), close position and calculate earnings (TG14) three parts. As a transition, order decision (TF1) includes four behaviors such as expected price (TR1), count price (TG1), calculate volume (TG2), and place an order (TG3).

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1) The Expected Price (TR1) In this behavior, non‐commercial traders calculate expected prices of futures (Pt+1) and decide whether trade or not, buy or sell futures. With the reference for classification of financial market traders, we can divide traders into three types: basic value analysis traders, trend analysis traders and noise traders. Three types of traders account for 50%, 40%, and 10%, and calculate the expected price by different methods respectively.

The first kind: basic value analysis traders. They investigate the discretion of the futures market based on their rational expectations on spot prices, and thus make futures trading decisions. Their rational expectations on cash price will be adjusted with the market changing. The specific rule setting is shown as follows: Pstd  AVS2  e Pt 1  Pstd

(1) (2)

Pstd is the psychological benchmark price of traders, AVS2 is short‐term moving average cash price, e is

previous expected price error.

The second kind: trend analysis of traders. Their trading rule is the simple moving average rule. According to the current futures price trend, they buy futures when short‐term moving average is less than long term moving average ; on the contrary, when short‐term moving average is greater than the long term moving average, they sell futures. The computational formula of expected futures price is: Pt 1  Pt （AVF2 -AVF1）/AVF1 (3) AVF2 is Short‐term moving average futures price, AVF1 is Long‐term moving average futures price.

The third kind: noise traders. They make futures trading decisions according to the noise information that they have gained and their trading behavior is randomness as a whole. Therefore, we assume that the noise traders forecast price rise and fall on the basis of a setting probability and decide their trading .The computational formula of expected futures price is: Pt 1  Pt  r1 ,

r1 （0.9，1.1） (4)

r1 is ROC of the noise traders expected price.

Traders decide their transactions after calculating the expected price. Buy futures when Pt 1  Pt ; no futures trading when Pt 1  Pt , sell futures when Pt 1  Pt .

So in a similar way, these behavior rules, such as TG1 (Calculate the bidding price) and TG2 (calculate the trading volume) etc., should also be designed.

Analysis of Simulation Result According to the model in the crude oil futures market which is based on the Multi‐Agent, we implement the model on swarm platform by Java from the object‐oriented program design perspective.

After the model’s program implementation on swarm, related parameters can be set according to the objective of this experiment, run programs and then the data can be generated such as the virtual crude oil futures market prices, funds, trading volume, gains and so on and show or output to files by graph. The data and graph are updating constantly with the running of the simulation program. In this study, we made many simulation experiments by changing the market initial margin ratio, and analyzed different deposit system’s influence to the operation of the market.

In order to study the influence of different ratio of margin on the crude oil futures market’s stability, we set different initial margin ratios to analyze the fluctuation of futures prices of market under different margin ratio.

The total capital of the initial market is set as $60000000000 were randomly assigned to each trader. On the premise of all other conditions which are the same, we set the margin ratios as four cases 10%, 5%, 1% and 0.5% to get different futures price time sequence diagrams and analysis comparatively.

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(1) Set the initial margin ratio as 10%. The program runs 400 times, and results of futures price are shown in fig. 4 (unit: US dollars / barrel). The results are obtained in the SQL Server Database, calculating the value and variance of futures price in the database. We can get that the minimum value of futures price is 78.3 and the maximum value is 83.5, the variance is 1.72.

(2) Set the initial margin ratio as 5%. The result is shown as fig. 5. It worked out that the futures price’s minimum value is 77.1, the maximum value is 84.7 and the variance is 3.51.

FIG. 4 SIMULATION RESULT OF FUTURES PRICE WHEN K=10% FIG. 5 SIMULATION RESULT OF FUTURES PRICE WHEN K=5%

(3) Set the initial margin ratio as 0.5%. The result is shown as fig.6. It worked out that the futures price’s minimum value is 66.5, the maximum value is 85.2 and the variance is 18.9.

FIG. 6 SIMULATION RESULT OF FUTURES PRICE WHEN K=0.5%

We can see the growing variance between the futures price’s maximum and minimum and the variance increases gradually with the reduced margin ratio by comparatively analyzing the running results of the futures price under the above four margin ratio. It can be explained that the lower margin ratio is, the stronger leverage effect is caused and the greater volatility of futures price is produced, the greater risk of market in the futures market will be.

Conclusions The setting of the margin of the crude petrol futures market must be careful. As the credit guarantee of the performance of traders, the margin of oil futures market is a kind of commitment that traders promise to buys or sells futures and it’s the collateral to sign futures contract. At the same time, margin should be regarded as recompense for traders to pay off the profit and loss. On the one hand, margin leverage has increased the efficiency of the oil future market; on the other hand, it will increase the market risk and cause the increase of the petroleum futures price’s volatility which is not conducive to the stability of the futures market. We can see from the result of the simulation that the lower the margin ratio is, the greater the fluctuation of oil prices is produced and unhealthy of the market will be. Therefore, it’s necessary to choose reasonable margin level and to design the margin system carefully.

REFERENCES

[1] Chatrath, Arjun; Adrangi, Bahram; Allender, Mary. The impact of margins in futures markets: evidence from the gold and silver markets.[J] Quarterly Review of Economics & Finance;Summer2001, Vol. 41 Issue 2, p279.

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[2] GAO Bao‐jun, DAI Hui, XUAN Hui‐yu. An Agent‐based Stock Market Simulation Model [J]. Systems Engineering‐Theory Methodology, 2005 (12) .

[3] HU Gui‐fang. Simulation of Herd Behavior in Stock Market.[D] Xiang Tan University, 2007.

[4] Hokky Situngkie, Yohanes Surya. Agent‐based Model Construction In Financial Economic System.[D] http://cogprints.org/3767/1/hokky_new2004.pdf: 2009‐8‐15.

[5] Lux T., and M. Marchesi. Volatility Clustering in Financial Markets: A Micro‐Simulation of Interactive Agents.[J] Nature,1999:397‐498.

[6] Marco Rabertoa, Silvano Cincottia, Sergio M.Focardib, and Michele Marchesic. Agent‐Based Simulation of a Fnancial Market[J]. Physica, 2001 , A 299:319‐327.

[7] Zheng Wang1 and Jingling Zhang. Agent‐Based Modeling and Genetic Algorithm Simulation for the Climate Game Problem. Mathematical Problems in Engineering.[J] Volume 2012, Article ID 709473.

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