Initial Public Offering (IPO) pricing using a multi-agent system

Badiâa Hedjazi Information Systems Division

CERIST Research Center5 Rue des Frères Aissou Ben Aknoun , Algiers, Algeria

badiaa.hedjazi@yahoo.fr

Mohamed Ahmed-Nacer Information Systems Laboratory

USTHB University BP 32 El Alia 16111 Bab Ezzouar, Algiers, Algeria.

anacer@cerist.dz

Samir Aknine LIRIS, Université Claude Bernard Lyon

LIRIS UMR 5205 INSA de Lyon, Campus de la Doua,

Bâtiment Blaise Pascal, 20, Avenue Albert Einstein

69621 VILLEURBANNE CEDEX France samir.aknine@univ-lyon1.fr

Karima BenatchbaESI, National high School of computer science,

BP 68M OUED SMAR, El-Harrach, Algiers, Algeria benatchba@yahoo.fr

Abstract—Open complex systems such as financial markets evolve in highly dynamic and uncertain environments. They are often subject to significant fluctuations due to unanticipated behaviours and information. Modelling and simulating these systems by means of multi-agent systems, i.e., through artificial markets is a valuable approach. Initial Public Offering (IPO) is a process based on finding a reasonable offering price or the price of the first assets sale by a firm to public. The study of the firms' strategic choices at the IPO requires the use of formal tools like game theory. This article is about the study, analysis and simulation of a firm's dynamic evolution at IPO using the EGT (Evolutionary Game Theory) as a formal framework for IPO strategies (offering prices) through modeling a financial market by multi-agent system. The firm in the system is a cognitive agent built around a classifier system. Simulations with our prototype allow us to deduce the factors that cause IPO underpricing.

Financial market; multi-agent system; evolutionary game theory; initial public offering (IPO); underpricing; classifier system

I. INTRODUCTION

Many financial studies have examined IPO anomalies [11][12][13][14][15]. These studies are based on analytical, mathematical or statistical methods that do not allow the IPO to be satisfactorily explained. This lack is due to the fact that financial markets are complex systems and evolve in uncertain environments. Multi-agent systems (MAS) technology allows modelling, simulating and better understanding the financial markets [1][2]. Classifier systems (CS) [3] [4] are powerful tools to model economic agents adaptability. Our work is the development of an artificial financial market [5] to study the factors influencing firm's IPO underpricing and to support firm decision to go public and to continue selling its shares after the IPO or not depending on the financial factors and the other market participants (investors, ...). The main objective of our contribution is to determine the degree of influence of each

factor on the asset's underpricing at IPO and consequently the reduction of IPO underpricing by eliminating the founded risk factors. In Section 2 of our paper, we present IPO, IPO underpricing and the application of evolutionary game theory in IPO pricing process. Section 3 presents various works on underpricing at IPO. Section 4 is devoted to our model and Section 5 to implementation and simulation results. We conclude in Section 6 with some research prospects.

II. EVOLUTIONARY GAME THEORY FOR IPO The IPO is the first listing of firm assets on a financial

market. This process allows firms or their shareholders to raise capital to support new investment, reducing debt, enhancing partnerships or increase awareness of the firm. IPO involves the assistance of an "investment bank" known as "underwriter" to sell firm assets to the public. The common and most utilized procedures include direct admission, fixed-price offer, minimum-price offer, open-price offer (OPO) [6]. OPO is the most commonly used procedure for calculating the asset's theoretical value which corresponds to the average price and calculated as in equation (1):

Average price = ∑ (proposed prices x proposed quantity) / number of shares (1)

Assets underpricing (undervaluation) and firms' underperformance during IPO [7] occur when the minimum offering price at IPO is less than its theoretical value.

The IPO process requires for firms formal and powerful tools as the EGT [8] that allow them to choose the best strategies depending on the other market participants' choices. Game theory studies antagonistic strategies. A game is defined by: G=<N, S, U>, where N is the set of players, S the set of strategies and U the utility function. Each strategic choice of a player has an impact on the earnings of another player. When game theory is applied to study investment

2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology

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DOI 10.1109/WI-IAT.2012.151

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strategies, buyers and sellers represent the players, and the rules represent investment strategic choices. This theory assumes rational players in interaction. Due to beliefs, information level and players’ subjectivity, rationality concept cannot be reached. Evolutionary game theory avoids this problem basing its approach on the hypothesis that lasting strategies in games are those obtaining best profits. IPO market and firms success can be thought of in terms of game theory [9][10]. Firms decide to issue their assets through IPO when there are positive market conditions. But these conditions may only be confirmed through the forecast of the other market participants and especially the investors' behaviour.

III. RELATED WORK

The IPO underpricing has been studied in many works to find the factors causing underpricing. It was studied in the Tunisian context [11] through the measurement of initial returns of listed firms and the determination of a set of factors (age, activity sector, confidence, etc.) identified as critical in explaining the underpricing level. Geraldine Broye and Alain Schatt [12] have shown that financial information (when asymmetry: managers against investors) and the choice of intermediaries who certify and monitor this information are among the ways that reduce uncertainty and therefore the underpricing. A credibility problem remains however, that intermediaries can be suspected to favor their interests over those of investors. Ann-Kristin Achleitner [13]presented the ISI (IPO Sentiment Indicator) which has two components: the underpricing sentiment and the IPO climate.ISI takes into account the undervaluation sentiment (underpricing sentiment, USI) and the IPO climate corresponding to the survey of market. But ISI indicator lacks precision because it is calculated from subjective data. Radhouane Kammoun and Sabrina Khemiri [14] have stated assumptions on the hierarchy of debt in a context of information asymmetry to mitigate the undervaluation. This work lacks empirical studies and poses constraints on firms that diverges them from their objectives. David Quintana et al [15] proposed a classifier system that predicts the closing price based on seven classic variables. This model although it shows the effectiveness of classifier systems, presents astatic environment that is not the case of a financial market where the behaviour of firms also depends on the behaviourof the other market participants. In models [9] and [10] the authors used game theory to study IPO process. In [9] the authors used game theory and fuzzy logic to optimize the IPO pricing and in [10] the authors showed the relationship between the offering price and venture enterprises reputation. The previous works have studied the problem of underpricing based on surveys and therefore subjective and unrepresentative or mathematical analytical methods that cannot identify the entire system (consisting of strongly interacting entities) by mathematical equations. These works are limited by the difficulty to take all the factors influencing underpricing in simple equations. Therefore, we model our system by using multi-agent technology.

IV. MULTI-AGENT SIMULATION MODEL

Any artificial financial market model is structured around three main components: the market, the agents that compose it and the external world [5]. Our model focuses on the study of firms underpricing during IPO. The factors influencing the underpricing are of three categories: (1) Factors based on the information (good, bad, true, false) exchanged between investors and the other market participants or related to noise investors using noise rather than relevant information. (2) Factors related to firm behaviour such as optimism, pessimism, confidence, size (small, medium, large) or reputation as well as of investment banks (reputation, experience). (3) Factors related to the market itself as IPO process and market quality (liquidity, performance). In our model we have the market institution that manages real-time transactions, the investors who provide funding, and a firm going public (Figure 1). The investors offer their prices for trading assets, and the firm decides on its IPO and its subsequent investments.

Figure 1. System representation.

Our system is built around a MAS consisting of a firm agent, a market agent and investor agents accessing to a database (DB) containing all data on the firms and the market. The firm agent uses its Classifier system to decide its IPO and the number of assets being sold. If launching IPO decision, the firm agent sends to market agent the number of shares being sold. Investor agents begin to offer their prices to the market agent who calculates the average price and sends the result to the firm agent that in turn calculates its performance for this transaction.

A. Market agent The market agent represents the market institution and

has the following main tasks (Figure 2.): (1) Receiving the number of shares that the firm wants to place in the market. (2) Receiving investor agents' proposed prices. (3) Calculating (with OPO) the investor agents' assets average price. (4) Performing Transactions with the average price. (5) Saving persistent data in Database as the simulation results.

Market DB

InvestorsIn

Parametrization

Informations

Simulation results

InformationMarket institution

Firm

Investment bankers and market

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Figure 2. Market agent features.

B. Investor agents These are agents who buy and sell shares. We are

interested in criteria: type (noisy, ordinary), capital and offered price. An investor agent is a reactive agent and has the following tasks: (1) Propose a price for the firm assets to the market agent. (2) Send the number of shares (to buy or sell) to the market agent.

C. Firm agent The firm agent is an agent that makes IPO decision and

assets placements decisions. It's a cognitive agent and built around a Classifier system (CS in Figure 3) allowing it to learn from past experiences to improve its performance. Classifier systems had many applications in creating artificial financial market and especially for constructing the reasoning model of investor agents [16], [17], but were not used to treat the problem of underpricing at IPO. In our model and for the strategic IPO decisions of the firms, we combine a repeated game with an eXtended Classifier System (XCS) [3]. The choice of XCS classifier systems instead of LCS or ACS for example is justified by the fact that they are very suitable for modeling economic systems and especially the firms' adaptability in dynamic markets. This has been demonstrated and well explained in the work of Lilia Rejeb [19]. The strategies of the game correspond to the possible proposed prices. The reward function depends on the introduced parameters, which are the Classifier system message corresponding to the evaluation of the current condition part of a rule with the introduced parameters (1), the utility function of one iteration of the game (2), the gain or loss of the previous iteration (3) and the value of the action part of the selected rule of the current Classifier system cycle (4). The advantage of this design is to make the decision of the firm more efficient. The influence of these parameters on the reward in formalized in equation (5).

Figure 3. Firm agent internal architecture.

The firm agent has the following tasks: (1) Assets pricing based on EGT to propose optimal offering price on the market. (2) Sending to the market agent the number of shares and the optimal offering price. (5) Receiving the average price from the market agent. (6) Decision making for the IPO through its Classifier system (6) Calculating performance: when the firm agent decides to sell shares, it calculates its performance corresponding to the gain or loss from this transaction as in equation (2):

Performance = Average price – Optimal offering price (2)

An optimal offering price is generated by one game stage (iteration).

� If Performance > 0 then overpricing. � If Performance = 0 then non underpricing. � If Performance < 0 then underpricing.

1) Classifier system of Firm agent

The Classifier system (CS in Figure 3) of Firm agent is of XCS type [3]. A classifier is a rule consisting of three parts:

condition, action and fitness.

a) Condition part:

Firm type: Coded on 2 bits. There are three types of firms (small, medium, large) according to their capitals, their activities and their activities fields. Firm behaviour: Coded on 2 bits and gives the firm behaviour which can be: optimistic, pessimistic, slightly optimistic, slightly pessimistic.Confidence: On 2 bits. Is the firm's confidence (low,medium-low, medium, high).

Firm Set of Investors

Number of assets

Financial investment

Transactions

Assets proposed

Calculate assets average i

Save / extractdata

Database

User

Market

Assets number Average price

IPO decision Parameters

CSRules:

R1R2…Rn

Prepare CSmessage

Reward

Define price(by game theory)

Calculategain

DB

Noise agents

Information

Overconfide

Forecast

Behaviour

Type of firm

1

2 3

4

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Forecasts (FQ): Coded on 2 bits. It corresponds to forecasts quality (bad, less bad, less good or good) and depends on profits at time t compared to expected benefits. FQ is in the interval [0, 1]. If FQ in [0, 0.25] (bad), coded 00. If FQ in [0.25, 0.5] (less bad), coded 01. If FQ in [0.5, 0.75] (less good), coded 10. If FQ in [0.75, 1] (good), coded 11.

Noise investors rate (NR): The noise investors can influence firms and expose them to great losses (underpricing). NR corresponds to the number of noise investors compared to total number of investors in the market. NR is calculated as follows (3):

NR = NbrN / NbrI (3)

Where: NR : Noise investors rate and in the interval [0, 1] ;NbrN: Number of the noise investors in the market. NbrI: Number of investors in the market. If NR in [0, 0.1] (low), coded 00. If NR in [0.1, 0.25] (medium-low), coded 01. If NR in [0.25, 0.4] (medium), coded 10. If NR in [0.4, 0.55] (high), coded 11.

Informations: The Information Rate (IR) of the firm depends on the variables:

NbrII: Number of investors that the firm knows their natures (noisy or ordinary).

NbrI: Number of investors in the market. From which: IR= NbrII/ NbrI.IR is in the interval [0, 1]. If IR in [0, 0.25] (low), coded 00. If IR in [0.25, 0.5] (medium-low), coded 01. If IR in [0.5, 0.75] (medium), coded 10. If IR in [0.75, 1] (high), coded 11.

Asset price: This factor is based on an evolutionary game allowing the firm agent to propose a price improving its performance relative to the average price for investors. This game is described as follows:

� Players: The firm and the set of investors. � Strategies : Assets average prices. � Utility function: Firm gain or loss when choosing a

strategy and defined as (4):

� f(Si) = Investor_price – Firm_price �����

We assume that X is the optimal price of the firm asset and i, j, k and p are integer values randomly chosen from [1, 20] for the evaluation of prices.

TABLE 1. PAYOFF MATRIX OF THE GAME

Investors strategies

Firmstrategies

Firm/investor X-k X X+p

X-i (X-k)-(X-i) X-(X-i) (X+p)-(X-i)

X (X-k)-X 0 (X+p)-XX+j (X-k)-(X+j) X-(X+j) (X+p)-(X+j)

Example: X=100 and the random values are: (i= 3, j=15, k=7, p=2)

TABLE 2. GAME STRATEGIES EXAMPLE.

Investors strategiesFirm

strategies Firm/investor 93 100 102

97 -4 +3 +5100 -7 0 +2115 -22 -15 -13

After filling the table and calculating the utility function, we calculate the number of positive values, nbrP (including 0) and the number of negative values. If there are more positive values than negative ones, the system returns 1 otherwise it returns 0. This value is used in the input message of the Classifier system. The final asset price (or line strategy in the table) is the one with more positive values. For the example (Table 2) we have: (5 negative values and 4 positive) then the system returns 0 and final price 97.

b) Action part: Coded on 1 bit and corresponds to IPO decision (1) or not

(0). Example: The Classifier system input message:

(small, optimistic, yes, good, 0.38, 0.74, 0) is coded as: 000111010100

c) Reward function: Reward function is used to evaluate the Classifier system rules by updating the fitness of each one (rule). This function depends on IR, NR, FQ, nbrP and the result (gain or loss) of the previous iteration noted, IP. It depends also on the action part (AP) of the selected rule of the classifier system. It is calculated using the formula (5).

Reward = AP+IP+nbrP/9+FQ]/3+NR)-[(IR ����� (5)

9 correspond to the number of values in the game matrix (Table 1 and 2). The rules are rewarded if the forecasts of the firm are good, the difference between information rate and noise investors' rate greater than 0.3 (for example), the number of positive results of the utility function greater than 5, gain at the previous iteration and AP is equal to 1 which means Go to public (positive IPO decision).

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If Reward>= 2 Then Reward=1 Else Reward=0

Examples:

If IR=0. 65, NR =0.35, FQ=1, nbrP = 6, IP =1 Then Reward = 2.09 � Reward=1;

If IR=0.6, NR =0.3, FQ=0, nbrP= 4, IP =1 Then Reward = 1.54 � Reward=0;

V. IMPLEMENTATION AND SIMULATION We have implemented our system with the java

programming language, JADE multi-agent platform and the package XCSjava 1.0 for programming the Classifier system.The Firm agent which is the most important agent in our system can execute several behaviours concurrently. Each behaviour corresponds to a specific task (Figure 4), as the behaviour Proposing_evolutionary_asset_price() or Calculating_performance(). The genetic algorithm (GA) and the Q-Learning algorithm are implemented in the XCSjava 1.0 library. We have introduced our GA parameters values as the population size (number of rules in the Classifier system equal to 100), the genome length or the initial fitness for all the rules.

Figure 4. Firm agent principal behaviours

When launching a simulation, the firm agent and the market agent receive initialization parameters given by the user (firm type, noise investors' rate, etc.). Investor agents are activated. The firm agent uses its Classifier system to decide of its IPO. If IPO decision, Firm agent sends to Market agent assets number to place in market. After receiving this message investors start offering their prices. When the market agent receives all the prices, it calculates the average price and sends it to investor agents and to firm agent which computes its performance for this transaction. The following simulations are made with a number of iterations (periods) equal to 700 and the results show the evolution of the performance (gain) of Firm agent.

On the y-axis we have the gain of Firm agent after its IPO, and on the x-axis the number of iterations.

Simulation 1: Firm Type: small; IR = 0; NR= 0; Firm number= 1; Confidence= no; FQ= bad; Behaviour= pessimistic; Investment Bank number= 1.

Figure 5: Firm agent gain evolution in simulation 1

In simulation 1 (Figure 5) , we note that the firm does not have many IPO decisions (points on the graph) on the market and on 700 iterations; the firm has 32 underpricing (negative values of gain).

Simulation 2: Firm Type: medium; IR=0; NR=0; Firm number=1; Confidence=no; FQ= bad; Behaviour= pessimistic; Investment Bank number =1.

Figure 6. Firm agent gain evolution in simulation 2

Firm agent

Calculating_performance()

Proposing_evolutionary_asset_price()

Setup (); Create initial CS rules of at the beginning of a settlement day

IPO_CS_cycle()

Receiving_investors_average_parice()

GA Q-Learning

CS (rules)

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In simulation 2 (Figure 6), we note that the firm has many IPO decisions and 26 underpricing.

Simulation 3: Firm type : large ; IR= 0.898 ; NR= 0.11; Firm number= 1; Confidence=high; FQ= good; Behaviour=optimistic ; Investment Bank number =1.

Figure 7. Firm agent gain evolution in simulation 3

In simulation 3 (Figure 7), we have a lot of IPO decisions and 20 underpricing.

Simulation 4: Firm type : medium ; IR= 0.7 ; NR= 0.13; Firm number=1; Confidence= medium ; FQ= less good; Behaviour= slightly optimistic; Investment Bank number =1.

Figure 8. Firm agent gain evolution in simulation 4

In simulation 4 (Figure 8), we note that the firm does not have a lot of IPO decisions with 13 underpricing.

Simulation 5: Firm type : small ; IR= 0 ; NR= 0.98; Firm number=1; Confidence= no; FQ= less good; Behaviour=pessimistic; Investment Bank number =1.

Figure 9. Firm agent gain evolution in simulation 5

In simulation 5 (Figure 9), the firm does not have many IPO decisions with 72 underpricing.

Based on these results, we note that: (1) despite the firm type, if the other conditions are bad it does not have positive IPO decision. (2) if the firm is pessimistic, there is a lot of underpricing. (3) If the firm is small, pessimistic, no confidence and no information then there are a lot of underpricing (72). (4) If the firm has no information, no confidence with low optimism then it has few IPO decisions. For example, in the second case where the firm is pessimistic with the others factors in the good state there is a lot of underpricing. To validate this partial result, we can mention a study which was conducted for the Athens stock exchange in 1990 [18]. This study shows that the pessimistic behaviour has an important impact in the underpricing of the firms. In this case, we can propose then that a firm must be optimistic to proceed to IPO operation and to optimistic it must proceed for example to a publicity campaign which is crucial to generate profits at IPO and avoid underpricing. These results show that when it is possible to quantify the impact of each factor on the degree of underpricing it is consequently possible to avoid this underpring. We can note also that the firm agent is able to learn and to adapt to its environment because there are relatively fewer underpricing at the end of each the previous simulations. To validate our results we must also have real data on a number of firms at IPO and to consider their situations (underpricing or not at IPO).

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6 Conclusion

Our simulation model of financial market by MAS focuses on the process of IPO decision making of a firm and its performance in the market. We built our model based on the most important factors for the IPO. Our model allows us to deduce the influence of each factor on firm underpricing and hence its performance. It is intended for managers who want to go public, to finance specialists, financial analysts and / or anyone interested in financial markets and the IPO wishing to observe their functioning and to draw a clearer vision. Our work could be improved by: (1) using architecture based on several cognitive investor agents, (2) by introducing other factors affecting IPO underpricing (3) deducing the values of the IPO factors from agents behaviours by learning and not by introducing them as application parameters as is the case for our present model.

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