Financial risk analysis of real estate bubble based on machine learning and factor analysis model

Abstract

The regional real estate price bubble regulation policy is an external factor for the real estate industry. The effect of real estate regulation is difficult to determine, which is a typical problem of uncertain system analysis and forecasting, and the gray Bayesian network forecasting model is to solve the forecasting problem of economic system subject to external regulation. Based on machine learning and factor analysis models, this paper constructs a real estate bubble financial risk analysis model based on machine learning and factor analysis models. Moreover, starting from the real estate price bubble, which is a hot and difficult issue of the social economy, this paper discusses the causes of the formation of real estate price bubbles and the mechanism of the formation of real estate price bubbles, looks for the importance of policy regulation of real estate price bubbles, and clarifies the functional game model of policy regulation of real estate price bubbles. In addition, this paper uses examples to study the model constructed in this paper. The results show that the model constructed in this paper has a certain effect.

Keywords

Machine learning factor analysis real estate bubble financial risk

1 Introduction

In recent years, my country’s real estate market has developed very rapidly, and the reform of the housing market has continued to advance, and real estate prices have been rising accordingly. In the latest round of housing price fluctuations that began in 2015 and continues to this day, driven by a series of stimulus policies and irrational markets, housing prices in first- and second-tier cities have risen rapidly, followed by third- and fourth-tier cities. In 2016, the real estate market ushered in the high point of this cycle. In the face of the obvious accumulation of bubbles in China’s real estate market, in order to prevent the bursting of the housing price bubble and prevent the systemic financial risks caused by it, the Central Economic Work Conference held at the end of 2016 emphasized that “prevention and control of financial risks should be placed in a more important position” and “while supporting residents to buy houses for self-occupation, more attention should be paid to curbing investment speculative demand, so as to prevent the risk of bubbles in hot cities and the ups and downs of the market.” In October 2017, General Secretary Xi Jinping pointed out in the report of the 19th National Congress of the Communist Party of China that “adhere to the positioning of houses are for living, not for speculation”, which further emphasized the importance of regulating the real estate market. The Central Economic Work Conference held at the end of 2018 further pointed out that “a long-term mechanism for the healthy development of the real estate market should be established, and policies and classified guidance should be implemented according to the city.” Therefore, the development and regulation of the real estate market is undoubtedly a vital part of my country’s current economic development. The development of the real estate industry is highly related to the development of the national economy. The reason is that the rapid development of the real estate market is often accompanied by a large amount of financial capital investment, which makes the national economy highly dependent on the real estate industry. When the real estate bubble bursts and housing prices fall sharply, the adverse effects of real estate credit will spread to the entire society through the financial system, causing distortions in resource allocation, harming the development of the real economy, triggering financial crises, widening the gap between the rich and the poor, and greatly undermining economic development. Japan had a real estate bubble burst crisis in the late 1980 s, which caused a strong impact and serious damage to the economy. This caused the Japanese economy to enter a long-term recession and is still stuck in a quagmire. In recent years, whether there is an asset bubble in my country’s real estate market has become a key discussion topic in the industry. In the past few rounds of housing price increases, with the increasing popularity of real estate speculation, many industrial enterprises have also flocked to the real estate industry to seek speculation, affecting industrial development. In view of the precedent of the real estate bubble in Japan, both academic circles and the industry are concerned, worried and actively discussing whether my country will repeat a similar tragedy. Therefore, it is very necessary to thoroughly understand and fully study the bubble situation in my country’s real estate market, accurately measure the financial risks contained therein, and propose comprehensive, effective and feasible countermeasures [1].

The relationship between real estate bubbles and real estate financial risks has an important position in financial practice and theoretical research. In practice, accurately measuring the size of the real estate price bubble and the degree of financial risk caused by the real estate bubble is the prerequisite for the formulation of housing policies and other macro policies [2]. In theory, clarifying the formation mechanism of the real estate bubble and the influence mechanism of the real estate bubble on the financial risk of real estate helps to understand the relationship between the real estate bubble and financial market stability and economic growth. In recent years, the proportion of property income in my country’s residents’ income has continued to increase, and the role of the financial market in economic growth has become more prominent. However, the current real estate prices in my country are at a high level, and the problem of continuous and accelerating deviation of urban housing prices from basic values is very prominent, which has become an important factor hindering the orderly development of my country’s urban housing market and the structural optimization of the financial system. At present, our country must hold the bottom line of avoiding systemic financial risks in order to deal with the complicated international and domestic economic situation. The issue of increasing price bubbles in the real estate market urgently requires comprehensive and in-depth theoretical analysis and practical research. At present, we need to clarify the theoretical mechanism of the impact of the real estate bubble on the real estate financial risk, accurately measure and test the size of the real estate bubble, propose countermeasures to suppress and eliminate the real estate bubble, prevent and dissolve real estate financial risks, dredge the mechanism that the real estate bubble causes to real estate financial risks, and establish a long-term mechanism to promote the stable and healthy development of the real estate market. These measures are of great significance for the Chinese authorities to accurately understand and accurately grasp the stable operation of the financial market under the current severe background, hold the bottom line of avoiding systemic financial risks, effectively free funds from the virtual and enter the reality, and promote the steady growth of the real economy [3].

2 Related work

The related theory of rational bubble proposed in literature [4] laid the foundation for this research. In addition, foreign scholars’ initial awareness of bubble theory is not based on the real estate industry, but from the stock market. However, there are very few researches on bubbles in the real estate industry. After the outbreak of a large-scale real estate bubble phenomenon in Japan at the end of the 20th century, countries similar to Japan were affected by a severe financial crisis. The outbreak of this incident has caused relevant experts and scholars to shift their attention to the real estate market bubble. The literature [5] believed that a moderate bubble has a positive effect on economic development. The literature [6] put forward the theory of real estate cyclical fluctuations and pointed out how to use the theory of cyclical fluctuations through the investigation of the bubble problem in the western real estate market, collating survey research data. The literature [7] found that the real estate bubble phenomenon and bank financing are closely related to each other through the related research on the financing of various local banks, and the implementation of bank policies has a certain degree of influence on the real estate bubble. The literature [8] through the study of speculative behavior, found that one of the reasons for the impact of house price changes is speculative behavior, and further explained the reason and degree of influence through the method of model construction. The literature [9] analyzed the situation and conditions of Thailand, and believed that if people are overly optimistic about the future situation of the real estate bubble, the generation of the real estate bubble will further accelerate, which is not conducive to the healthy and stable development of the real estate market. The literature [10] measured the real estate bubble in the United States. The results show that the bubble phenomenon in the US real estate market does exist, which is caused by the excessive increase in housing prices. However, the literature [11] reached the opposite conclusion through research. Through data analysis, he concluded that there is no bubble in the US real estate market. The literature [12] extracted data from more than forty cities in the United States1 and found that there is no bubble in the US real estate market. The literature [13] used the income reduction model to analyze and calculate New Zealand’s data. Through the analysis, it is concluded that the real estate market in New Zealand has been overpriced in the past 35 years and there is a bubble]. The literature [14] used the method of measuring the basic value of real estate to conduct a comprehensive analysis of the bubble in the Hong Kong real estate market. The results show that there is a certain bubble phenomenon in the real estate market in Hong Kong. The literature [15] adopted the controlled variable method and took corresponding early warning measures against the real estate bubble phenomenon in the western region. The literature [16] used the vacancy rate of commercial housing to analyze the degree of bubble in the real estate market by comparing supply and demand. The research results show that when the vacancy rate of commercial housing is the same, the information asymmetry between the supply and demand sides will break the existing pattern of the real estate market, promote the rise of housing prices, and generate bubble problems in the real estate market. The literature [17] analyzed the process of real estate bubbles in the United States, Japan, Sweden, Thailand and other countries that developed and burst, and found that bank credit has a profound impact on the development of the real estate industry, and excessive capital inflows into real estate are the direct cause of the real estate bubble. the reason. However, the literature [18] held different opinions. They found that bank credit does not directly affect the real estate market, but indirectly affects it. The literature [19] believed that the price rise and real estate bubble are caused by the imperfections of the housing security system, bank credit system, etc., on the one hand, and on the other hand, it is caused by the rise in land prices, the rise in material prices, the rise in labor costs and other factors that trigger the rise in prices. The literature [20] analyzed the causes of the real estate bubble from a micro level. Moreover, through the analysis of the four aspects of cognitive bias, emotional bias, herding effect, and feedback mechanism, it was concluded that investors’ behavior will be affected by their own psychological factors. The literature [21] analyzed the real estate bubble through a regression model and concluded that the financial attributes of real estate promote the formation of the real estate bubble, but financial products have played a role in suppressing the bubble. The literature [22] used factor analysis to measure and analyze my country’s real estate bubble. Moreover, it selected six indicators to calculate the comprehensive score of the real estate bubble and concluded that the degree of the real estate bubble reflected by each individual indicator varied in the past 13 years. The literature [23] used the index method to analyze the real estate bubble in Hangzhou through the PCA-LP model and selected 7 relevant indicators for analysis.

3 Solving GERT network model based on the interest flow of game subjects

Theorem 1: In the GERT network model of real estate development in the series, the transfer function of the sum of independent random variables is equal to the product of the transfer functions of each random variable.

Proof: It is assumed that node decision i → j and node decision j → k are mutually independent events in the GERT network model of real estate development in series. Equivalent parameters of the GERT network model of the serial real estate development as show in Fig. 1; and Equivalent parameters for real estate development in parallel regions as show in Fig. 2.

Fig. 1

Equivalent parameters of the GERT network model of the serial real estate development.

Fig. 2

Equivalent parameters of the GERT network model for real estate development in parallel regions.

Therefore, there is $M_{ik} (s) = M_{ij} (s) \cdot M_{jk} (s)$ (1)

In addition, because in the GERT network model of real estate development in series. $p_{ik} = p_{ij} \cdot p_{jk}$ (2)

Therefore, there is $\begin{matrix} W_{ik} (s) = p_{ik} \cdot M_{ik} (s) = p_{ij} p_{jk} M_{ij} (s) M_{jk} (s) = \\ p_{ij} M_{ij} (s) p_{jk} M_{jk} (s) = W_{ij} (s) W_{jk} (s) \end{matrix}$ (3)

It can be extended to a GERT network with multiple nodes connected in series, $W_{iz} (s) = W_{ij} (s) \cdot W_{jk} (s) \cdot W_{kl} (s) \dots W_{yz} (s)$ (4)

Theorem 2: The transfer function in the GERT network model of real estate development in the parallel area is equal to the sum of the transfer functions of independent random variables. Equivalent parameters of the GERT network model for real estate development in the self-loop structure area as show in Fig. 3.

Fig. 3

Equivalent parameters of the GERT network model for real estate development in the self-loop structure area.

Proof: In the parallel structure of the regional real estate development GERT network model, it is assumed that the decision realization from node i to node j can be realized through different paths, and the decision realization process is independent of each other. Two mutually independent decisions are a : i → j, b : i → j, the probability of decision a : i → j being executed is p_{a
_ij}, and the probability of decision b : i → j being executed is p_{b
_ij}. At the same time, the probability of two parallel decision activities being realized is, $p_{ij} = p_{a_{ij}} \cup p_{b_{ij}} = p_{a_{ij}} + p_{b_{ij}} - p_{a_{ij}} \cap p_{b_{ij}}$ (5)

Since in the GERT network model of real estate development in parallel areas, only one activity is executed when node i is realized. Therefore, there is $p_{a_{ij}} \cap p_{b_{ij}} = 0$ (6)

That is $p_{ij} = p_{a_{ij}} + p_{b_{ij}}$ (7)

When decision a is executed a : i → j, the moment generating function is M_{a
_ij} (s). When decision b is executed b : i → j, the moment generating function is M_{b
_ij} (s). Because in the GERT network model of real estate development in parallel areas, only one activity is executed once, and the activity of i → j must be realized, the following results are obtained: $M_{ij} (s) = \frac{p_{a_{ij}} M_{a_{ij}} (s) + p_{b_{ij}} M_{b_{ij}} (s)}{p_{a_{ij}} + p_{b_{ij}}}$ (8)

Therefore, there is $\begin{matrix} W_{ij} (s) = p_{ij} \cdot M_{ij} (s) = (p_{a_{ij}} + p_{b_{ij}}) \cdot \\ \frac{p_{a_{ij}} M_{a_{ij}} (s) + p_{b_{ij}} M_{b_{ij}} (s)}{p_{a_{ij}} + p_{b_{ij}}} = W_{a_{ij}} (s) + W_{b_{ij}} (s) \end{matrix}$ (9)

can be extended to the GERT network model of multi-node parallel regional real estate development. There is [24]: $W_{ij} (s) = \sum_{n = 1}^{k} W_{n_{ij}} (s)$ (10)

Theorem 3: In the GERT network model of regional real estate development, the transfer function of the node with self-loop is equal to the transfer function of the direct path connected in series divided by 1 minus the transfer function of the self-loop.

Proof: From Theorem 1 and Theorem 2: $W_{i j} (s) = W_{b_{i j}} (s) + W_{a_{i i}} (s) W_{b_{i j}} (s) + W_{a_{i i}}^{2} (s) W_{b_{i j}} (s) + \dots = W_{b_{i j}} (s) [1 + \sum_{n = 1}^{\infty} W_{a_{i i}}^{n} (s)]$ (11)

Therefore, there is $W_{ij} (s) = \frac{W_{b_{ij}} (s)}{1 - W_{a_{ii}} (s)}$ (12)

Theorem 4: In the regional real estate development GERT network model, if the equivalent transfer function from node i to node j is W_ij (s) , i = 1, 2, ⋯ , m, j = 1, 2, ⋯ , l, then the average increment E [X] of decision information from node i to node j is equal to W_ij (s). After taking the derivative of s, the value of s is equal to the value of 0. The fluctuation variance V [X] of the decision information increment from node i to node j is equal to the difference between the second derivative of W_ij (s) and s, and the value of s equal to 0 and the square of the average increment of decision information.

Proof:

$\begin{matrix} E [X] = \frac{\partial M_{ij} (s)}{\partial s} |_{s = 0} = \\ \frac{\partial}{\partial s} [\frac{W_{ij} (s)}{W_{ij} (0)}] |_{s = 0} \end{matrix}$ (14) $E [X^{2}] = \frac{\partial^{2} M_{ij} (s)}{\partial s^{2}} |_{s = 0} = \frac{\partial^{2}}{\partial s^{2}} [\frac{W_{ij} (s)}{W_{ij} (0)}] |_{s = 0}$ (15)

Therefore, there is $\begin{matrix} V [X] = E [X^{2}] - {(E [X])}^{2} \\ = \frac{\partial^{2}}{\partial s^{2}} [\frac{W_{ij} (s)}{W_{ij} (0)}] |_{s = 0} - \\ {(\frac{\partial}{\partial s} [\frac{W_{ij} (s)}{W_{ij} (0)}] |_{s = 0})}^{2} \end{matrix}$ (16)

According to the GERT network model of regional real estate development, the decision probability of a node is a mapping function of the external environment, as well as a mapping function of decision information between its neighboring nodes, and the restriction constraints come from many aspects. Therefore, it is difficult to directly obtain the optimal decision probability of a node. By exploring the decision-making process of the negotiation game between the node and the external environment and neighboring nodes, a maximum entropy model is established to solve the decision probability of the regional real estate development GERT network model, as shown in the following formula. $\begin{matrix} max F = - \sum_{j = 1}^{m} p_{ij} log p_{ij} \\ s . t . = {\begin{matrix} \sum_{j = 1}^{m} p_{ij} = 1 \\ p_{ij} \in ({\underline{p}}_{ij min}, {\bar{p}}_{ij max}) \\ {\underline{D}}_{i min} ⩽ D_{i} ⩽ {\bar{D}}_{i max} \\ {\underline{p}}_{ij min} = min (\frac{min (x_{ij} (1))}{max (x_{i} (1))}, \frac{min (x_{ij} (2))}{max (x_{i} (2))}, \dots \frac{min (x_{ij} (n))}{max (x_{i} (n))}) \\ {\bar{p}}_{ij max} = max (\frac{max (x_{ij} (1))}{min (x_{i} (1))}, \frac{max (x_{ij} (2))}{min (x_{i} (2))}, \dots \frac{max (x_{ij} (n))}{min (x_{i} (n))}) \\ {\underline{p}}_{i min} = E ({\underline{p}}_{ij min}) \\ {\bar{p}}_{i max} = E ({\bar{p}}_{ij max}) \\ {\underline{D}}_{i min} = \frac{1}{m} \sum_{j = 1}^{m} {({\underline{p}}_{ij min} - {\underline{p}}_{i min})}^{2} \\ \begin{matrix} {\underline{D}}_{i max} = \frac{1}{m} \sum_{j = 1}^{m} {({\underline{p}}_{ij max} - {\underline{p}}_{i max})}^{2} \\ i = 1, 2, \dots, l; j = 1, 2, \dots, m \end{matrix} \end{matrix} \end{matrix}$ (17)

Among them, there is i = 1, 2, ⋯ , l ; j = 1, 2, ⋯ , m. p_ij (k) is the decision probability from the i-th node to the j-th node.

4 Research on GERT network model of regional real estate development

This paper uses the amount of investment funds in various sectors of the real estate industry to characterize the amount of decision-making information. By sorting out the data in the yearbook, this paper obtains the amount of funds invested in real estate in my country’s commercial banks, real estate developers, real estate investors, and real estate rigid demanders from 2015 to 2019, as shown in Table 1.

Table 1
2015–2019 real estate industry total funds table, Unit: 100 million yuan

years Total real estate value Real estate agent’s total investment Total currency held by commercial banks

2015 30987 81766 349060

2016 41707 105718 407476

2017 39241 141390 479919

2018 61251 169021 612287

2019 72874 226061 733032

years	Total real estate value	Real estate agent’s total investment	Total currency held by commercial banks
2015	30987	81766	349060
2016	41707	105718	407476
2017	39241	141390	479919
2018	61251	169021	612287
2019	72874	226061	733032

The probability range of capital and loan allocation decisions of my country’s commercial banks from 2015 to 2019 is shown in Table 2. Among them: P₁₁ indicates the proportion of the amount of funds held by the commercial bank, P₁₂ indicates the proportion of the loan quota of the commercial bank to the real estate developer, and P₁₃ indicates the proportion of the commercial bank’s loan amount to the real estate investor. At the same time, P₁₄ represents the ratio of commercial banks’ loans to rigid real estate demanders, and P₁₅ represents the ratio of commercial banks’ loans to the external environment.

Table 2

Probability range of commercial bank loan allocation decision

years		2015	2016	2017	2018	2019
P11	Upper Bound	0.158	0.216	0.275	0.35	0.319
	Lower bound	0.065	0.097	0.146	0.165	0.162
P12	Upper Bound	0.383	0.404	0.394	0.395	0.377
	Lower bound	0.066	0.087	0.077	0.079	0.06
P13	Upper Bound	0.173	0.162	0.177	0.126	0.124
	Lower bound	0.042	0.036	0.043	0.03	0.03
P14	Upper Bound	0.571	0.713	0.518	0.632	0.604
	Lower bound	0.304	0.446	0.251	0.366	0.337
P15	Upper Bound	0.708	0.679	0.697	0.696	0.714
	Lower bound	0.164	0.134	0.153	0.15	0.17

Table 3 shows the probability range of capital decision-making for Chinese real estate developers from 2015 to 2019. Among them: P₂₂ represents the proportion of real estate developers developing real estate value and the value of reserved undeveloped land, P₂₃ represents the proportion of real estate developers completing investment quotas to real estate investors, and P₂₄ represents the proportion of real estate developers completing investment quotas to real estate rigid demanders At the same time, P₂₅ represents the proportion of real estate developers turning to other industries for investment funds.

Table 3

Probability range of real estate developers’ funding decisions

years		2015	2016	2017	2018	2019
P22	Upper Bound	0.022	0.019	0.018	0.016	0.014
	Lower bound	0.174	0.171	0.17	0.168	0.166
P23	Upper Bound	0.235	0.148	0.136	0.085	0.036
	Lower bound	0.639	0.552	0.54	0.489	0.44
P24	Upper Bound	0.053	0.049	0.048	0.046	0.044
	Lower bound	0.214	0.211	0.21	0.208	0.206
P25	Upper Bound	0.022	0.019	0.018	0.016	0.014
	Lower bound	0.222	0.22	0.218	0.216	0.214

Table 4 shows the probability range of investment decision-making for Chinese real estate investors from 2015 to 2019. Among them: P₃₃ represents the proportion of real estate investors’ own internal real estate value, P₃₄ represents the proportion of real estate investors selling real estate value to rigid real estate demanders, and P₃₅ represents the proportion of real estate investors turning to other industries for investment funds.

Table 4

Probability range of real estate investors’ investment decision

years	P33		P34		P35
	Upper Bound	Lower bound	Upper Bound	Lower bound	Upper Bound	Lower bound
2015	0.104	0.336	0.600	0.933	0.023	0.124
2016	0.064	0.296	0.644	0.978	0.018	0.119
2017	0.132	0.365	0.559	0.892	0.036	0.137
2018	0.091	0.323	0.627	0.961	0.010	0.111
2019	0.087	0.319	0.631	0.965	0.009	0.110

Table 5 shows the variance fluctuation range of each stakeholder decision in the regional real estate GERT network from 2015 to 2019. Among them: D₁ represents the variance of decision volatility of commercial banks, D₂ represents the variance of decision volatility of real estate developers, and D₃ represents the variance of decision volatility of real estate investors. Moreover, D₄ represents the variance of decision-making fluctuations of rigid demanders of real estate.

Table 5

Variance fluctuation range of each stakeholder decision in the GERT network

years	D1		D2		D3
	Upper Bound	Lower bound	Upper Bound	Lower bound	Upper Bound	Lower bound
2015	0.009	0.047	0.008	0.036	0.064	0.116
2016	0.021	0.052	0.003	0.023	0.080	0.136
2017	0.005	0.033	0.002	0.022	0.051	0.099
2018	0.013	0.042	0.001	0.016	0.074	0.129
2019	0.012	0.043	0.000	0.012	0.076	0.131

In order to obtain the optimal ratio of commercial banks to real estate developers’ loan lines, this paper establishes the 2015 decision probability maximum entropy model of commercial banks to solve the optimal ratio and uses Lingo software to solve the optimal ratio. In 2015, the optimal loan quota ratio of Chinese commercial banks to real estate developers was 0.0417, the optimal loan quota ratio to other industries was 0.5283, and the optimal holding fund ratio of commercial banks to maintain the normal operation of banking business was 0.0641. Similarly, the maximum entropy model of decision probability can be used to find the corresponding value for 2007–2019. In the same way, we can similarly find the optimal investment decision ratio of real estate developers from 2015 to 2019 and the optimal decision ratio of real estate investors. The optimal decision probability of the GERT network in the real estate industry from 2015 to 2019 is shown in Table 6.

Table 6

Optimal decision probability of GERT network nodes

years	2015	2016	2017	2018	2019
P11	0.065	0.097	0.146	0.165	0.161
P12	0.066	0.087	0.077	0.078	0.06
P13	0.042	0.036	0.043	0.031	0.03
P14	0.304	0.446	0.252	0.365	0.337
P22	0.174	0.171	0.17	0.168	0.165
P23	0.639	0.552	0.54	0.489	0.441
P24	0.175	0.211	0.21	0.208	0.206
P33	0.104	0.064	0.133	0.09	0.086
P34	0.882	0.927	0.841	0.91	0.914

$\begin{matrix} max F = - \sum_{j = 1}^{5} p_{1 j} ln p_{1, j} \\ s . t . = {\begin{matrix} \sum_{j = 1}^{5} p_{1 j} = 1 \\ 0.064 ⩽ p_{11} ⩽ 0.1 \\ 0.065 ⩽ p_{12} ⩽ 0.379 \\ 0.042 ⩽ p_{13} ⩽ 0.171 \\ 0.301 ⩽ p_{14} ⩽ 0.565 \\ 0.162 ⩽ p_{15} ⩽ 0.701 \\ 0.0093 ⩽ D_{1} ⩽ 0.0461 \end{matrix} \end{matrix}$ (18)

Using the Mason formula in the signal flow graph, the decision information transfer function from node 1 to node 4 is set to W_E, and the connection is drawn from node 4 to node 1. The decision information transfer function is set to $\frac{1}{W_{E} (s)} (W_{41} = \frac{1}{W_{E} (s)})$ (19)

The closed activity is based on the property that the closed network characteristic is equal to zero.

$\begin{matrix} H = 1 - W_{11} - W_{22} - W_{33} - W_{12} W_{23} W_{34} W_{41} \\ - W_{12} W_{24} W_{41} - W_{13} \\ W_{34} W_{41} - W_{11} W_{22} + W_{11} W_{33} + W_{22} W_{33} \\ + W_{22} W_{33} - W_{11} W_{22} W_{33} = 0 \end{matrix}$ (20)

The decision information transfer function from node 1 to node 4 is $W_{E} (s) = \frac{(\begin{matrix} p_{12} p_{23} p_{34} esp (a_{12} + a_{23} + a_{34}) s + p_{14} esp (a_{14}) s + \\ p_{13} p_{34} esp (a_{13} + a_{34}) s + p_{12} p_{24} esp (a_{12} + a_{24}) s \end{matrix})}{(\begin{matrix} 1 - p_{11} esp (a_{11}) s - p_{22} esp (a_{22}) s - p_{33} esp (a_{33}) s \\ + p_{11} p_{22} esp (a_{11} + a_{22}) s + p_{11} p_{33} esp (a_{11} + a_{33}) s + \\ p_{22} p_{33} esp (a_{22} + a_{33}) s - p_{11} p_{22} p_{33} esp (a_{11} + a_{22} + a_{33}) s \end{matrix})}$ (21)

When s = 0, the transfer function from node 1 to node 4 is $W_{E} (s) = \frac{p_{12} p_{23} p_{34} + p_{12} p_{24} + p_{13} p_{34} + p_{14}}{(\begin{matrix} 1 - p_{11} - p_{22} - p_{33} + p_{11} p_{22} + p_{11} p_{33} + \\ p_{22} p_{33} - p_{11} p_{22} p_{33} \end{matrix})}$ (22)

The parameter distribution of the regional real estate GERT network from 2015 to 2019 is shown in Table 7. Among them: A₁₁ represents the amount of funds retained by the commercial bank to maintain its business operations, A₁₂ represents the loan line obtained by the real estate developer from the commercial bank, and A₁₃ represents the loan line obtained by the real estate investor from the commercial bank. At the same time, A₁₄ represents the amount of loans that rigid demanders of real estate obtain from commercial banks, A₂₂ represents the value of unfinished real estate developed by real estate developers, and A₂₃ represents the value of real estate sold by real estate developers to real estate investors. Moreover, A₂₄ represents the value of real estate developers selling real estate to rigid real estate demanders, A₃₃ represents the value of real estate investors who retain the value of real estate in order to obtain more profits, and A₃₄ represents the value of real estate investors selling real estate to rigid real estate demanders. Since the parameter mean and variance in the parameter distribution have little effect on the network’s decision information transfer function, it is assumed that all parameter distributions are constant distributions, the optimal decision of nodes in the GERT network is used instead of parameter settings, and the investment decision value of the real estate industry GERT network is used as a parameter.

Table 7

Parameter distribution of GERT network in real estate industry Unit: 100 million yuan

years	2015	2016	2017	2018	2019
P11	39595	55437	84898	135316	146362
P12	6017	7086	7682	11479	12690
P13	9102	8112	9654	11869	14174
P14	18008	20658	17129	31051	35649
P22	76417	67753	86459	149525	249138
P23	26457	22990	27374	34562	40032
P24	728	829	981	1145	1080
P33	5522	5147	7024	9249	10731
P34	26390	29359	24338	43653	52169

V represents the amount of change for each unit invested in the bank node in the GERT network of the real estate industry after being passed through the GERT network. The average growth rate of real estate value is: $E [V] = \frac{\partial}{\partial s} [\frac{W_{E} (s)}{W_{E} (0)}] |_{s = 0}$ (23)

The fluctuation standard deviation rate of real estate value growth rate is: $\begin{matrix} D [V] = E [V^{2}] - E {[V]}^{2} = \frac{\partial^{2}}{\partial s^{2}} [\frac{W_{E} (s)}{W_{E} (0)}] |_{s = 0} \\ {(\frac{\partial}{\partial s} [\frac{W_{E} (s)}{W_{E} (0)}] |_{s = 0})}^{2} = \frac{\partial}{\partial s} (\frac{\partial}{\partial s} [\frac{W_{E} (s)}{W_{E} (0)}]) |_{s = 0} \\ {(\frac{\partial}{\partial s} [\frac{W_{E} (s)}{W_{E} (0)}] |_{s = 0})}^{2} \end{matrix}$ (24)

Bringing the data in Tables 6 and 7 into equations (23) and (24), the real estate value growth rate and the real estate value growth rate fluctuation standard deviation can be obtained, as shown in Table 8.

Table 8

2015–2019 real estate value realization fluctuations

years	2015	2016	2017	2018	2019
Probability of real estate output scale	0.5555	0.7676	0.5454	0.6969	0.6262
Real estate value growth rate	1.1716	1.1615	1.2726	1.5352	1.4443
Standard deviation of fluctuation of real estate value growth rate	0.021715	0.017776	0.024543	0.026462	0.027876

5 Forecast and analysis of regional real estate development

(1) By comparing and analyzing multiple models, it can be seen that the model proposed in this paper is more reasonable in predicting the development of regional real estate.

The results in Table 8 show that the growth rate of real estate prices is relatively high, all above 1.7, and the growth deviation of the fixed-base growth rate is relatively small. After comparing and analyzing the real estate price growth rate measured by the model proposed in this paper and the actual real estate price growth rate, it is found that the model estimation deviation is relatively small, within 8%. However, the deviation of the price growth rate calculated by the linear regression model is relatively large, and the deviation of the price growth rate calculated by the gray system theory is also relatively large, as shown in Fig. 4.

Fig. 4

Comparative analysis diagram of real estate price growth rates measured by multiple models.

It can be seen from Table 8 that through the regional real estate development GERT network model, real estate value can be successfully estimated. Moreover, the real estate value prediction accuracy is high, and the deviation of the absolute value of the error does not exceed 8%, as shown in Fig. 4.

After that, this paper uses multiple models to predict and analyze the growth rate of real estate prices, as shown in Fig. 5. The growth rate of real estate prices predicted by the regression analysis model is too fast, basically showing an exponential growth, which is basically not in line with reality. The growth rate of real estate price predicted by the gray model GM (1, 1) is above 3.0, so its predicted real estate price growth rate is relatively high. However, the growth rate of real estate prices predicted by the model proposed in this paper is relatively reasonable.

Fig. 5

The annual output value of the real estate industry and the development trend of the annual output value of the real estate industry.

(2) The results of using this model to measure the price growth rate of my country’s real estate in the past five years show that the proportion of people who meet rigid demands in the real estate industry is constantly decreasing. Comparative analysis diagram of real estate price growth rates predicted by multiple models as show in Fig. 6.

Fig. 6

Comparative analysis diagram of real estate price growth rates predicted by multiple models.

The results in Table 8 show that the proportion of people who meet rigid demands in the real estate industry is continuously decreasing, which is consistent with the actual situation. Due to the continuous rise of real estate prices, the rate of increase of residents’ wages is much lower than that of real estate prices, which makes residents’ pressure to purchase real estate continues to increase and reduces the probability of real estate output value realization. After that, this paper uses the model to predict and estimate regional real estate. The results show that in the next few years, the proportion of people meeting rigid demands in the real estate industry will continue to decrease, which also shows that the pressure of Chinese residents to purchase real estate is still increasing, as shown in Fig. 7.

Fig. 7

Proportion of rigid demanders satisfied by regional real estate.

(3) The results of using the model to simulate and predict the future trend of real estate prices in my country show that the growth rate of real estate prices is relatively fast.

The results in Table 9 show that the growth rate of real estate prices from 2015 to 2019 is above 1.7, which is a relatively fast growth rate. Under my country’s current real estate control policies, this paper predicts the growth rate of real estate prices in regional real estate and finds that the growth rate of real estate prices from 2015 to 2019 is still relatively high, all above 2.0. The result shows that my country’s real estate prices will not fall sharply in recent years, and there will still be an upward trend, as shown in Fig. 8.

Fig. 8

The growth rate of real estate prices in our country calculated and predicted by the model.

The government can observe the operation of the real estate industry by exploring the law of real estate price formation. If the real estate value realization probability is too high, it indicates that the real estate development is overheated. At this time, the government can regulate the real estate loan quota of commercial banks, which can slow down the real estate operation. Similarly, if the probability of real estate value realization is too low, it indicates that real estate development is slow. At this time, the government can invest a lot of money in real estate to stimulate the rapid development of real estate. The current state control measures also show that my country has achieved certain results in regulating the operation of real estate according to the degree of easing of commercial banks’ loans to the real estate industry.

We can obtain the influence of real estate developers, real estate investors, and rigid real estate demanders on the realization of real estate value, the growth rate of real estate value and the fluctuation standard deviation of real estate value growth. Moreover, we can obtain a series of values such as the realization of the input and output of different economic sectors in the value of real estate, the probability of investment decision among various sectors, the growth rate of real estate value, and the fluctuation standard deviation of real estate value growth. These values fully reflect the dynamic input and output of the real estate industry, the value appreciation situation and the value appreciation process accompanying the value flow process and provide effective quantitative support for real estate macro-control. The government can predict the annual real estate operations according to the investment plans made by various real estate industry participants at the beginning of each year, and implement control policies through the predicted results, so that the real estate industry can develop in a healthy and orderly manner. The price of real estate contains a deviation from its intrinsic real value, so this kind of shock in real estate prices will affect the healthy development of my country’s economy. In addition, the complexity of the real estate bubble issue puts forward higher requirements for the pertinence of government policy regulation, the forward-looking nature of policy regulation, and the controllability of its effect. It is necessary to suppress the expansion rate of the bubble, effectively eliminate the bubble, and maintain the rapid and stable growth of the regional economy.

We need to consider that the essence of the policy’s hedging effect on the economic bubble in the GERT network is the reconfiguration of related resources in the network and consider how each stakeholder can readjust its trading strategy from the perspective of maximizing their own interests. We need to study the dynamic characteristics of the transaction strategy selection behavior, target attributes, mutual imitation and learning of a certain node(s) in the network after being hedged by the policy. factor. Moreover, we need to divide the policy effect and its follow-up process into different stages based on some of the fluctuation characteristics and laws it exhibits. In addition, we need to study the objectives of each game subject at different stages of the role of these hedging policies and their related resource constraints and mutual constraints, and establish a multi-stage, multi-objective planning model. Finally, we need to study and reveal that the upper-level multi-objective planning plays a leading and standard role in the lower-level multi-objective planning in the game multi-objective planning model. Moreover, the lower-level target planning also plays a feedback role to the higher-level target planning, and the multi-target planning at the same level influences and restricts each other.

6 Conclusion

Starting from the real estate price bubble, a social and economic hotspot and difficult issue, this paper draws on existing research results to explore the causes of the real estate price bubble and the mechanism of the real estate price bubble. Moreover, based on the GERT network model, this paper analyzes the importance of regional real estate policy regulation and functional game research on regional real estate policy regulation. In addition, based on the real estate price bubble evolution GERT network model and control policy analysis and research as the main line, this paper sets the parameters of stakeholders and their relationships. Finally, this paper studies the causes of economic bubble formation, the mechanism of economic bubble formation, the key points of bubble policy, and the effect of policy control.

In the entire national economic system, real estate is an important component. They are not only partly and integrally related but are closely related to each other. This paper uses the logarithmic growth model to analyze the correlation between the national economy and the real estate industry and uses Granger causality test to find that the real estate economy and the national economic growth are in a coordinated development relationship. Moreover, this paper further builds a model of the interaction between the national economy and the real estate economy and found that the real estate economy plays a very important role in promoting the development of the national economy through marginal analysis and elastic analysis. In addition, this paper finds through the GERT network model of the real estate expected value chain that each stakeholder formulates their own trading strategies and proposes their own transaction prices based on their own judgments on future information. Moreover, this paper finds that the expectation that real estate prices continue to rise between the two parties in real estate transactions is driven by psychological expectations, which in turn produces a typical herd effect. In addition, this paper finds that there is a phenomenon of learning and imitation in real estate. Under the learning and imitation of various transaction entities, the price of real estate will continue to rise, and finally the actual price of real estate will rise higher than the expected price rise.

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