Systemic financial risk indicators and securitised assets: an agent-based framework

Abstract

The paper presents an agent-based model of a credit economy which includes a securitisation process and a bailout mechanism for bank bankruptcies. Within this framework, banks are able to sell mortgages to a financial vehicle corporation, which finances its activity by creating mortgage-backed securities and selling them to a mutual fund. In turn, the mutual fund collects liquidity by selling shares to households and remunerates them with a monthly interest. The impact of this mechanism is analysed by means of computational experiments for different levels of banks’ securitisation propensity. Furthermore, we study a set of systemic risk indicators which have the aim of assessing the imbalances in the financial system. Two of them are the mortgage-to-GDP ratio and the capital adequacy ratio, which are constructed to detect only the on-balance sheet changes in banks’ credit exposure. We consider two additional indicators, similar to the previous ones with the only difference that they are also able to account for the off-balance sheet items. Moreover, we adopt an indicator, the so-called “virtuous–unvirtuous cycle” indicator, which, besides off-balance assets, targets also the GDP. The results show that higher securitisation propensity weakens the financial stability of banks with relevant effects on different sectors of the economy. Most importantly, the analysis of systemic risk reveals the important issue of designing suitable systemic risk indicators for predicting incoming financial crises, finding that an essential feature of these indicators should be to integrate banks’ off-balance sheet assets.

Appendix

1.1 Balance sheet matrices

In order to provide an exhaustive description of agents’ balance sheets and the stock-flow relations among sectors in Eurace, we present a set of four tables. Table 8 shows the asset and liability entries of each particular agent type. Table 9 represents the balance sheet matrix, describing all assets and liabilities for each sector. (Here, a sector has to be seen as a class of agents.) In this matrix, a plus (minus) sign corresponds to agents’ assets (liabilities), and each column can be read as the aggregated balance sheet of a specific sector. Rows show assets and claims of assets among sectors, thus generally adding up to 0. Exceptions are capital and inventories, which are accumulated by CGPs, and households’ equity shares of CGPs and banks that do not add up to 0 because market price and book value can be different. However, the equity shares being of capital goods producer (KGP), financial vehicle corporation (FVC), and mutual fund (MF) not traded in the financial market, their market price and book value coincide. Table 10, called transaction flow matrix, shows all the stock and monetary flows among agent classes. The top part, i.e. cash flows from cash receipts/outlays, describes the flows of revenues (plus sign) and payments (minus sign) that agents receive and make. Agents are reported in the columns, and monetary flows are reported in the rows. The result of agents’ sector transactions is the net cash flow (NCF). The bottom part of Table 10 describes the changes in financial/monetary assets/liabilities among periods. Finally, Table 11, called equity capital change matrix, reports the variation of agents’ equity capital between two periods, due to net cash flows, price changes in assets and liabilities, stock changes in real assets, and issues of equity shares.

Table 8 Agent class balance sheets

Table 9 Sectorial balance sheet matrix

Table 10 Sectorial transaction flow matrix of agents populating the EURACE economy

Table 11 Equity capital change matrix

1.2 Stylised facts and validation

Since in the explanation of computational experiment results we often refer to the synchronisation among different variables during the business cycle, we have performed a cross-correlation analysis, in order to objectively assess the correlation of those variables for different time lags. Figure 11 shows some cross-correlation figures. We consider monthly HP detrended time series averages of 50 simulation runs, one for each seed used for the pseudo-random number generator. In Fig. 11, we show the cross-correlations for 20 positive and negative lags, as well as the upper and lower confidence bounds. We observe that real GDP is positively correlated to consumption and investment, and it is anti-correlated to the unemployment rate. GDP also shows a positive correlation with loans to firms, which are leading the business cycle expansion, while stock and bond prices are anti-correlated. These results are in line with the main stylised facts on credit and business cycle [see for instance Watson and Stock (1999), Napoletano et al. (2006), Cappiello et al. (2010) and Uribe and Schmitt-Grohé (2017)].

Fig. 11

Cross-correlations. Time series considered are monthly and hp filtered

Concerning the validation of the model, it is worth remarking that Eurace initialisation complies with two main requirements: stock-flow consistency and input validation. In particular, we use a specific model software that is able to initialise the model in an automatic way. We define in this software all the cross-relations between the balance sheet items of the economic agents and we check for the consistency of the process. The initialisation starts by setting at 1 the initial value of the nominal monthly wage, and from this reference variable, we go on computing all the others.

In this way, we are able to provide an “input validation,” where model’s fitness is ensured by setting parameter values and variable ratios according to empirical analysis of actual data.²²

1.3 Housing market

We use the housing market setting described in Ozel et al. (2019). In this framework, the access to the housing market by the households is driven by an exogenous probability $\varPhi _\mathrm{H}$; once in the housing market, households may randomly take the role of buyer or seller, except in the case of a fire sale, when households enter the housing market because they are forced to sell their housing units due to financial distress, which is defined as:

$$\begin{aligned} \frac{R_{U_h}}{Z_l + Z_e} \ge \varPsi _S \end{aligned}$$

(10)

where $R_{U_h}$ are the quarterly payments (principal and interests) related to mortgages $U_h$ of household h, $Z_l + Z_e$ is the sum of quarterly labour and capital income after taxes, and $\varPsi _S$ is a given threshold. If the financial distress is critically high and oversteps a threshold $\iota _S$, the household undergoes a mortgage restructuring with a consequent equity loss of the credit bank.

It is worth noting that in the eventuality of fire sales, the selling price set by the household is lower than the last average market price ($p_{X_{t}}$), in order to increase the probability of selling the housing unit and obtaining liquidity. In particular, we distinguish between sell orders and fire sell orders. In the first case, the price set by the household is:

$$\begin{aligned} p_{X_{t}} = p_X(1+ \xi \varphi _H) \end{aligned}$$

(11)

where $\xi$ is a random component drawn from uniform distribution between 0 and 1 and $\varphi _H$ is the maximum percentage price increase in monthly housing price.²³

In the second case, fire seller households post one of their housing unit for sale at price $p_{X_{t}}$, given by:

$$\begin{aligned} p_{X_{t}} = p_X(1- \xi \varphi _S) \end{aligned}$$

(12)

where $\varphi _S$ is the maximum fire sale price reduction.

Households with the buyer role are randomly queued and each buyer in the queue in turn selects the cheapest available housing unit to buy and a transaction takes place at the posted sale price. When all buyers have had their turn in the housing market or there are no more housing units for sale, the housing market closes and a new housing price $p_H$ is computed as the average of the realised transaction prices. This process takes place each month.

Households may buy a housing unit by means of their liquidity resources or, if they are not sufficient, through a mortgage from a bank. All mortgages last 20 years, and each month the borrowers repay mortgage instalments, which are made up of a constant principal component and an variable interest component on remaining instalments, computed as central bank interest plus a fixed spread of 1%. The rationale behind this choice is to mimic variable rate mortgages, whose interests are mostly tied to reference rates or indices that are linked with the central bank policy rate (e.g. EURIBOR in Europe). The spread represents the bank’s margin. Although we consider a fixed bank margin that is not linked with household creditworthiness, it is worth remarking that banks check upstream that the applicant borrowers comply with two constraints. In particular, a stock and flow thresholds are included, namely equity-to-assets ratio (ETA) and debt-service-to-income ratio (DSTI). Therefore, bank checks that:

• household net wealth (Equity $E_{h}$) to her total wealth (Assets $A_{h}$) ratio is higher than a threshold $T_{\mathrm{ETA}}$:

  $$\begin{aligned} \frac{E_h}{A_h} \geqslant T_{\mathrm{ETA}} \end{aligned}$$

  (13)

• household debt payments for the upcoming quarter to income is lower than a threshold $T_\mathrm{DSTI}$:

  $$\begin{aligned} \frac{R_{U_h} + R_{{\widehat{U}}_h}}{(Z_l + Z_e)} \leqslant T_\mathrm{DSTI} \end{aligned}$$

  (14)