Abstract
This paper provides an analytical approach to designing macroeconomic scenarios and behavioral models for measuring the interest rate risk in the banking book (IRRBB). First, we build fully-fledged alternative scenarios that link interest rates with the rest of economy. Second, we design forward-looking behavioral models with explicit linkages between behavioral metrics for assets and liabilities with macroeconomic drivers. This approach is consistent with regulatory requirements and it combines economic intuition with statistical rigor and computational efficiency. Such scenario-conditional forecasting models result in coherent scenario spreading of the key behavioral factors in balance sheet cashflows
1. Introduction: New Approaches to Old Problems
Interest rate shocks don’t materialize in isolation. Central banks may increase rates when macroeconomic conditions are favorable and lower them when the economy underperforms and needs a jolt. Changing an interdependent macroeconomic and interest rate environment poses a challenge to interest rate risk management in banks, influencing clienteles’ decisions, such as prepaying loans and withdrawing deposits. Such behavioral optionality can have a significant impact on the interest rate risk in the banking book (IRRBB) profile for both assets and liabilities.
To understand and manage the underlying IRRBB exposures and risks, analysis should rely on modeling and forecasting clients’ behavior under alternative scenarios. In recent years, regulators across the globe have required banks to incorporate a wide range of macroeconomic factors or drivers into behavioral models. These drivers are limited not only to interest rates but also should include measures of economic output from the labor market, stock market, and prices. Nevertheless, regulators do not provide alternative scenario forecast assumptions for the full spectrum of macroeconomic drivers. Prominent examples are the regulatory standardized interest rate scenarios, including parallel up and down, steepening and flattening, and short rates up and down, which do not include information about how these interest rates assumptions transmit to the rest of the macroeconomic drivers.
In this paper, we present a forward-looking approach for modeling and predicting client behavior under alternative scenarios. Leveraging Moody’s Analytics Global Macro Model, scenarios, and dynamic model-building algorithm, we design behavioral models with a wide range of macroeconomic and interest rate drivers. The models are used for forecasting under alternative scenarios, ensuring consistency between the drivers’ forecasts and the behavioral metrics projections. These behavioral models provide valuable insights for impact analysis of cashflows.
The overall structure of our approach is depicted in Figure 1. The interest rate-sensitive banking book positions are allocated to one of three categories: amenable, less amenable, and not amenable to standardization. For behavioral modeling, our focus is on positions that are not amenable to standardization.1 These are products with quantifiable uncertainties, as they are subject to optionality risk and require behavioral models to capture customer behavior under different scenarios. Such products include non-maturing demand and savings deposits, term deposits with a termination option, early redemption options, such as termination rights by law or unscheduled redemptions, and non-drawn fixed interest rate credit lines.
This paper is organized as follows. Section 2 introduces our Global Macro Model and scenario design, highlighting how the model structure produces real-world scenarios with interest rate shocks. Section 3 provides an overview of how we model explicit links between behavioral metrics and their drivers to incorporate macroeconomic scenarios and present case studies for loan prepayment and non-maturing deposits. Section 4 concludes.
2. Expanding Interest Rate Shocks to Fully-fledged Scenarios
A carefully planned macroeconomic scenario for interest rate risk should not consider interest rate developments alone but draw consistent paths for other macroeconomic drivers. Macroeconomic factors such as interest rates, unemployment rate, and price indices reflect the situation of the economy and can play an important role in defining customer behavior. For instance, when there is an increase in the unemployment rate accompanied by a reduction of monetary policy to stimulate the economy, some bank clients might lose their jobs and withdraw their deposits to meet financial needs. Similarly, loan prepayments may be driven by factors including unemployment rate, income, and prices, in addition to interest rates.
There are various methodologies to model the interdependency between interest rates and other macroeconomic factors. These models are needed to generate consistent forecasts for a wide range of macroeconomic factors, including interest rates under alternative scenarios. At one end of the model spectrum are nonstructural data-driven models that rely on reduced-form specifications, such as vector autoregression. On the opposite end are models built from strict theoretical foundations, such as dynamic stochastic general equilibrium models, whose value is derived from the strength of the assumptions that theory imposes on data. In the middle are structural macroeconomic models supported by both theory and data, employed by professional forecasters, including those at Moody’s Analytics.
Our Global Macro Model captures relevant economic spillovers and feedbacks across sectors and countries by using economic theory that underpins the set of individually specified equations.2 The model allows us to produce forecasts for a variety of macroeconomic factors across alternative scenarios that fits the purposes of IRRBB. The model consists of a single, simultaneous system of structural economic equations capturing relationships across series within each national economy. The forecast of the macroeconomic variables in the system is therefore consistent with interest rate shocks. Figure 2 visually depicts the relationship between the core variables for a country.
The great advantage of structural models is the rich detail they provide, such as the composition of both spending and industrial activity, the entire maturity yield curve, many other interest rates, and prices for goods, services, and assets throughout the economy. Figure 3 illustrates the forecast of key macroeconomic factors that contribute to explaining customer behavior in illustrative baseline and two stress scenarios for a representative country.
Our baseline scenario is designed as the most likely outcome and is constructed to fall in the middle of a distribution of possible outcomes. The baseline is therefore viewed as representing an outcome in which there is a 50% probability that economic conditions will worsen and a corresponding 50% probability that they will improve over the forecast horizon. Alternative scenarios, such as Downside S3 and Severe Downside S4, are also designed with different predefined probabilities of occurrence, simplifying the implementation process, as there is no need for cumbersome simulations to determine the scenarios.
In the downside shocks, GDP and HPI growth decreases relative to the baseline and the labor market experiences higher unemployment. The combination of lower inflation and worse economic conditions triggers regulators to cut policy rates, leading to other interest rates being lower than expected in the baseline. The development of money markets depends not only on the economy itself but also on the response of monetary authorities to an economic situation, such as the COVID-19 pandemic.
In addition to the core factors, forecasts for a multitude of financial variables consistent with the projected macroeconomic environment are required for the behavioral models. Linking the global macroeconomic model to satellite models of financial variables, such as a term structure of government bond yields, swaps, and credit default swaps (CDS) provides a simple yet robust way to meet these needs. In a satellite model, we forecast the curves using principal component analysis to condense the cross-section of rates by maturity at a point in time into a lower-dimensional set of factors that are driven by forecasts produced in the global model.3
Figure 4 displays an example of projections for an entire term structure and the yield curve for two forecast points under baseline and stress scenarios. We can observe the evolution of the interest rates as the economic environment evolves. In the baseline scenario, the term structure remains stable and smoothly converges to the long-term trend. In contrast, in the stress scenario, the level of interest rates drops and the spread across maturities reduces, as there is stimulus to recover the economic activity. Once the economic conditions improve in late 2024, the interest rates start raising.
3. Designing Forward-looking Behavioral Models
The main objective of the behavioral models is to understand and project customers’ decisions to deviate from contractual terms. Traditionally, institutions employed silo systems to calculate the different types of risks, such as credit risk and asset and liability management risk, but recently the systems are converging in many aspects, due to the prevalence of models and scenarios. Hence, models can be designed to calculate risk exposures across different types of risks and are used to forecast behaviors of customers across the board, including asset and liability behaviors.
The methodologies for modeling loan prepayment, which are connected to default models, credit drawdown, and term deposit early withdrawals, are similar as they aim to find the key factors driving customer behavior. Non-maturing deposits (NMD), on the other hand, represent a distinct bank liability, since they do not pose predetermined maturity; and customers have the right to withdraw money at any point of time, sometimes without penalty. Therefore, the timing of cashflows and volumes are uncertain and require different modeling considerations.
A good model that is compliant with regulatory requirements should include all important factors, while still being parsimonious, suitable for forecasting, easily interpretable, and in line with economic theory. Multi-factor dynamic models allow us to include numerous variables driving the execution of the behavioral optionality. The key factors can be broadly grouped into three major categories: macroeconomic drivers, market characteristics, and instrument and customer characteristics.
Figure 5 shows our approach to building forward-looking behavioral models. The granularity of the model depends on data availability, the size of the portfolio, and system characteristics. We start by collecting and analyzing the portfolio data to define the appropriate modeling approach and the potential drivers for each instrument class, portfolio, and segment.
The next step in building the forecasting models is to link the behavioral target metric and drivers. A common challenge is to find the optimal combination of drivers, test model robustness, and rank-order all the possible model variants. To account for this, our proposed model-building process consists of three steps. First, we select potential drivers of the target metric that are likely to be the most important, based on economic intuition, experience with similar models, and historical data analysis. Second, we run a dynamic model-building algorithm to choose the optimal combination of drivers. Finally, the subset of likely models is diagnosed and validated to identify a handful of the best-performing forecast models. This process is an efficient, transparent, and concise way to identify drivers that best explain the customer behavior in question.
In the variable selection algorithm, the potential drivers undergo an exhaustive search process, where all possible combinations of selected potential drivers are tested.4 Only the models with significant coefficients at a conventional level and expected sign are included in the short list of potential models. In the next step, top candidate models are examined by analyzing the forecast relative to historical developments, the consistency with drivers and scenario assumptions, and by performing back-testing and sensitivity analysis. These results then guide the selection of the final model.
The next sections illustrate how to apply our model-building procedure to behavioral models. We include case studies of forward-looking behavioral models for loan prepayment, term deposit early redemption, and non-maturing deposits withdrawal.
3.1 Loan Prepayment and Early Deposit Redemption Risk Modeling
Prepayment and early deposit redemption are behavioral option risks arising from the flexibility embedded implicitly or within the terms of financial contracts. Banks may experience a higher proportion of fixed rate loans as prepaid, if the spread over the reference rate is lower, since some clients may want to refinance their loans and benefit from the market conditions. On the deposit side, if rates increase, the market value of fixed deposits declines, and customers may withdraw their term deposits early and place them elsewhere at a higher rate.
Our case study uses loan-level origination performance data for mortgages underlying residential mortgage-backed-securities (RMBS) transactions obtained from the European Data Warehouse (EDW). The data contains over 4.3 million loans from January 2013 to January 2020. We adopt Cox’s Proportional Hazards model that captures the competing risks of the probability of loan prepayment and the probability of loan default; if a loan defaults, it cannot prepay and if it prepays, it cannot default. The models for prepayment and default are related through common dependence on macroeconomic as well as loan-specific factors.
To build a robust model for the conditional probabilities of default and prepayments on survival, in addition to interest rates, we also consider macroeconomic factors, customer and loan characteristics, loan seasoning, seasonality, and geographical location. In this analysis, we demonstrate that prepayments are affected by a wide range of macroeconomic variables and are sensitive to different economic growth paths.
Figure 7 displays the forecast of the prepayment rate under alternative scenarios and the impact on the scheduled cashflows for a loan. As expected, a sharp increase of interest rates in the stress scenario reduced refinance incentives, resulting in lower prepayments. Other macro drivers also helped explain consumers’ prepayment behaviors. Specifically, we observed that prepayments augmented when the unemployment rate and house prices recovered after the recession period.
Putting it all together, projected cashflows are calculated considering the impact of prepayments, delinquency, and any recoveries of loans that are written off. Projected cashflows with behavioral optionality taken into account are different than cashflows without any optionality. The uncertainty of the cash inflows lies in both the amount and timing and can be easily calculated once the behavioral options are forecast across scenarios. When incorporating the behavioral effects on cashflows, we obtain prepayments contracted from the scheduled balance, which otherwise would be over-estimated if the prepayments were not included.
3.2 Non-maturing Deposits Modeling
The goal of non-maturing deposits (NMDs) analysis for evaluating IRRBB is to distinguish what is the proportion of deposits unlikely to reprice, even under a scenario with significant changes in the interest rate, and to establish the optimal repricing term. Examples of these liabilities are saving accounts, current accounts, and demand deposits.
Our approach for analyzing NMDs consists first in identifying the ratio of balances that are not volatile or stable across observation windows. Typically, the horizon for stability analysis is 10 years of historical data or at least all the available data, based on BCBS recommendations. The analysis allows us to identify the stable portion of the deposits for the vintages with sufficient history, i.e. the full stability horizon.
We then conduct a sensitivity analysis to differentiate those stable deposits that are less subject to repricing when there are significant changes in interest rates, generally referred to as core deposits. In other words, we determine core deposits that remain in the bank despite significant interest rate movements. Lastly, we define an optimal duration for the core deposits. Below we demonstrate the sensitivity analysis by building forward-looking models for the interest rate and deposit balance, and we determine corresponding behavioral duration.
Modeling Deposit Interest Rate and Volume
We develop forward-looking models to quantify how changes in drivers, including prevailing market interest rates and macroeconomic factors, influence the volumes and the rates of NMDs. The prevailing interest rates include the policy rates, interbank money market rates, and swap and government bond rates. The macroeconomic factors include a wide range of variables describing economic growth, labor market, prices, and inflation. A bank may change the deposit rate to prevent some of the deposit outflows, and this response is modeled to determine pass-through from the market rates to the deposit rates. Finally, the reaction of the depositors to the external environment should be considered, such as any available information on the competition from other banks, bank reputation, and any relevant characteristics of customer base.
Our case study presents a model for deposit rates and volumes for a large commercial bank in Hong Kong. The development sample covers more than 600,000 retail saving accounts for the 10-year estimation period from 2009 to 2019. For drivers, we use historical data and alternative scenario forecasts from the Global Macro Model. We first model deposit rates leveraging the correlation between the deposit rate and market rates, using a multivariate regression model. We then model the deposit volumes using the level of interest rates in the market to encapsulate medium-term inflation expectations, interest rate spreads to account for opportunity costs obtained, and additional macroeconomic factors that explain deposit behavior as drivers.
Figure 8 presents the forecasts for deposit volumes. The results show how deposit volumes are affected by the economic conditions even for updates of the baseline scenario. For instance, prior COVID-19 pandemic, the prediction of deposit volumes growth remained stable throughout the forecast period. Once the pandemic was declared, deposit volumes decrease as a result of higher unemployment and economic uncertainty, driving customers to use their savings. Under the stress scenarios, deposit volumes drop sharper than baseline and recover when economic conditions stabilize.
The empirical analysis allows us to look at the sensitivity of deposit volumes under realistic scenarios. This methodology can be broadened to account for additional factors, such as changes in the client structure of the bank or customer switching to other products or competitors, whenever the data are available and relevant for capturing risk in the bank. Another challenge is to model interest rate sensitivities when interest rates are flat or low for a long period of time. Thus, analysts should use a sufficiently long history covering at least one business cycle. Moreover, if a bank applies arbitrary pricing, finding a meaningful relationship with market rates can be more challenging.
Determining Behavioral Deposit Duration
We now demonstrate how to determine what is the optimal repricing term for core deposits. Replicating portfolio model (RPM) is commonly used in the industry to assign a behavioral maturity to NMDs. This method assumes a proportion of NMDs is akin to a perpetual liability that can be invested over time in fixed rate assets such as bonds or swaps.
RPM selects an optimal portfolio split of investment terms based on an optimization problem that minimizes the volatility of the margin between the average portfolio interest rate and the deposit rate, while simultaneously maximizing the portfolio return over time to obtain the efficient frontier (see Figure 9). Then, the repricing term of the NMD portfolio is the optimal portfolio from RPM, which represents the terms at which it would be most sensible to invest the deposits in the open market.
In this case study, we employ the forward-looking RPM, applying the scenario forecast of the core deposit volume and deposit rate obtained above. We also make use of scenario-consistent forecasts of market risk instruments, such as the term structure of sovereign bond yields and interest rate swaps. Figure 10 and Figure 11 show the historical and forecast dynamics for baseline and downside scenarios of the term structure of interest rate swaps (maturities 1-month, 3-months, 6-months, 9-months, 1-year, 3-years, 5-years, 7-years, and 10-years).
Table 1 displays the resulting optimal portfolio from RPM for three different cases. The first case uses historical data of the deposit rate and the term structure of interest rate swaps, and accounts for changes on the deposit volumes in history. The other two cases leverage baseline and stress forecasts of the deposit rate and term structure and consider the changes in the deposit volumes throughout the forecast horizon.
We observe the results are sensitive to the data used for solving the optimization problem, since different economic conditions can alter investment decisions. For instance, high volatility in short or long end of interest rate term structure would result in a lower weight for corresponding tenors, as observed in Figure 11 and the resulting allocation of weights in Table 1. Accounting only for historical data would end up assigning weights to tenors with lower yield in the scenarios, and therefore would result in a smaller share of deposits with shorter duration.
The results of the optimal weights are also sensitive to the changes in deposit volumes. Even though there is inversion in the term structure in both scenarios, being more pronounced in the stress, the investment portfolio still assigns weight to medium-term tenors since the economy is expected to recover after a five-year period in our illustrative scenario.
4. Summary
Economic shocks and turbulences, such as the COVID-19 pandemic, highlight the need to run realistic enterprise-wide scenarios covering all balance sheet risks, including the impact of client behavior. In this paper, we show how our forward-looking approach to behavioral modeling provides insights into how customers respond to different economic conditions on both sides of banks’ balance sheets.
Leveraging our macroeconomic data and scenarios, we introduce a robust approach to dynamically link customer behavior to macroeconomic indicators, including interest rates. These models result in scenario-conditional customer behavior for any realistic scenarios, such as interest rate risk shocks and market-wide shocks. Banks can use these results to identify key risks that impact balance sheets under forecasted economic changes, quantify consequent impacts in profits and economic value, and define strategic responses and planning.
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1 The amenable position has deterministic cashflows with a defined time to maturity until the end of the contract, such as fixed-interest housing loans, term deposits, savings bonds, and securities. The less amenable position has partly deterministic cash flows with uncertainties, such as explicit interest rate options, option rights embedded in securities, caps or floors, and swaptions.
2 A more detailed explanation can be found in Zemcik (2019).
3 A more detailed explanation can be found in Licari, Loiseau-Aslanidi, and Suárez-Lledó, 2017.
4 More details about variable selection algorithm can be found in Licari, Loiseau-Aslanidi, and Vikhrov (2017).
