Oil Prices and Banking Instability: A Jump-Diffusion Model for Bank Capital Structure.

• Author: Semmler, Willi

1. INTRODUCTION

   This paper contributes to recent academic research on the topic of overleveraging and the effects of large oil and political instability shocks on asset prices, financial markets, and the balance sheets of banks. We show that those shocks might be destabilizing rather than mean reverting. In order to capture the large oil policy shocks, we introduce a jump-diffusion process into the type of banking model as proposed by Stein (2012) and further extended by Gross, Henry, and Semmler (2017). In our paper, we are dealing with the oil market and the volatility of oil prices in terms of a jump-diffusion process that not only helps one understand and stylize how the commodity market is affected, but also how the stability of the banking system is influenced. The theoretical model, the measuring of optimal debt of banks, the use of the MCMC methodology in this framework, and the empirical results contribute to the existing studies, as the different components of the jump-diffusion model are significant and have, in relevant cases, expected signs. Moreover, the results on the disparity in the behavior of different components among countries constitute an added value of the paper. Commodity futures prices and options prices are frequently treated as a jump-diffusion process. For instance, Hilliard and Reis (1999) show empirical evidence that jump diffusion models are most suitable for commodity price estimation due to the stochastic nature underlying the commodity markets. Moreover, the use of jump-diffusion models for commodity option and futures markets goes back a long time. Jump-diffusion processes have actually become a standard modeling tool in commodity and energy derivatives markets since Merton's (1976) pioneering work. Later on, Bates (1991, 1996) has extended the model and developed a jump-diffusion model that permits jump risk to be systematic, by allowing jumps in the asset return process. On the other hand, Duffie et al. (2000) allow jumps both in the asset return process and in the variance process. In oil-producing countries, much of the commodity price jumps are intensively felt in the banking system. Oil-producing countries are exposed to global financial markets, which are affected by the changes in oil prices. In oil-exporting countries, the banks can be resilient to direct oil price changes; however, financial strains may eventually intensify (Baffes et al., 2015).

   Several researchers agree that there exists a connection between overleveraging and the oil market. For example, an interesting discussion on the credit cycle connection with oil and commodities markets is presented by Kablan et al. (2017). The authors take a sample of African commodity exporters and apply a co-spectral analysis, as opposed to time series analysis. They find that in exporting countries, credit expansion is a result of commodity price booms, which in turn increases the capital inflows and liquidity. They also show that during price booms and troughs, one can more readily see the correlation between credit cycles and crude oil indices. Another study by Ftiti et al. (2016) examines the commodity prices and the private sector credit, by using wavelet analysis on a sample of three commodity-exporting nations in Sub-Saharan Africa. The authors find that the length of the time span affects the relationship between credit and commodities. For instance, they are strongly related over long timescales, while over short/medium timescales, the interdependence is only pronounced during economic turmoil.

   When we speak about overleveraging, we are actually referring to lending booms. It is well known that lending booms may precede banking system instability, because they imply increased risk-taking in the financial system. This has the potential to result in financial turmoil if the economy is hit by a negative, adverse shock in asset prices, as occurred during the crisis of 2008. Many studies have investigated issues related to asset price channels through which the banking system's instability is triggered. Some of these important academic contributions include: Brunnermeier and Sannikov (2014), Mittnik and Semmler (2012a, 2013), Stein (2011, 2012), and Gross, Henry, and Semmler (2017).

   Brunnermeier and Sannikov (2014) focused specifically on the banking sector. The authors stated that a shock to asset prices created a vicious cycle through the balance sheets of the banks. In other words, risk-taking and excessive borrowing occurred when asset prices were rising. According to Mittnik and Semmler (2012a, 2013), the unconstrained growth of capital assets through excessive borrowing, facilitated by the lack of regulations imposed on financial intermediaries, was considered the main cause for banking sector instability. On the other hand, large payouts by the banking managers, with no "skin in the game", affected banks' risk-taking behaviors, equity development, and leveraging. In summary, the increased risk spreads and risk premia, especially at a time when defaults begin, exposed banks to vulnerabilities and financial stress triggered by security price movements.

   Stein (2011, 2012) argues that the destabilizing mechanism results from a link between asset prices and borrowing. He specifies that overleveraging begins when assets that are held by banks become overvalued. Above average returns, due to housing prices that increase owners' equity, induce a greater demand by banks for mortgages and funds. Thus, banks enjoy capital gains above some normal returns and begin to become overleveraged compared to optimally leveraged. The basis of Stein's model is that the optimal capital structure reflects the threshold beyond which net worth declines. His analysis is based on the assumption that the mean interest rate exceeds long-term capital gains, a constraint that he refers to as "no free lunch." Therefore, for overleveraging to occur, a violation of this constraint should take place. Stein suggests using the trends/drifts in capital gains and interest rates to measure optimal debt better. He also defines excess debt as the difference between the actual and optimal debt.

   This paper presents an extended model of bank capital structure, which originates from Stein's (2012) model, but goes a step further to include a jump-diffusion term that aims at capturing the mechanism between the sustainable leverage of a bank and various oil-related, politically-related, and regulation-related events that drive asset prices and bank returns contributing to frequent portfolio value volatility and rebalancing. To study this issue, we focus on oil-producing and oil-importing countries, the former in the Middle East and the latter in the Western hemisphere. Our approach builds on Stein's (2012) model by adding a jump-diffusion component that captures the jump size and intensity of oil prices and political instability predictors. The optimal debt is derived and then estimated for a sample of six banks in three countries for the period of 2006 to 2016. We employ the banks' balance sheet dynamics of Stein (2012) and build in the aforementioned jump-diffusion process. The idea of excess debt is pursued further in Gross, Henry, and Semmler (2017), while Semmler and Parker (2017) examine the dynamics of the wealth disparity using the same model by Stein (2012).

   The purpose of this paper is to present an original theoretical jump-diffusion model of bank capital structure. We further demonstrate the use of the MCMC methodology in a new framework to estimate this model of banking instability when encountered by stochastic shocks, and an empirical estimation applied to Bahrain, the United States, and the United Kingdom. This paper, therefore, contributes to the literature by illustrating the added value of surpassing the traditional estimation of bank leverage, which has been the norm thus far, and adding oil prices and political instability as major elements in the model. The idea of the model is to present the cash flow function of the banks as the difference between incoming and outgoing cash flows, as well as to emphasize study of the portfolio holdings when the banks invest following a jump diffusion model.

   The remainder of the paper is organized as follows: Section 2 discusses the background and the descriptive analysis related to oil prices. Section 3 presents the rationale and motivation behind the theoretical model used herein. Section 4 describes the methodology and the data used in this study to illustrate the problem and to answer our research question, as well as the findings and the policy implications. Section 5 concludes the paper.

2. STYLIZED FACTS AND RELATED LITERATURE

   Historically, periods of oil price shocks were followed by or have basically caused recessions, periods of excessive inflation, low productivity, and low economic growth as mentioned by several researchers; see Darby (1982), Hamilton, J. D. (1996), and Burbidge, J., & Harrison, A. (1984). Moreover, detailed studies on oil price movements as a predictor for low growth and recessions can be found in works by James Hamilton. For instance, Hamilton (2008) emphasizes the relationship between oil price swings and the macroeconomy in the U.S., and states that oil shocks directly increase unemployment and decrease income level. In addition, he shows that a reduction in real GDP growth leads to a much stronger reduction in the demand for new homes and an increase in delinquency rates. Moreover, Hamilton (2011b) shows that oil price increases are the reason behind ten recent recessions in the U.S., leaving only a single recession not being associated with an increase in oil prices. On the other hand, Gilje et al. (2017) present a novel method for analyzing the effect of oil prices on the financial market. The authors find that natural gas shale discoveries positively influence the financial market through a chain of positive reactions originating from the increase in...