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International audience; The seminal Modigliani-Miller (1958) theorem is a cornerstone of corporate finance theory. It provides conditions under which changes in a firm’s capital structure do not affect its fundamental value. A recent controversial debate around the relevancy of the Modigliani-Miller theorem regarding the banking sector has been raised since the 2008 financial crisis. In this paper, we provide an overview of the theorem with recent developments when considering several extensions of the initial model. We reformulate the Modigliani-Miller theorem under a Markowitz perspective. Under this approach, we consider the case of implicit government guarantees offered to banks. Our main result shows that a bank does not satisfy the Modigliani-Miller theorem, precisely banks will favor leverage instead of equity.

We consider the problem of characterizing and computing the fair credit risk premium that a firm should pay when borrowing money from a bank. Using a risk-neutral approach, we show that there is a unique credit risk premium for a commercial loan depending on the firm's strategy such that the expected discounted value of the bank's payoff coincides with the loan's par value. We then propose a numerical procedure to estimate the premium.

The capital structure of banks has become the focus of an extended debate among policy-makers, regulators and academics. The seminal Modigliani-Miller (1958) theorem is seen as supportive of regulators' drive to require higher equity capital to banks. This raises the question on to what extent does Modigliani-Miller theorem hold for banks. This article brings a new insight of the Modigliani-Miller theorem by considering the implicit government guarantee offered to banks. Our theorem shows that a bank does not satisfy the Modigliani-Miller theorem. The main result indicates that banks will favor leverage instead of equity.

The seminal works of Modigliani-Miller and Markowitz-Sharpe remain the cornerstone of financial theory. We reconcile these seemingly distinct approaches, in a unified theorem, by showing that the agents acting on the market defined by Modigliani-Miller are Markowitz rational when deriving the arbitrage reasoning in terms of Sharpe ratios. As a main policy implication, we show that government guarantees modify market's equilibrium as they provoke arbitrage opportunities.

Asymmetric volatility in equity markets has been widely documented in finance (Bekaert and Wu (2000)). We study asymmetric volatility for daily S&P 500 index returns and VIX index changes, thereby examining the relation between extreme changes in risk-neutral volatility expectations and in aggregate asset prices. To this aim, we model market returns, implied VIX market volatility and volatility of VIX volatility, showing that volatility of volatility is asymmetric in that past positive volatility shocks drive positive shocks to volatility of volatility. Our results document the existence of a significant extreme asymmetric volatility effect, i.e. there is contemporaneous volatility-return tail dependence for crashes but not for booms. We then outline aggregate market price implications of extreme asymmetric volatility, indicating, for example, that a one-in-a-hundred trading day innovation to average VIX volatility under volatility feedback relates to an expected market drop of more than 4 percent.

International audience

International audience; Asymmetric volatility occupies a central role in the risk-return relation. However, this asymmetry has not been examined during stress periods. This article fills this gap by studying this relation at the tail distribution level with an empirical test on the French market from the creation of the implied volatility index in October 1997 until January 2013. Using a complete set of econometrical analysis before applying the multivariate extreme value theory, this article shows that the asymptotic dependence occurs only for the crash scenario in which the feedback effect dominates the leverage effect. This result has implications on the pricing and hedging of options contracts.

National audience

National audience; The post-crisis financial reforms address the need for systemic regulation, focused not only on individual banks but also on the whole financial system. The regulator principal objective is to set banks' capital requirements equal to international minimum standards in order to mimimise systemic risk. Indeed, Basel agreement is designed to guide a judgement about minimum universal levels of capital and remains mainly microprudential in its focus rather than being macroprudential. An alternative model to Basel framework is derived where systemic risk is taken into account in each bank's dynamic. This might be a new departure for prudential policy. It allows for the regulator to compute capital and risk requirements for controlling systemic risk. Moreover, bank regulation is considered in a two-scale level, either at the bank level or at the system-wide level. We test the adequacy of the model on a data set containing 19 banks of 5 major countries from 2005 to 2012. We compute the capital ratio threshold per year for each bank and each country and we rank them according to their level of fragility. Our results suggest to consider an alternative measure of systemic risk that requires minimal capital ratios that are bank-specic and time-varying.

The capital structure of banks has become the focus of an extended debate among policy-makers, regulators and academics. The seminal Modigliani-Miller (1958) theorem is seen as supportive of regulators' drive to require higher equity capital to banks. This raises the question on to what extent does Modigliani-Miller theorem hold for banks. This article brings a new insight of the Modigliani-Miller theorem by considering the implicit government guarantee offered to banks. Our main theorem shows that a bank can no longer be considered as a classical firm and will favor leverage instead of equity.

In this paper, we develop a financial stress index for France that can be used as a real-time composite indicator for the state of financial stability in France. We take 17 financial variables from different market segments and extract a common stress component using a dynamic approximate factor model. We estimate the model with a combined maximum-likelihood and Expectation-Maximization algorithm allowing for mixed frequencies and an arbitrary pattern of missing data. Using a Markov-Switching Bayesian VAR model, we show that an episode of high financial stress is associated with significantly lower economic activity, whereas movements in the index in a low-stress regime do not incur significant changes in economic activity. Therefore, this index can be used in real time as an early warning signal of systemic risk in the French financial sector.