Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.     

NO‐ARBITRAGE PRICING UNDER SYSTEMIC RISK: ACCOUNTING FOR CROSS‐OWNERSHIP

We generalize Merton’s asset valuation approach to systems of multiple financial firms where cross‐ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no‐arbitrage. An existence result and a uniqueness result are proven. Examples and an algorithm for the simultaneous calculation of all no‐arbitrage prices are provided. A result on capital structure irrelevance for groups of firms regarding externally held claims is discussed, as well as financial leverage and systemic risk caused by cross‐ownership.     

How does competition affect bank systemic risk?

Using bank level measures of competition and co-dependence, we show a robust negative relationship between bank competition and systemic risk. Whereas much of the extant literature has focused on the relationship between competition and the absolute level of risk of individual banks, in this paper we examine the correlation in the risk taking behavior of banks. We find that greater competition encourages banks to take on more diversified risks, making the banking system less fragile to shocks. Examining the impact of the institutional and regulatory environment on bank systemic risk shows that banking systems are more fragile in countries with weak supervision and private monitoring, greater government ownership of banks, and with public policies that restrict competition. We also find that the negative effect of lack of competition can be mitigated by a strong institutional environment that allows for efficient public and private monitoring of financial institutions.     

Default and Recovery Risk Dependencies in a Simple Credit Risk Model

This paper provides evidence for the relationship between credit quality, recovery rate, and correlation. The paper finds that rating grade, rating shift, and macroeconomic factors provide a highly significant explanation for default risk and recovery risk of US bond issues. The empirical data suggest that default and recovery processes are highly correlated. Therefore, a joint approach is required for estimating time‐varying default probabilities and recovery rates that are conditional on default. This paper develops and applies such a model.     

On equity market inefficiency during the COVID-19 pandemic

We show that during the weeks following the initiation of the COVID-19 pandemic, the United States equity market was inefficient. This is demonstrated by showing that utility maximizing agents over the time period ranging from mid-February to late March 2020 can generate statistically significant profits by utilizing only historical price and virus related data to forecast future equity ETF returns. We generalize Merton’s optimal portfolio problem using a novel method based upon a likelihood ratio in order to construct a dynamic trading strategy for utility maximizing agents. These strategies are shown to have statistically significant profitability and strong risk and performance statistics during the COVID-19 time-frame.     

基于Merton模型的存款保险定价研究

存款保险制度的核心是存款保险费率的厘定。本文以Merton存款保险定价的看跌期权模型为基础,引入监管宽容和未保险存款的利率两个参数,给出了商业银行存款保险定价公式。选择不同的银行对其保险费率进行估算,所得的保险费率之间有一定的差距,表明不同银行的存款保险费率是不同的,中国不适合单一费率,而适合风险费率。本文对我国正在酝酿出台的存款保险制度具有一定的指导意义。     

On break-even correlation: the way to price structured credit derivatives by replication

We consider the pricing of European-style structured credit pay-off under the Gaussian Copula Model (GCM). When no sudden jump-to-default events occur, the perfect replication of these pay-offs under the GCM is obtained if and only if the underlying single-name credit spreads follow a particular family of dynamics and if the pricing parameters are given by so-called ‘break-even’ correlations. We exhibit a class of Merton-style models that are consistent with this result. We calculate break-even correlations explicitly to price nth-to-default baskets under the GCM. Finally, we illustrate the usefulness of this concept as a relative-value tool.     

风险水平调整下的存款保险定价机制研究——基于Merton与违约预期损失定价模型

存款保险定价模型应建立在所面临的违约风险水平基础上,现行的Merton模型和违约预期损失定价模型忽略了银行资产负债结构、监管外部性、非系统性风险相关性和银行规模等风险因素的影响,因而采取改变风险敞口额、加强监管协调提高监管宽容参数、统一国家范围承保和建立二元保费定价机制等措施可实现存款保险价格与违约风险水平相一致的目标,促进存款保险机制的合理健康发展,为我国今后建立存款保险定价机制提供一定的参考。关键词：Merton模型;RV分析方法;监管外部性;系统性风险;风险分散     

Applications of Eigenfunction Expansions in Continuous-Time Finance

We provide exact solutions for two closely related valuation problems in continuous-time finance. The first problem is to value generalized European-style options on stocks that pay dividends at a constant dollar rate. The second problem is to find the yield curve associated with the economy of R. C. Merton's "An Asymptotic Theory of Growth Under Uncertainty." In Merton's economic growth model, the interest rate process has a volatility linear in the rate level and a linear/quadratic drift. Both problems are solved by an eigenfunction expansion technique. The main technical difficulty is handling the problem of payoff functions that are not square-integrable with respect to the natural weight function of the models.