Interbank credit and the money manufacturing process: a systemic perspective on financial stability

Interbank lending and borrowing occur when financial institutions seek to settle and refinance their mutual positions over time and circumstances. This interactive process involves money creation at the aggregate level. Coordination mismatch on interbank credit may trigger systemic crises. This happened when, since summer 2007, interbank credit coordination did not longer work smoothly across financial institutions, eventually requiring exceptional monetary policies by central banks, and guarantee and bailout interventions by governments. Our article develops an interacting heterogeneous agent-based model of interbank credit coordination under minimal institutions. First, we explore the link between interbank credit coordination and the money generation process. Contrary to received wisdom, interbank credit has the capacity to remove the inner limits of monetary system capacitance. Second, we develop simulation analysis on imperfect interbank credit coordination, studying impact of interbank dynamics on financial stability and resilience at individual and aggregate levels. Systemically destabilizing forces prove to be related to the working of the banking system over time, especially interbank coordination conditions and circumstances.

     

No arbitrage of the first kind and local martingale numéraires

A supermartingale deflator (resp. local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp. local martingales). A supermartingale numéraire (resp. local martingale numéraire) is a wealth process whose reciprocal is a supermartingale deflator (resp. local martingale deflator). It has been established in previous works that absence of arbitrage of the first kind (\(\mbox{NA}_{1}\)) is equivalent to the existence of the (unique) supermartingale numéraire, and further equivalent to the existence of a strictly positive local martingale deflator; however, under \(\mbox{NA}_{1}\), a local martingale numéraire may fail to exist. In this work, we establish that under \(\mbox{NA}_{1}\), a supermartingale numéraire under the original probability \(P\) becomes a local martingale numéraire for equivalent probabilities arbitrarily close to \(P\) in the total variation distance.     

In the insurance business risky investments are dangerous: the case of negative risk sums

We investigate models with negative risk sums when the company invests its reserve into a risky asset whose price follows a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of exponentially distributed benefits. As in the case of non-life insurance with exponential claims, the ruin probabilities are either decreasing with a rate given by a power function (the case of small volatility) or equal to one identically (the case of large volatility). The result allows us to quantify the share of reserve to invest into such a risky asset to avoid a catastrophic outcome, namely the ruin with probability one. We address also the question of smoothness of the ruin probabilities as a function of the initial reserve for generally distributed jumps.     

Inertia in the key currency

This paper empirically analyzes inertia in the position of the dollar as the key currency. We extend a money-in-the-utility model to one with parallel international currencies. We use an extended model to estimate a parameter in the utility function. Also, given the estimated parameter, we simulate a relation between depreciation and share of the dollar. The result indicates that the share of the dollar will not decrease even if the dollar depreciates at a moderate rate. Thus the dollar will keep its position as the key currency – inertia works in the key currency.     

On the law of one price

We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. We also give an application to the CAPM.Received: November 2003, Mathematics Subject Classification (2000): 60G44JEL Classification: G13, G11Freddy Delbaen: This research was done during the stay of the author at Université de Franche-Comté.     

Financial accumulation implies ever-increasing wealth inequality

Wealth inequality is an important matter for economic theory and policy. The recent rise in wealth inequality has been discussed in connection with the recent development of active global financial markets. The existing literature on wealth distribution links wealth inequality to a variety of drivers. Our approach develops a minimalist modelling strategy that combines three featuring mechanisms: active financial markets, individual wealth accumulation and compound interest structure. We provide mathematical proof that accumulated financial investment returns involve ever-increasing wealth concentration and inequality across individual investors most of the time. This cumulative effect over space and time depends on financial accumulation processes, including under efficient financial markets, which generate a fair investment game that individual investors repeatedly play through time.

     

A remark on static hedging of options written on the last exit time

In this paper, several different static hedges of the option written on the last exit time are given. One of them was originally presented in Akahori et al. (Methodol Comput Appl Probab 11(4): 661–668, 2009). Another one is derived from an expression in Madan et al. (Asia Pac Financ Mark 15(2): 97–115, 2008d). It is remarked in this paper that these static hedges are also obtained by applying a method in Carr and Chou (Hedging complex barrier options, 2001).