Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time

In recent years, the counterparty credit risk measure, namely the default risk in \emph{Over The Counter} (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of \emph{Basel II} and \emph{Basel III.} More explicitly, to obtain the related risk figures, one has first obliged to compute intermediate output functionals related to the \emph{Mark-to-Market} (MtM) position at a given time $t \in [0, T],$ T being a positive, and finite, time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value

Polynomial Chaos Expansion Approach to Interest Rate Models

The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantityξ, hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper, we use the PCE approach in order to analyze some equity and interest rate models. In particular, we take into consideration those models which are based on, for example, the Geometric Brownian Motion, the Vasicek model, and the CIR model. We present theoretical as well as related concrete numerical approximation results considering, without loss of generality, the one-dimensional case. We also provide both an efficiency study and an accuracy study of our approach by comparing its outputs with the ones obtained adopting the Monte Carlo approach, both in its standard and its enhanced version

Systemic risk and banking regulation: some facts on the new regulatory framework

The recent financial crisis highlighted the relevant role of the systemic effects of banks’ defaults on the stability of the whole financial system. In this work we draw an organic picture of the current regulations, moving from the definitions of systemic risk to the issues concerning data availability. We show how a more detailed flow of data on traded deals might shed light on some systemic risk features taken into account only partially in the past. In particular, we analyse how the new regulatory framework allows regulators to describe OTC derivatives markets according to more detailed partitions, thus depicting a more realistic picture of the system. Finally, we suggest to study sub-markets illiquidity conditions to consider possible spill over effects which might lead to a worsening for the entire system

Systemic importance of financial institutions: from a global to a local perspective? A network theory approach

After the systemic effects of bank defaults during the recent financial crisis, and despite a huge amount of literature over the last years to detect systemic risk, no standard methodologies have been set up until now. We aim to build a concise but comprehensive picture of the state of the art, illustrating the open issues, and outlining pathways for future research. In particular, we propose the analysis of some examples of local systems that attract the attention of the financial sector. This work is directed to both academic researchers and practitioners

Assessing financial distress dependencies in OTC markets: a new approach by Trade Repositories data

After the recent financial crisis, it is undoubtedly recognized the importance of assessing not only the risk of distress for a single \financial entity", but also the distress dependencies between the different \entities", where by \entities" we mean in a broad sense any relevant cluster of products, risk factors, counterparties. In this paper, we focus on the Interest Rate Swap (IRS) segment as a significant fraction of the OTC market. We define a distress indicator by combining some distress drivers, such as averaged volumes, liquidity, volatility and bid-ask proxies. Hence, we analyse the distress dependencies among sub-markets identified by the segmentation of the IRS market according to contractual and financial features. We try to combine in an innovative way some new ingredients, namely the more granular data on OTC derivatives available from the trade repositories along with the classical JPoD approach introduced in the recent years by the IMF for studying the distress interdependence structure among financial institutions. The proposed technique seems to be quite promising. Indeed, the results are quite close to the practical intuition. At the best of our knowledge, this work is the first empirical study based on trade repositories' data for assessing systemic risk

The Default Risk Charge approach to regulatory risk measurement processes

In the present paper we consider the Default Risk Charge (DRC) measure as an effective alternative to the Incremental Risk Charge (IRC) one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets issued by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible because of both the new regulation and to the high speed - low cost technology available nowadays. Concrete algorithms and numerical examples are provided to illustrate the effectiveness of the proposed techniques

Implicit Trigger Price Determination for Contingent Convertible Bond

In this paper we provide concrete evaluations for the trigger price that causes the conversion of Convertible Contingent (CoCo) bond contracts.In particular we exploit prices for CoCo bonds traded in real financial markets and the values obtained by the credit derivative as well as by the equity derivative method, to determine the associated implicit trigger price. Because of the computational characteristics of the proposed approaches, we also provide related algorithms

Counterparty Credit Risk evaluation for Accumulator derivatives: the Brownian Local Time approach

In this paper we aim at exploiting the properties of the Brownian Local Time to estimate the Counterparty Credit Risk for a specific class of financial derivatives, i.e. the so called Accumulator derivatives , within a Black and Scholes-type market. The comparison with the results obtained by made use of a standard Monte Carlo approach, clearly shows the superiority of our proposal, which runs in smaller execution times and with better estimation accuracy

Systemic importance of financial institutions: regulations, research, open issues, proposals

In the field of risk management, scholars began to bring together the quantitative methodologies with the banking management issues about 30 years ago, with a special focus on market, credit and operational risks. After the systemic effects of banks defaults during the recent financial crisis, and despite a huge amount of literature in the last years concerning the systemic risk, no standard methodologies have been set up to now. Even the new Basel 3 regulation has adopted a heuristic indicator-based approach, quite far from an effective quantitative tool. In this paper, we refer to the different pieces of the puzzle: definition of systemic risk, a set of coherent and useful measures, the computability of these measures, the data set structure. In this challenging field, we aim to build a comprehensive picture of the state of the art, to illustrate the open issues, and to outline some paths for a more successful future research. This work appropriately integrates other useful surveys and it is directed to both academic researchers and practitioners