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At least 271 records · Page 15Linked to original sources
arXiv2012

A Dynamical Approach to Operational Risk Measurement

We propose a dynamical model for the estimation of Operational Risk in banking institutions. Operational Risk is the risk that a financial loss occurs as the result of failed processes. Examples of operational losses are the ones generated by internal frauds, human errors or failed transactions. In order to encompass the most heterogeneous set of processes, in our approach the losses of each process are generated by the interplay among random noise, interactions with other processes and the efforts the bank makes to avoid losses. We show how some relevant parameters of the model can be estimated from a database of historical operational losses, validate the estimation procedure and test the forecasting power of the model. Some advantages of our approach over the traditional statistical techniques are that it allows to follow the whole time evolution of the losses and to take into account different-time correlations among the processes.

q-fin.RM↗
arXiv2012

Iterated risk measures for risk-sensitive Markov decision processes with discounted cost

We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A straightforward modification to discounted expected utility leads to inconsistent decision making over time. We will show that an iterated risk measure can represent the preference that cannot be represented by any discounted expected utility and that the decisions based on the iterated risk measure are consistent over time.

cs.GT↗
arXiv2012

Active margin system for margin loans and its application in Chinese market: using cash and randomly selected stock as collateral

An active margin system for margin loans is proposed for Chinese margin lending market, which uses cash and randomly selected stock as collateral. The conditional probability of negative return(CPNR) after a forced sale of securities from under-margined account in a falling market is used to measure the risk faced by the brokers, and the margin system is chosen under the constraint of the risk measure. In order to calculate CPNR, a recursive algorithm is proposed under a Markov chain model, which is constructed by sample learning method. The resulted margin system is an active system, which is able to adjust actively with respect to the changes of stock prices and the changes of different collateral. The resulted margin system is applied to 30,000 margin loans of 150 stocks listed on Shanghai Stock Exchange. The empirical results show the number of margin calls and the average costs of the loans under the proposed margin system are less than their counterparts under the system required by SSE and SZSE.

q-fin.RM↗
arXiv2012

Active margin system for margin loans using cash and stock as collateral and its application in Chinese market

Margin system for margin loans using cash and stock as collateral is considered in this paper, which is the line of defence for brokers against risk associated with margin trading. The conditional probability of negative return is used as risk measure, and a recursive algorithm is proposed to realize this measure under a Markov chain model. Optimal margin system is chosen from those systems which satisfy the constraint of the risk measure. The resulted margin system is able to adjust actively with respect to the changes of stock prices. The margin system required by the Shanghai Stock Exchange is compared with the proposed system, where 25,200 margin loans of 126 stocks listed on the SSE are investigated. It is found that the number of margin calls under the proposed margin system is significantly less than its counterpart under the required system for the same level of risk, and the average costs of the loans are similar under the two types of margin systems.

q-fin.RM↗
arXiv2013

Set-valued average value at risk and its computation

New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both version over finite probability spaces. Several examples illustrate various features of the theoretical constructions.

q-fin.RM↗
arXiv2012

Bounds for rating override rates

Overrides of credit ratings are important correctives of ratings that are determined by statistical rating models. Financial institutions and banking regulators agree on this because on the one hand errors with ratings of corporates or banks can have fatal consequences for the lending institutions and on the other hand errors by statistical methods can be minimised but not completely avoided. Nonetheless, rating overrides can be misused in order to conceal the real riskiness of borrowers or even entire portfolios. That is why rating overrides usually are strictly governed and carefully recorded. It is not clear, however, which frequency of overrides is appropriate for a given rating model within a predefined time period. This paper argues that there is a natural error rate associated with a statistical rating model that may be used to inform assessment of whether or not an observed override rate is adequate. The natural error rate is closely related to the rating model's discriminatory power and can readily be calculated.

q-fin.RM↗
arXiv2012

Percentiles of sums of heavy-tailed random variables: Beyond the single-loss approximation

A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it is random. The zeroth order approximation is the percentile of the maximum term in the sum. Higher orders in the perturbative series involve the right-truncated moments of the individual random variables that appear in the sum. These censored moments are always finite. As a result, and in contrast to previous approximations proposed in the literature, the perturbative series has the same form regardless of whether these random variables have a finite mean or not. The accuracy of the approximations is illustrated for a variety of distributions and a wide range of parameters. The quality of the estimate improves as more terms are included in the perturbative series, specially for higher percentiles and heavier tails.

stat.AP↗
arXiv2012

Using Decision Tree Learner to Classify Solvency Position for Thai Non-life Insurance Companies

This paper introduces a Decision Tree Learner as an early warning system for classification of the non-life insurance companies according to their financial solid as strong, moderate, weak, or insolvency. In this study, we ran several experiments to show that the proposed model can achieve a good result using standard 10 fold crossvalidation, split train and test data set, and separated test set. The results show that the method is effective and can accurately classify the solvency position.

q-fin.RM↗
arXiv2012

Empirical Evidence for the Structural Recovery Model

While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to be estimated. The recovery rate is often modeled independently with regard to the default probability, whereas the Merton model yields a functional dependence of both variables. We use Moody's Default and Recovery Database in order to investigate the relationship of default probability and recovery rate for senior secured bonds. The assumptions in the Merton model do not seem justified by the empirical situation. Yet the empirical dependence of default probability and recovery rate is well described by the functional dependence found in the Merton model.

q-fin.RM↗
arXiv2012

Ordinal Classification Method for the Evaluation Of Thai Non-life Insurance Companies

This paper proposes a use of an ordinal classifier to evaluate the financial solidity of non-life insurance companies as strong, moderate, weak, and insolvency. This study constructed an efficient classification model that can be used by regulators to evaluate the financial solidity and to determine the priority of further examination as an early warning system. The proposed model is beneficial to policy-makers to create guidelines for the solvency regulations and roles of the government in protecting the public against insolvency.

q-fin.RM↗
arXiv2012

The Mathematics of the Relationship between the Default Risk and Yield-to-Maturity of Coupon Bonds

The paper analyzes the mathematics of the relationship between the default risk and yield-to-maturity of a coupon bond. It is shown that the yield-to-maturity is driven not only by the default probability and recovery rate of the bond but also by other contractual characteristics of the bond that are not commonly associated with default risk, such as the maturity and coupon rate of the bond. In particular, for given default probability and recovery rate, both the level and slope of the yield-to-maturity term structure depend on the coupon rate, as the higher the coupon rate the higher the yield-to-maturity term structure. In addition, the yield-to-maturity term structure is upward or downward sloping depending on whether the coupon rate is high or low enough. Similar qualitative results also holds for CDS spreads. Consequently, the yield-to-maturity is an indicator that must be used cautiously as a proxy for default risk.

q-fin.PR↗
arXiv2012

Systemic losses in banking networks: indirect interaction of nodes via asset prices

A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing individual banks; associated with each node is a balance sheet consisting of assets and liabilities. Initial node failures are triggered by external correlated shocks applied to the asset sides of the balance sheets. These defaults lead to further reductions in asset values of all nodes which in turn produce additional failures, and so on. This mechanism induces indirect interactions between the nodes and leads to a cascade of defaults. There are no interbank links, and therefore no direct interactions, between the nodes. The resulting probability distribution for the total (direct plus systemic) network loss can be viewed as a modification of the well-known Vasicek distribution.

q-fin.RM↗
arXiv2012

A proposal for impact-adjusted valuation: Critical leverage and execution risk

The practice of valuation by marking-to-market with current trading prices is seriously flawed. Under leverage the problem is particularly dramatic: due to the concave form of market impact, selling always initially causes the expected leverage to increase. There is a critical leverage above which it is impossible to exit a portfolio without leverage going to infinity and bankruptcy becoming likely. Standard risk-management methods give no warning of this problem, which easily occurs for aggressively leveraged positions in illiquid markets. We propose an alternative accounting procedure based on the estimated market impact of liquidation that removes the illusion of profit. This should curb the leverage cycle and contribute to an enhanced stability of financial markets.

q-fin.GN↗
arXiv2012

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

We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.

q-fin.PR↗
arXiv2014

Comparative and qualitative robustness for law-invariant risk measures

When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and we propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz space. This concept of robustness captures the tradeoff between robustness and sensitivity and can be quantified by an index of qualitative robustness. By means of this index, we can compare various risk measures, such as distortion risk measures, in regard to their degree of robustness. Our analysis also yields results that are of independent interest such as continuity properties and consistency of estimators for risk measures, or a Skorohod representation theorem for ψ-weak convergence.

q-fin.RM↗
arXiv2012

Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method

In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an analytical perturbation procedure for generic non-linear FBSDEs. There appear multiple species of particles, where the first one follows the diffusion of the original underlying state, and the others the Malliavin derivatives with a grading structure. The number of branching points are capped by the order of perturbation, which is expected to make the scheme less numerically intensive. The proposed method can be applied to semi-linear problems, such as American and Bermudan options, Credit Value Adjustment (CVA), and even fully non-linear issues, such as the optimal portfolio problems in incomplete and/or constrained markets, feedbacks from large investors, and also the analysis of various risk measures.

q-fin.CP↗
arXiv2012

The Variance of Standard Option Returns

The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is possible to give explicit formulae for the variance of European option returns (vanilla calls and puts, as well as barrier options), and that for American options the variance can be computed using a PDE approach, involving a modified Black-Scholes PDE. We show how the need to consider risk parameters, such as the variance, and also the probability of expiring worthless (PEW), arises naturally for individual investors in options. Furthermore, we show that a volatility smile arises in a simple model of risk-seeking option pricing.

q-fin.PR↗