SEARCH · Searcharxiv

Results for “q-fin.RM”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22Linked to original sources

arXiv2013

Computational Dynamic Market Risk Measures in Discrete Time Setting

Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and implement dynamic market risk measures based on recursion and state economy representation. The proposed approach is to be implementable and to inherit properties from static market risk measures.

q-fin.RM↗

arXiv2013

Moderate deviations for importance sampling estimators of risk measures

Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a way to speed up computations. This paper considers moderate deviations for the weighted empirical process, the process analogue of the weighted empirical measure, arising in importance sampling. The moderate deviation principle is established as an extension of existing results. Using a delta method for large deviations established by Gao and Zhao (Ann. Statist., 2011) together with classical large deviation techniques, the moderate deviation principle for the weighted empirical process is extended to functionals of the weighted empirical process which correspond to risk measures. The main results are moderate deviation principles for importance sampling estimators of the quantile function of a distribution and Expected Shortfall.

math.PR↗

arXiv2013

The Meaning of Probability of Default for Asset-backed Loans

The authors examine the concept of probability of default for asset-backed loans. In contrast to unsecured loans it is shown that probability of default can be defined as either a measure of the likelihood of the borrower failing to make required payments, or as the likelihood of an insufficiency of collateral value on foreclosure. Assuming expected loss is identical under either definition, this implies a corresponding pair of definitions for loss given default. Industry treatment of probability of default for asset-backed loans appears to inconsistently blend the two types of definition. The authors develop a mathematical treatment of asset-backed loans which consistently applies each type of definition in a framework to produce the same expected loss and allows translation between the two frameworks.

q-fin.RM↗

arXiv2013

Risk Without Return

Risk-only investment strategies have been growing in popularity as traditional in- vestment strategies have fallen short of return targets over the last decade. However, risk-based investors should be aware of four things. First, theoretical considerations and empirical studies show that apparently dictinct risk-based investment strategies are manifestations of a single effect. Second, turnover and associated transaction costs can be a substantial drag on return. Third, capital diversification benefits may be reduced. Fourth, there is an apparent connection between performance and risk diversification. To analyze risk diversification benefits in a consistent way, we introduce the Risk Diversification Index (RDI) which measures risk concentrations and complements the Herfindahl-Herschman Index (HHI) for capital concentrations.

q-fin.ST↗

arXiv2013

Assessing Financial Model Risk

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk and the local measure of model risk. Each of the measures has a specific purpose and so allows for flexibility. We illustrate the various notions by studying some relevant examples, so as to emphasize the practicability and tractability of our approach.

q-fin.RM↗

arXiv2014

Heavy tailed time series with extremal independence

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information about limiting behavior of time series with extremal independence by introducing a sequence of scaling functions and conditional scaling exponent. Both quantities provide more information about joint extremes than a widely used tail dependence coefficient. We calculate the scaling functions and the scaling exponent for variety of models, including Markov chains, exponential autoregressive model, stochastic volatility with heavy tailed innovations or volatility.

math.ST↗

arXiv2013

Contraction or steady state? An analysis of credit risk management in Italy in the period 2008-2012

Credit risk management in Italy is characterized, in the period June 2008 to June 2012, by frequent (frequency=0.5 cycles per year) and intense (peak amplitude: mean=39.2 billion Euros, s.e.=2.83 billion Euros) quarterly contractions and expansions around the mean (915.4 billion Euros, s.e.=3.59 billion Euros) of the nominal total credit used by non-financial corporations. Such frequent and intense fluctuations are frequently ascribed to exogenous Basel II procyclical effects on credit flow into the economy and, consequently, Basel III output based point in time Credit to GDP countercyclical buffering advocated. We have tested the opposite null hypotheses that such variation is significantly correlated to actual default rates, and that such correlation is explained by fluctuations of credit supply around a steady state. We have found that, in the period June 2008 to June 2012 (n=17), linear regression of credit growth rates on default rates reveals a negative correlation of r=minus 0.6903 with R squared=0.4765, and that credit supply fluctuates steadily around the default rate with an Internal Steady State Parameter SSP=0.00245 with chi squared=37.47 (v=16, P<.005). We conclude that fluctuations of the total credit used by non-financial corporations are exhaustively explained by variation of the independent variable default rate, and that credit variation fluctuates around a steady state. We conclude that credit risk management in Italy has been effective in parameterizing credit supply variation to default rates within the Basel II operating framework. Basel III prospective countercyclical point in time output buffers based on filtered Credit to GDP ratios and dynamic provisioning proposals should take into account this underlying steady state statistical pattern.

q-fin.RM↗

arXiv2013

A Remark on the Structure of Expectiles

Expectiles were defined using a minimisation principle. They form a special class of coherent risk measures. We will describe the scenario set and we will show that there is a most severe commonotonic risk measure that is smaller than the given expectile.

math.PR↗

arXiv2013

Where Do Thin Tails Come From?

The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general dose-response curve and argue that the left and right-boundedness or saturation of the response in natural things leads to thin-tails, even when the "underlying" random variable at the source of the exposure is fat-tailed.

q-fin.RM↗

arXiv2013

Systematic and non-systematic mortality risk in pension portfolios

We study the effects of non-systematic and systematic mortality risks on the required initial capital in a pension plan, in the presence of financial risks. We discover that for a pension plan with few members the impact of pooling on the required capital per person is strong, but non-systematic risk diminishes rapidly as the number of members increases. Systematic mortality risk, on the other hand, is a significant source of risk is a pension portfolio.

q-fin.RM↗

arXiv2013

Liability-driven investment in longevity risk management

This paper studies optimal investment from the point of view of an investor with longevity-linked liabilities. The relevant optimization problems rarely are analytically tractable, but we are able to show numerically that liability driven investment can significantly outperform common strategies that do not take the liabilities into account. In problems without liabilities the advantage disappears, which suggests that the superiority of the proposed strategies is indeed based on connections between liabilities and asset returns.

q-fin.RM↗

arXiv2014

Gold, Oil, and Stocks

We employ a wavelet approach and conduct a time-frequency analysis of dynamic correlations between pairs of key traded assets (gold, oil, and stocks) covering the period from 1987 to 2012. The analysis is performed on both intra-day and daily data. We show that heterogeneity in correlations across a number of investment horizons between pairs of assets is a dominant feature during times of economic downturn and financial turbulence for all three pairs of the assets under research. Heterogeneity prevails in correlations between gold and stocks. After the 2008 crisis, correlations among all three assets increase and become homogenous: the timing differs for the three pairs but coincides with the structural breaks that are identified in specific correlation dynamics. A strong implication emerges: during the period under research, and from a different-investment-horizons perspective, all three assets could be used in a well-diversified portfolio only during relatively short periods.

q-fin.ST↗

arXiv2014

The Financing of Innovative SMEs: a multicriteria credit rating model

Small Medium-sized Enterprises (SMEs) face many obstacles when they try to access credit market. These obstacles are increased if the SMEs are innovative. In this case, financial data are insufficient or even not reliable. Thus, when building a judgemental rating model, mainly based on qualitative criteria (soft information), it is very important to finance SMEs' activities. Until now, there isn't a multicriteria credit risk model based on soft information for innovative SMEs. In this paper, we try to fill this gap by presenting a multicriteria credit risk model, specifically, ELECTRE-TRI. To obtain robust SMEs' assignments to the risk classes, a SMAA-TRI analysis is also implemented. In fact, SMAA-TRI incorporates ELECTRE-TRI by considering different sets of preference parameters with Monte Carlo simulations. Finally, we carry out some real case studies, with the aim of illustrating the multicriteria credit risk model proposed.

q-fin.RM↗

arXiv2014

The Skin In The Game Heuristic for Protection Against Tail Events

Standard economic theory makes an allowance for the agency problem, but not the compounding of moral hazard in the presence of informational opacity, particularly in what concerns high-impact events in fat tailed domains (under slow convergence for the law of large numbers). Nor did it look at exposure as a filter that removes nefarious risk takers from the system so they stop harming others. \textcolor{red}{ (In the language of probability, skin in the game creates an absorbing state for the agent, not just the principal)}. But the ancients did; so did many aspects of moral philosophy. We propose a global and morally mandatory heuristic that anyone involved in an action which can possibly generate harm for others, even probabilistically, should be required to be exposed to some damage, regardless of context. While perhaps not sufficient, the heuristic is certainly necessary hence mandatory. It is supposed to counter voluntary and involuntary risk hiding$-$ and risk transfer $-$ in the tails. We link the rule to various philosophical approaches to ethics and moral luck.

q-fin.RM↗

arXiv2013

Optimal Dynamic Portfolio with Mean-CVaR Criterion

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of Neyman-Pearson type binary solution. We add a constraint on expected return to investigate the Mean-CVaR portfolio selection problem in a dynamic setting: the investor is faced with a Markowitz type of risk reward problem at final horizon where variance as a measure of risk is replaced by CVaR. Based on the complete market assumption, we give an analytical solution in general. The novelty of our solution is that it is no longer Neyman-Pearson type where the final optimal portfolio takes only two values. Instead, in the case where the portfolio value is required to be bounded from above, the optimal solution takes three values; while in the case where there is no upper bound, the optimal investment portfolio does not exist, though a three-level portfolio still provides a sub-optimal solution.

q-fin.PM↗

arXiv2013

Achieving Speedup in Aggregate Risk Analysis using Multiple GPUs

Stochastic simulation techniques employed for the analysis of portfolios of insurance/reinsurance risk, often referred to as `Aggregate Risk Analysis', can benefit from exploiting state-of-the-art high-performance computing platforms. In this paper, parallel methods to speed-up aggregate risk analysis for supporting real-time pricing are explored. An algorithm for analysing aggregate risk is proposed and implemented for multi-core CPUs and for many-core GPUs. Experimental studies indicate that GPUs offer a feasible alternative solution over traditional high-performance computing systems. A simulation of 1,000,000 trials with 1,000 catastrophic events per trial on a typical exposure set and contract structure is performed in less than 5 seconds on a multiple GPU platform. The key result is that the multiple GPU implementation can be used in real-time pricing scenarios as it is approximately 77x times faster than the sequential counterpart implemented on a CPU.

cs.DC↗

arXiv2014

Measuring risk with multiple eligible assets

The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and continuity properties of these risk measures with respect to multiple eligible assets. Our finiteness and continuity results highlight the interplay between the acceptance set and the class of eligible portfolios. We present a simple, alternative approach to the dual representation of convex risk measures by directly applying to the acceptance set the external characterization of closed, convex sets. We prove that risk measures are nondegenerate if and only if the pricing functional admits a positive extension which is a supporting functional for the underlying acceptance set, and provide a characterization of when such extensions exist. Finally, we discuss applications to set-valued risk measures, superhedging with shortfall risk, and optimal risk sharing.

q-fin.RM↗

arXiv2013

A pricing measure to explain the risk premium in power markets

In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump Lévy process and models the characteristic spikes observed in such markets. When it comes to pricing, a popular choice of pricing measure is given by the Esscher transform that preserves the probabilistic structure of the driving Lévy processes, while changing the levels of mean reversion. Using this choice one can generate stochastic risk premiums (in geometric spot models) but with (deterministically) changing sign. In this paper we introduce a pricing change of measure, which is an extension of the Esscher transform. With this new change of measure we also can slow down the speed of mean reversion and generate stochastic risk premiums with stochastic non constant sign, even in arithmetic spot models. In particular, we can generate risk profiles with positive values in the short end of the forward curve and negative values in the long end. Finally, our pricing measure allows us to have a stationary spot dynamics while still having randomly fluctuating forward prices for contracts far from maturity.

q-fin.PR↗