arXiv subjects

Gareth W. Peters

Publications and source records attributed to Gareth W. Peters.

At least 55 records · Page 3Linked to original sources

arXiv2015

SMC-ABC methods for the estimation of stochastic simulation models of the limit order book

In this paper we consider classes of models that have been recently developed for quantitative finance that involve modelling a highly complex multivariate, multi-attribute stochastic process known as the Limit Order Book (LOB). The LOB is the primary data structure recorded each day intra-daily for all assets on every electronic exchange in the world in which trading takes place. As such, it represents one of the most important fundamental structures to study from a stochastic process perspective if one wishes to characterize features of stochastic dynamics for price, volume, liquidity and other important attributes for a traded asset. In this paper we aim to adopt the model structure which develops a stochastic model framework for the LOB of a given asset and to explain how to perform calibration of this stochastic model to real observed LOB data for a range of different assets.

q-fin.CP↗

arXiv2015

New Perspectives on Multiple Source Localization in Wireless Sensor Networks

In this paper we address the challenging problem of multiple source localization in Wireless Sensor Networks (WSN). We develop an efficient statistical algorithm, based on the novel application of Sequential Monte Carlo (SMC) sampler methodology, that is able to deal with an unknown number of sources given quantized data obtained at the fusion center from different sensors with imperfect wireless channels. We also derive the Posterior Cramér-Rao Bound (PCRB) of the source location estimate. The PCRB is used to analyze the accuracy of the proposed SMC sampler algorithm and the impact that quantization has on the accuracy of location estimates of the sources. Extensive experiments show that the benefits of the proposed scheme in terms of the accuracy of the estimation method that are required for model selection (i.e., the number of sources) and the estimation of the source characteristics compared to the classical importance sampling method.

cs.IT↗

arXiv2015

Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators

We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discrete space, that a multidimensional correlated generalized diffusion is a linear combination of processes that originate from the decomposition of the starting multidimensional semimartingale. This result not only reconciles with the existing theory of diffusion approximations and decompositions, but defines the general representation of infinitesimal generators for both multidimensional generalized diffusions and as we will demonstrate also for the specification of copula density dependence structures. This new result provides immediate representation of the approximate solution for correlated stochastic differential equations. We demonstrate desirable convergence results for the proposed multidimensional semimartingales decomposition approximations.

math.ST↗

arXiv2015

Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models

In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

stat.CO↗

arXiv2014

Location Verification Systems for VANETs in Rician Fading Channels

In this work we propose and examine Location Verification Systems (LVSs) for Vehicular Ad Hoc Networks (VANETs) in the realistic setting of Rician fading channels. In our LVSs, a single authorized Base Station (BS) equipped with multiple antennas aims to detect a malicious vehicle that is spoofing its claimed location. We first determine the optimal attack strategy of the malicious vehicle, which in turn allows us to analyze the optimal LVS performance as a function of the Rician $K$-factor of the channel between the BS and a legitimate vehicle. Our analysis also allows us to formally prove that the LVS performance limit is independent of the properties of the channel between the BS and the malicious vehicle, provided the malicious vehicle's antenna number is above a specified value. We also investigate how tracking information on a vehicle quantitatively improves the detection performance of an LVS, showing how optimal performance is obtained under the assumption of the tracking length being randomly selected. The work presented here can be readily extended to multiple BS scenarios, and therefore forms the foundation for all optimal location authentication schemes within the context of Rician fading channels. Our study closes important gaps in the current understanding of LVS performance within the context of VANETs, and will be of practical value to certificate revocation schemes within IEEE 1609.2.

cs.NI↗

arXiv2014

Location Spoofing Detection for VANETs by a Single Base Station in Rician Fading Channels

In this work we examine the performance of a Location Spoofing Detection System (LSDS) for vehicular networks in the realistic setting of Rician fading channels. In the LSDS, an authorized Base Station (BS) equipped with multiple antennas utilizes channel observations to identify a malicious vehicle, also equipped with multiple antennas, that is spoofing its location. After deriving the optimal transmit power and the optimal directional beamformer of a potentially malicious vehicle, robust theoretical analysis and detailed simulations are conducted in order to determine the impact of key system parameters on the LSDS performance. Our analysis shows how LSDS performance increases as the Rician K-factor of the channel between the BS and legitimate vehicles increases, or as the number of antennas at the BS or legitimate vehicle increases. We also obtain the counter-intuitive result that the malicious vehicle's optimal number of antennas conditioned on its optimal directional beamformer is equal to the legitimate vehicle's number of antennas. The results we provide here are important for the verification of location information reported in IEEE 1609.2 safety messages.

cs.IT↗

arXiv2014

Location Verification Systems Under Spatially Correlated Shadowing

The verification of the location information utilized in wireless communication networks is a subject of growing importance. In this work we formally analyze, for the first time, the performance of a wireless Location Verification System (LVS) under the realistic setting of spatially correlated shadowing. Our analysis illustrates that anticipated levels of correlated shadowing can lead to a dramatic performance improvement of a Received Signal Strength (RSS)-based LVS. We also analyze the performance of an LVS that utilizes Differential Received Signal Strength (DRSS), formally proving the rather counter-intuitive result that a DRSS-based LVS has identical performance to that of an RSS-based LVS, for all levels of correlated shadowing. Even more surprisingly, the identical performance of RSS and DRSS-based LVSs is found to hold even when the adversary does not optimize his true location. Only in the case where the adversary does not optimize all variables under her control, do we find the performance of an RSS-based LVS to be better than a DRSS-based LVS. The results reported here are important for a wide range of emerging wireless communication applications whose proper functioning depends on the authenticity of the location information reported by a transceiver.

cs.IT↗

arXiv2014

Opening discussion on banking sector risk exposures and vulnerabilities from virtual currencies: An operational risk perspective

We develop the first basic Operational Risk perspective on key risk management issues associated with the development of new forms of electronic currency in the real economy. In particular, we focus on understanding the development of new risks types and the evolution of current risk types as new components of financial institutions arise to cater for an increasing demand for electronic money, micro-payment systems, Virtual money and cryptographic (Crypto) currencies. In particular, this paper proposes a framework of risk identification and assessment applied to Virtual and Crypto currencies from a banking regulation perspective. In doing so, it addresses the topical issues of understanding important key Operational Risk vulnerabilities and exposure risk drivers under the framework of the Basel II/III banking regulation, specifically associated with Virtual and Crypto currencies. This is critical to consider should such alternative currencies continue to grow in utilisation to the point that they enter into the banking sector, through commercial banks and financial institutions who are beginning to contemplate their recognition in terms of deposits, transactions and exchangeability for fiat currencies. We highlight how some of the features of Virtual and Crypto currencies are important drivers of Operational Risk, posing both management and regulatory challenges that must start to be considered and addressed both by regulators, central banks and security exchanges. In this paper we focus purely on the Operational Risk perspective of banks operating in an environment where such electronic Virtual currencies are available. Some aspects of this discussion are directly relevant now, whilst others can be understood as discussions to raise awareness of issues in Operational Risk that will arise as Virtual currency start to interact more widely in the real economy.

q-fin.RM↗

arXiv2014

Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence

Currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the markets have rational risk-neutral investors, then one would not expect profits from such strategies. That is, according to uncovered interest rate parity (UIP), changes in the related exchange rates should offset the potential to profit from such interest rate differentials. However, it has been shown empirically, that investors can earn profits on average by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, whilst allowing for any losses from exchanging back to their domestic currency at maturity. This paper explores the financial risk that trading strategies seeking to exploit a violation of the UIP condition are exposed to with respect to multivariate tail dependence present in both the funding and investment currency baskets. It will outline in what contexts these portfolio risk exposures will benefit accumulated portfolio returns and under what conditions such tail exposures will reduce portfolio returns.

q-fin.PM↗

arXiv2014

Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression

We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting. In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies. In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.

q-fin.RM↗

arXiv2014

Reinvestigating the Uncovered Interest Rate Parity Puzzle via Analysis of Multivariate Tail Dependence in Currency Carry Trades

The currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the markets have rational risk-neutral investors, then one would not expect profits from such strategies. That is uncovered interest rate parity (UIP), the parity condition in which exposure to foreign exchange risk, with unanticipated changes in exchange rates, should result in an outcome that changes in the exchange rate should offset the potential to profit from such interest rate differentials. The two primary assumptions required for interest rate parity are related to capital mobility and perfect substitutability of domestic and foreign assets. Given foreign exchange market equilibrium, the interest rate parity condition implies that the expected return on domestic assets will equal the exchange rate-adjusted expected return on foreign currency assets. However, it has been shown empirically, that investors can actually earn arbitrage profits by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, whilst allowing for any losses (or gains) from exchanging back to their domestic currency at maturity. Therefore trading strategies that aim to exploit the interest rate differentials can be profitable on average. The intention of this paper is therefore to reinterpret the currency carry trade puzzle in light of heavy tailed marginal models coupled with multivariate tail dependence features in the analysis of the risk-reward for the currency portfolios with high interest rate differentials and low interest rate differentials.

q-fin.ST↗

arXiv2013

Optimal insurance purchase strategies via optimal multiple stopping times

In this paper we study a class of insurance products where the policy holder has the option to insure $k$ of its annual Operational Risk losses in a horizon of $T$ years. This involves a choice of $k$ out of $T$ years in which to apply the insurance policy coverage by making claims against losses in the given year. The insurance product structure presented can accommodate any kind of annual mitigation, but we present three basic generic insurance policy structures that can be combined to create more complex types of coverage. Following the Loss Distributional Approach (LDA) with Poisson distributed annual loss frequencies and Inverse-Gaussian loss severities we are able to characterize in closed form analytical expressions for the multiple optimal decision strategy that minimizes the expected Operational Risk loss over the next $T$ years. For the cases where the combination of insurance policies and LDA model does not lead to closed form expressions for the multiple optimal decision rules, we also develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.

q-fin.RM↗

arXiv2013

Optimal Information-Theoretic Wireless Location Verification

We develop a new Location Verification System (LVS) focussed on network-based Intelligent Transport Systems and vehicular ad hoc networks. The algorithm we develop is based on an information-theoretic framework which uses the received signal strength (RSS) from a network of base-stations and the claimed position. Based on this information we derive the optimal decision regarding the verification of the user's location. Our algorithm is optimal in the sense of maximizing the mutual information between its input and output data. Our approach is based on the practical scenario in which a non-colluding malicious user some distance from a highway optimally boosts his transmit power in an attempt to fool the LVS that he is on the highway. We develop a practical threat model for this attack scenario, and investigate in detail the performance of the LVS in terms of its input/output mutual information. We show how our LVS decision rule can be implemented straightforwardly with a performance that delivers near-optimality under realistic threat conditions, with information-theoretic optimality approached as the malicious user moves further from the highway. The practical advantages our new information-theoretic scheme delivers relative to more traditional Bayesian verification frameworks are discussed.

cs.IT↗

arXiv2013

Loss Distribution Approach for Operational Risk Capital Modelling under Basel II: Combining Different Data Sources for Risk Estimation

The management of operational risk in the banking industry has undergone significant changes over the last decade due to substantial changes in operational risk environment. Globalization, deregulation, the use of complex financial products and changes in information technology have resulted in exposure to new risks very different from market and credit risks. In response, Basel Committee for banking Supervision has developed a regulatory framework, referred to as Basel II, that introduced operational risk category and corresponding capital requirements. Over the past five years, major banks in most parts of the world have received accreditation under the Basel II Advanced Measurement Approach (AMA) by adopting the loss distribution approach (LDA) despite there being a number of unresolved methodological challenges in its implementation. Different approaches and methods are still under hot debate. In this paper, we review methods proposed in the literature for combining different data sources (internal data, external data and scenario analysis) which is one of the regulatory requirement for AMA.

q-fin.RM↗

arXiv2013

Understanding Operational Risk Capital Approximations: First and Second Orders

We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA). Our emphasis is to focus on the important loss processes with regard to those that contribute most to capital, the so called high consequence, low frequency loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard); Expected Shortfall (ES) and the Spectral Risk Measure. These then form the capital approximations.

q-fin.RM↗

arXiv2012

A Copula Based Bayesian Approach for Paid-Incurred Claims Models for Non-Life Insurance Reserving

Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of Heirarchical Bayesian Paid-Incurred-Claims models, combining the claims reserving models of Hertig et al. (1985) and Gogol et al. (1993). In the process we extend the independent log-normal model of Merz et al. (2010) by incorporating different dependence structures using a Data-Augmented mixture Copula Paid-Incurred claims model. The utility and influence of incorporating both payment and incurred losses into estimating of the full predictive distribution of the outstanding loss liabilities and the resulting reserves is demonstrated in the following cases: (i) an independent payment (P) data model; (ii) the independent Payment-Incurred Claims (PIC) data model of Merz et al. (2010); (iii) a novel dependent lag-year telescoping block diagonal Gaussian Copula PIC data model incorporating conjugacy via transformation; (iv) a novel data-augmented mixture Archimedean copula dependent PIC data model. Inference in such models is developed via a class of adaptive Markov chain Monte Carlo sampling algorithms. These incorporate a data-augmentation framework utilized to efficiently evaluate the likelihood for the copula based PIC model in the loss reserving triangles. The adaptation strategy is based on representing a positive definite covariance matrix by the exponential of a symmetric matrix as proposed by Leonard et al. (1992).

q-fin.RM↗

arXiv2012

Feynman-Kac particle integration with geometric interacting jumps

This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process is in continuous or discrete time. For the former, we consider discrete generation particle models defined by arbitrarily fine time mesh approximations of the Feynman-Kac models with continuous time path integrals. For the latter, we assume that the discrete process is observed at integer times and we design new approximation models with geometric interacting jumps in terms of a sequence of intermediate time steps between the integers. In both situations, we provide non asymptotic bias and variance theorems w.r.t. the time step and the size of the system, yielding what appear to be the first results of this type for this class of Feynman-Kac particle integration models. We also discuss uniform convergence estimates w.r.t. the time horizon. Our approach is based on an original semigroup analysis with first order decompositions of the fluctuation errors.

math.PR↗

arXiv2012

Generalized Interference Models in Doubly Stochastic Poisson Random Fields for Wideband Communications: the PNSC(alpha) model

A general stochastic model is developed for the total interference in wideband systems, denoted as the PNSC(alpha) Interference Model. It allows one to obtain, analytic representations in situations where (a) interferers are distributed according to either a homogeneous or an inhomogeneous in time or space Cox point process and (b) when the frequency bands occupied by each of the unknown number of interferers is also a random variable in the allowable bandwidth. The analytic representations obtained are generalizations of Cox processes to the family of sub-exponential models characterized by distributions from the alpha-stable family. We develop general parametric density representations for the interference models via doubly stochastic Poisson mixture representations of Scaled Mixture of Normal's via the Normal-Stable variance mixture. To illustrate members of this class of interference model we also develop two special cases for a moderately impulsive interference (alpha=3/2) and a highly impulsive interference (alpha=2/3) where closed form representations can be obtained either by the SMiN representation or via function expansions based on the Holtsmark distribution or Whittaker functions. To illustrate the paper we propose expressions for the Capacity of a BPSK system under a PNSC(alpha) interference, via analytic expressions for the Likelihood Ratio Test statistic.

stat.AP↗