373 research outputs found
Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces
Nonlinear non-Gaussian state-space models arise in numerous applications in
statistics and signal processing. In this context, one of the most successful
and popular approximation techniques is the Sequential Monte Carlo (SMC)
algorithm, also known as particle filtering. Nevertheless, this method tends to
be inefficient when applied to high dimensional problems. In this paper, we
focus on another class of sequential inference methods, namely the Sequential
Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising
alternative to SMC methods. After providing a unifying framework for the class
of SMCMC approaches, we propose novel efficient strategies based on the
principle of Langevin diffusion and Hamiltonian dynamics in order to cope with
the increasing number of high-dimensional applications. Simulation results show
that the proposed algorithms achieve significantly better performance compared
to existing algorithms
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
Multiple barrier-crossings of an Ornstein-Uhlenbeck diffusion in consecutive periods
We investigate the joint distribution and the multivariate survival functions
for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive
time-intervals. A PDE method, alongside an eigenfunction expansion is adopted,
with which we first calculate the distribution and the survival functions for
the maximum of a homogeneous OU-process in a single interval. By a
deterministic time-change and a parameter translation, this result can be
extended to an inhomogeneous OU-process. Next, we derive a general formula for
the joint distribution and the survival functions for the maxima of a
continuous Markov process in consecutive periods. With these results, one can
obtain semi-analytical expressions for the joint distribution and the
multivariate survival functions for the maxima of an OU-process, with piecewise
constant parameter functions, in consecutive time periods. The joint
distribution and the survival functions can be evaluated numerically by an
iterated quadrature scheme, which can be implemented efficiently by matrix
multiplications. Moreover, we show that the computation can be further
simplified to the product of single quadratures if the filtration is enlarged.
Such results may be used for the modelling of heatwaves and related risk
management challenges.Comment: 38 pages, 10 figures, 2 table
Trends in crypto-currencies and blockchain technologies: A monetary theory and regulation perspective
The internet era has generated a requirement for low cost, anonymous and
rapidly verifiable transactions to be used for online barter, and fast settling
money have emerged as a consequence. For the most part, e-money has fulfilled
this role, but the last few years have seen two new types of money emerge.
Centralised virtual currencies, usually for the purpose of transacting in
social and gaming economies, and crypto-currencies, which aim to eliminate the
need for financial intermediaries by offering direct peer-to-peer online
payments.
We describe the historical context which led to the development of these
currencies and some modern and recent trends in their uptake, in terms of both
usage in the real economy and as investment products. As these currencies are
purely digital constructs, with no government or local authority backing, we
then discuss them in the context of monetary theory, in order to determine how
they may be have value under each. Finally, we provide an overview of the state
of regulatory readiness in terms of dealing with transactions in these
currencies in various regions of the world
Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets
This paper poses a few fundamental questions regarding the attributes of the
volume profile of a Limit Order Books stochastic structure by taking into
consideration aspects of intraday and interday statistical features, the impact
of different exchange features and the impact of market participants in
different asset sectors. This paper aims to address the following questions:
1. Is there statistical evidence that heavy-tailed sub-exponential volume
profiles occur at different levels of the Limit Order Book on the bid and ask
and if so does this happen on intra or interday time scales ?
2.In futures exchanges, are heavy tail features exchange (CBOT, CME, EUREX,
SGX and COMEX) or asset class (government bonds, equities and precious metals)
dependent and do they happen on ultra-high (<1sec) or mid-range (1sec -10min)
high frequency data?
3.Does the presence of stochastic heavy-tailed volume profile features evolve
in a manner that would inform or be indicative of market participant behaviors,
such as high frequency algorithmic trading, quote stuffing and price discovery
intra-daily?
4. Is there statistical evidence for a need to consider dynamic behavior of
the parameters of models for Limit Order Book volume profiles on an intra-daily
time scale ?
Progress on aspects of each question is obtained via statistically rigorous
results to verify the empirical findings for an unprecedentedly large set of
futures market LOB data. The data comprises several exchanges, several futures
asset classes and all trading days of 2010, using market depth (Type II) order
book data to 5 levels on the bid and ask
A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing
In this article we investigate a state-space representation of the Lee-Carter
model which is a benchmark stochastic mortality model for forecasting
age-specific death rates. Existing relevant literature focuses mainly on
mortality forecasting or pricing of longevity derivatives, while the full
implications and methods of using the state-space representation of the
Lee-Carter model in pricing retirement income products is yet to be examined.
The main contribution of this article is twofold. First, we provide a rigorous
and detailed derivation of the posterior distributions of the parameters and
the latent process of the Lee-Carter model via Gibbs sampling. Our assumption
for priors is slightly more general than the current literature in this area.
Moreover, we suggest a new form of identification constraint not yet utilised
in the actuarial literature that proves to be a more convenient approach for
estimating the model under the state-space framework. Second, by exploiting the
posterior distribution of the latent process and parameters, we examine the
pricing range of annuities, taking into account the stochastic nature of the
dynamics of the mortality rates. In this way we aim to capture the impact of
longevity risk on the pricing of annuities. The outcome of our study
demonstrates that an annuity price can be more than 4% under-valued when
different assumptions are made on determining the survival curve constructed
from the distribution of the forecasted death rates. Given that a typical
annuity portfolio consists of a large number of policies with maturities which
span decades, we conclude that the impact of longevity risk on the accurate
pricing of annuities is a significant issue to be further researched. In
addition, we find that mis-pricing is increasingly more pronounced for older
ages as well as for annuity policies having a longer maturity.Comment: 9 pages; conference pape
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