330 research outputs found
Applications of hidden Markov models in financial modelling
No full textThis thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Various models driven by a hidden Markov chain in discrete or continuous time
are developed to capture the stylised features of market variables whose levels or
values constitute as the underliers of financial derivative contracts or investment
portfolios. Since the parameters are switching regimes, the changes and developments
in the economy as soon as they arise are readily reflected in these models.
The change of probability measure technique and the EM algorithm are fundamental
techniques utilised in the optimal parameter estimation. Recursive adaptive
filters for the state of the Markov chain and other auxiliary processes related to
the Markov chain are derived which in turn yield self-tuning dynamic financial
models. A hidden Markov model (HMM)-based modelling set-up for commodity
prices is developed and the predictability of the gold market under this setting is
examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed
and under this set-up, we address two statistical inference issues: the sensitivity
of the model to small changes in parameter estimates and the selection of the optimal
number of states. The extended OU model is implemented on a data set of
30-day Canadian T-bill yields. An exponential of a Markov-switching OU process
plus a compound Poisson process is put forward as a model for the evolution of
electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the
vast improvements gained in incorporating regimes in the model. A multivariate
HMM is employed as a framework in providing the solutions of two asset allocation
problems; one involves the mean-variance utility function and the other entails the
CVaR constraint. Finally, the valuation of credit default swaps highlights the important
considerations necessitated by pricing in a regime-switching environment.
Certain numerical schemes are applied to obtain approximations for the default
probabilities and swap rates.Brunel Research Initiative and Enterprise Fund (BRIEF) and European Union (Marie Curie Fellowship
Dynamical theory of dense groups of galaxies
No full textIt is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups
A partially linearized sigma point filter for latent state estimation in nonlinear time series models
No full textA new technique for the latent state estimation of a wide class of nonlinear time
series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process
Smoothed parameter estimation for a hidden Markov Model of credit quality
No full textWe consider a hidden Markov model of credit quality. We assume that the credit rating evolution can be described by a Markov chain but that we do not observe this Markov chain directly. Rather, it is hidden in “noisy” observations represented by the posted credit ratings. The model is formulated in discrete time with a Markov chain observed in martingale noise. We derive smoothed estimates for the state of the Markov chain governing the evolution of the credit rating process and the parameters of the model.Malgorzata W. Korolkiewicz and Robert J. Elliothttp://www.springer.com/business/operations+research/book/978-0-387-71081-
A new moment matching algorithm for sampling from partially specified symmetric distributions
No full textA new algorithm is proposed for generating scenarios from a partially specified symmetric multivariate distribution. The algorithm generates samples which match the first two moments exactly and match the marginal fourth moments approximately, using a semidefinite programming procedure. The performance of the
algorithm is illustrated by a numerical example
The term structure of interest rates in a hidden markov setting
No full textWe describe an interest rate model in which randomness in the shortterm interest rate is partially due to a Markov chain. We model randomness through the volatility and mean-reverting level as well as through the interest rate directly. The short- term interest rate is modeled in a risk-neutral setting as a continuous process in continuous time. This allows the valuation of interest rate derivatives using the martingale approach. In particular, a solution is found for the value of a zero-coupon bond. This leads to a non-linear regression model for the yield to maturity, which is used to filter the state of the unobservable Markov chain.Robert J. Elliot and Craig A. Wilsonhttp://www.springer.com/business/operations+research/book/978-0-387-71081-
A new algorithm for latent state estimation in nonlinear time series models
No full textWe consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in
engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing
the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples
A linear algebraic method for pricing temporary life annuities and insurance policies
No full textWe recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims
Pricing options and variance swaps in Markov-Modulated Brownian markets
No full textA Markov-modulated market consists of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on Markov process x. We study the pricing of options and variance swaps in such markets. Using the martingale characterization of Markov processes, we note the incompleteness of Markovmodulated markets and find the minimal martingale measure. Black-Scholes formulae for Markov-modulated markets with or without jumps are derived. Perfect hedging in a Markov-modulated Brownian and a fractional Brownian market is not possible as the market is incomplete. Following the idea proposed by F¨ollmer and Sondermann [13] and F¨ollmer and Schweizer [12]) we look for the strategy which locally minimizes the risk. The residual risk processes are determined in these situations. Variance swaps for stochastic volatility driven by Markov process are also studied.Robert J. Elliot and Anatoliy V. Swishchukhttp://www.springer.com/business/operations+research/book/978-0-387-71081-
MOND and cosmology
No full textI review various ideas on MOND cosmology and structure formation beginning with non-relativistic models in analogy with Newtonian cosmology. I discuss relativistic MOND cosmology in the context of Bekenstein's theory and propose an alternative biscalar effective theory of MOND in which the acceleration parameter, a(0) is identified with the cosmic time derivative of a matter coupling scalar field and cosmic CDM appears as scalar field oscillations of the auxiliary "coupling strength" field
- …
