arXiv subjects

Belal E. Baaquie

Publications and source records attributed to Belal E. Baaquie.

At least 19 recordsLinked to original sources

arXiv2019

The future of US-China relations: a scientific investigation

In earlier centuries kings and governments employed astrologists to help them take the best decisions. Present-day governments no longer employ astrologists but still have no clear analytical tool to replace them. Over the past two decades we have developed a methodology for the scientific investigation of recurrent historical events. It consists in two steps. (i) Identification and comparison of historical episodes driven by a common mechanism. (ii) Under the reasonable assumption that what has happened several times in the past is likely to happen again, one then derives testable predictions. This of course is nothing other than the protocol used in experimental science when exploring new phenomena. We believe such a tool can give decision makers much better insight. In the present paper we illustrate this analysis by considering challenges, that span more than a century, to US hegemony in the Pacific. The outcomes suggest that it is only through the sidelining of one of the contenders that the confrontation will end. At the time of writing (late 2018) early evidence of this confrontation is already visible at three levels. (i) Growing US concerns for domestic security that are leading to a new form of McCarthyism. (ii) Political instability due to China-US polarization in several Asian countries as well as in the countries participating in the Belt and Road Initiative. (iii) Tension and sanctions in procurement and trade.

physics.hist-ph↗

arXiv2012

Statistical Microeconomics

A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an independent random variable: all prices and quantities are considered to be stochastic processes, with the observed market prices being a random sample of the stochastic prices. The dynamics of market prices is determined by an action functional and, for concreteness, a specific model is proposed. The model can be calibrated from the unequal time correlation of the market commodity prices. A perturbation expansion for the correlation functions is defined in powers of the inverse of the total budget of the aggregate consumer and the propagator for the market prices is evaluated.

q-fin.GN↗

arXiv2012

Action with Acceleration I: Euclidean Hamiltonian and Path Integral

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity, and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of this unbounded transformation is explicitly evaluated. The mapping fails for a critical value of the coupling constants.

quant-ph↗

arXiv2012

Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

The Euclidean action with acceleration has been analyzed in [1], hereafter cited as reference I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation/destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian acting on a Hilbert space. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

quant-ph↗

arXiv2006

Hedging LIBOR Derivatives in a Field Theory Model of Interest Rates

We investigate LIBOR-based derivatives using a parsimonious field theory interest rate model capable of instilling imperfect correlation between different maturities. Delta and Gamma hedge parameters are derived for LIBOR Caps against fluctuations in underlying forward rates. An empirical illustration of our methodology is also conducted to demonstrate the influence of correlation on the hedging of interest rate risk.

physics.soc-ph↗

arXiv2005

A Common Market Measure for Libor and Pricing Caps, Floors and Swaps in a Field Theory of Forward Interest Rates

The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally for such models. To elaborate how the martingale for the Libor belongs to the general class of numeraire for the forward interest rates, two other numeraire's are considered, namely the money market measure that makes the evolution of the zero coupon bonds a martingale, and the forward measure for which the forward bond price is a martingale. The price of an interest rate cap is computed for all three numeraires, and is shown to be numeraire invariant. Put-call parity is discussed in some detail and shown to emerge due to some non-trivial properties of the numeraires. Some properties of swaps, and their relation to caps and floors, are briefly discussed.

physics.soc-ph↗

arXiv2003

Hamiltonian and Potentials in Derivative Pricing Models: Exact Results and Lattice Simulations

The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian formulation. We show here some applications of these methods for various potentials, which we have simulated via lattice Langevin and Monte Carlo algorithms, to the pricing of options. We focus on barrier or path dependent options, showing in some detail the computational strategies involved.

cond-mat.soft↗

arXiv2002

Hedging in Field Theory Models of the Term Structure

We use path integrals to calculate hedge parameters and efficacy of hedging in a quantum field theory generalization of the Heath, Jarrow and Morton (HJM) term structure model which parsimoniously describes the evolution of imperfectly correlated forward rates. We also calculate, within the model specification, the effectiveness of hedging over finite periods of time. We use empirical estimates for the parameters of the model to show that a low dimensional hedge portfolio is quite effective.

cond-mat.stat-mech↗

arXiv2002

Comparison of Field Theory Models of Interest Rates with Market Data

We calibrate and test various variants of field theory models of the interest rate with data from eurodollars futures. A model based on a simple psychological factor are seen to provide the best fit to the market. We make a model independent determination of the volatility function of the forward rates from market data.

cond-mat.soft↗

arXiv2002

Quantum Mechanics, Path Integrals and Option Pricing: Reducing the Complexity of Finance

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.

cond-mat.soft↗

arXiv2002

A Quantum Field Theory Term Structure Model Applied to Hedging

A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. Specifically, incorporating field theory into the term structure facilitates hedge parameters that reduce to their finite factor HJM counterparts under special correlation structures. Although investors are unable to perfectly hedge against an infinite number of term structure perturbations in a field theory model, empirical evidence using market data reveals the effectiveness of a low dimensional hedge portfolio.

cond-mat.soft↗

arXiv2002

Sigma Model Lagrangian for the Heisenberg Group

We study the Lagrangian for a sigma model based on the non-compact Heisenberg group. A unique feature of this model -- unlike the case for compact Lie groups -- is that the definition of the Lagrangian has to be regulated since the trace over the Heisenberg group is otherwise divergent. The resulting theory is a real Lagrangian with a quartic interaction term. After a few non-trivial transformations, the Lagrangian is shown to be equivalent -- at the classical level -- to a complex cubic Lagrangian. A one loop computation shows that the quartic and cubic Lagrangians are equivalent at the quantum level as well. The complex Lagrangian is known to classically equivalent to the SU(2) sigma model, with the equivalence breaking down at the quantum level. An explanation of this well known results emerges from the properties of the Heisenberg sigma model.

hep-th↗

arXiv2001

Quantum Field Theory of Forward Rates with Stochastic Volatility

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, firstly when volatility is taken to be a function of the forward rates, and secondly when volatility is taken to be an independent quantum field. Since volatiltiy is a positive valued quantum field, the full theory turns out to be an interacting nonlinear quantum field theory in two dimensions. The state space and Hamiltonian for the interacting theory are obtained, and shown to have a nontrivial structure due to the manifold moving with a constant velocity. The no arbitrage condition is reformulated in terms of the Hamiltonian of the system, and then exactly solved for the nonlinear interacting case.

cond-mat.soft↗

arXiv2001

Empirical investigation of a quantum field theory of forward rates

A new test of a wide class of interest rate models is proposed and applied to a recently developed quantum field theoretic model and the industry standard Heath-Jarrow-Morton model. This test is independent of the volatility function unlike other tests previously proposed in the literature. It is found that the HJM model is inconsistent with the data while the quantum field theoretic model is in significant agreement with data. We also show that a portion of the spread between long and short term interest rates is explicable in terms of this model.

cond-mat.stat-mech↗

arXiv2000

Microcanonical Simulation of Complex Actions: The Wess Zumino Witten Case

We present the main results of our microcanonical simulation of the Wess Zumino Witten action functional. This action, being highly non-trivial and capable of exhibiting many different phase transitions, is chosen to be representative of general complex actions. We verify the applicability of microcanonical simulation by successfully obtaining two of the many critical points of the Wess Zumino Witten action. The microcanonical algorithm has the additional advantage of exhibiting critical behaviour for a small $8\times 8$ lattice. We also briefly discuss the subtleties that, in general, arise in simulating a complex action. Our algorithm for complex actions can be extended to the study of D-branes in the Wess Zumino Witten action.

hep-lat↗

arXiv2000

Simulation of Stochastic Volatility using Path Integration: Smiles and Frowns

We apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of path integration. Using market data, we determine the parameters of the model. It is found that the market chooses a special class of models for which a more efficient algorithm, called the bisection method, is applicable. Using our simulated data, we generate some implied volatility curves. We also analyze and study in detail some of the characteristics of the volatility curves within the model.

cond-mat↗

arXiv1998

Quantum Field Theory of Treasury Bonds

The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM-model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.

cond-mat.soft↗

arXiv1998

(Supersymmetric) Kac-Moody Gauge Fields in 3+1 Dimensions

Lagrangians for gauge fields and matter fields can be constructed from the infinite dimensional Kac-Moody algebra and group. A continuum regularization is used to obtain such generic lagrangians, which contain new nonlinear and asymmetric interactions not present in gauge theories based on compact Lie groups. This technique is applied to deriving the Yang-Mills and Chern-Simons lagrangians for the Kac-Moody case. The extension of this method to D=4, N=(1/2,0) supersymmetric Kac-Moody gauge fields is also made.

hep-th↗