Publications
154 results found
Brody DC, Friedman RL, 2010, Information of interest, Life & Pension, Vol: February, Pages: 35-40
The flow of information in financial markets on future liquidity risk generates the rise and fall of demand for default-free bonds. Here, we present an approach to pricing these bonds and the associated derivatives, based on noisy information about the possible future liquidity crises, while deriving option pricing formulas and showing the impact of liquidity on the risk premium.
Brody DC, Hughston LP, Parry MF, 2010, Effects of quantum entanglement in phase transitions, PHYS LETT A, Vol: 374, Pages: 2424-2428
Brody DC, Graefe EM, 2010, Coherent states and rational surfaces, J PHYS A-MATH THEOR, Vol: 43
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of the underlying state space into higher dimensional state spaces. This construction is applied to the parameterisation of generalised coherent states, which is useful for practical calculations, and provides an elementary combinatorial approach to the geometry of the coherent state space. The results are extended to Hilbert spaces with indefinite inner products, leading to the introduction of a new kind of generalised coherent states.
BRODY D, 2010, Information and asset pricing, 7th International ISAAC Congress, Publisher: World Scientific Press, Pages: 381-388
Brody DC, Gustavsson ACT, Hughston LP, 2010, Nonlinearity and constrained quantum motion, J PHYS A-MATH THEOR, Vol: 43
The dynamical equation satisfied by the density matrix when a quantum system is subjected to one or more constraints arising from conserved quantities is derived. The resulting nonlinear evolution of the density matrix has the property that it is independent of the specific composition of the pure-state mixture generating the initial state of the system.
Brody DC, 2009, Dequantization of the Dirac monopole, P R SOC A, Vol: 465, Pages: 3047-3068
Using a sheaf-theoretic extension of conventional principal bundle theory, the Dirac monopole is formulated as a spherically symmetric model free of singularities outside the origin such that the charge may assume arbitrary real values. For integral charges, the construction effectively coincides with the usual model. Spin structures and Dirac operators are also generalized by the same technique.
Brody DC, Gustavsson ACT, Hughston LP, 2009, Metric approach to quantum constraints, Journal of Physics A, Vol: 42
A framework for deriving equations of motion for constrained quantum systems is introduced and a procedure for its implementation is outlined. In special cases, the proposed new method, which takes advantage of the fact that the space of pure states in quantum mechanics has both a symplectic structure and a metric structure, reduces to a quantum analogue of the Dirac theory of constraints in classical mechanics. Explicit examples involving spin-1/2 particles are worked out in detail: in the first example, our approach coincides with a quantum version of the Dirac formalism, while the second example illustrates how a situation that cannot be treated by Dirac's approach can nevertheless be dealt with in the present scheme.
Brody DC, Davis MHA, Friedman RL, et al., 2009, Informed traders, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 465, Pages: 1103-1122, ISSN: 1364-5021
An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market participants have access to a stream of noisy information concerning the future return of an asset, whereas the informed trader has access to a further information source which is obscured by an additional noise that may be correlated with the market noise. The informed trader uses the extraneous information source to seek statistical arbitrage opportunities, while at the same time accommodating the additional risk. The amount of information available to the general market participant concerning the asset return is measured by the mutual information of the asset price and the associated cash flow. The worth of the additional information source is then measured in terms of the difference of mutual information between the general market participant and the informed trader. This difference is shown to be nonnegative when the signal-to-noise ratio of the information flow is known in advance. Explicit trading strategies leading to statistical arbitrage opportunities, taking advantage of the additional information, are constructed, illustrating how excess information can be translated into profit.
Brody DC, Hook DW, 2009, Information geometry in vapour-liquid equilibrium, J PHYS A-MATH THEOR, Vol: 42, Pages: 1-33
Using the square-root map p → √p a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters, the image of the map forms a Riemannian submanifold M. The metric on M induced by the ambient spherical geometry of S is the Fisher information matrix. Statistical properties of the system modelled by a parametric density function p can then be expressed in terms of information geometry. An elementary introduction to information geometry is presented, followed by a precise geometric characterization of the family of Gaussian density functions. When the parametric density function describes the equilibrium state of a physical system, certain physical characteristics can be identified with geometric features of the associated information manifold M. Applying this idea, the properties of vapour–liquid phase transitions are elucidated in geometrical terms. For an ideal gas, phase transitions are absent and the geometry of M is flat. In this case, the solutions to the geodesic equations yield the adiabatic equations of state. For a van der Waals gas, the associated geometry of M is highly nontrivial. The scalar curvature of M diverges along the spinodal boundary which envelopes the unphysical region in the phase diagram. The curvature is thus closely related to the stability of the system.
Brody DC, Friedman RL, 2009, Information of interest, Risk Magazine, Vol: December, Pages: 101-106
The flow of information in financial markets on future liquidity risk generates the rise and fall of demand for default-free bonds. Here, Dorje Brody and Robyn Friedman present an approach to pricing these bonds and the associated derivatives, based on noisy information about the possible future liquidity crises, while deriving option pricing formulas and showing the impact of liquidity on the risk premium.
Brody DC, Ellis DCP, Holm DD, 2008, Hamiltonian statistical mechanics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, ISSN: 1751-8113
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- Citations: 7
Bender CM, Brody DC, Hook DW, 2008, Quantum effects in classical systems having complex energy, Journal of Physics A: Mathematical and Theoretical, Vol: 41, ISSN: 0305-4470
Brody DC, Hughston LP, Macrina A, 2008, Dam rain and cumulative gain, Proc. Roy. Soc. A, Vol: 464, Pages: 1801-1822, ISSN: 1364-5021
We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of reinsurance contracts. In the insurance setting, aggregate claims play the role of cumulative gains, and the terminal cash flow represents the totality of the claims payable for the given accounting period. A similar example arises when we consider the accumulation of losses in a credit portfolio, and value a contract that pays an amount equal to the totality of the losses over a given time interval. An expression for the value process of such an asset is derived as follows. We fix a probability space, together with a pricing measure, and model the terminal cash flow by a random variable; next, we model the cumulative gains process by the product of the terminal cash flow and an independent gamma bridge; finally, we take the filtration to be that generated by the cumulative gains process. An explicit expression for the value process is obtained by taking the discounted expectation of the future cash flow, conditional on the relevant market information. The price of an Arrow-Debreu security on the cumulative gains process is determined, and is used to obtain a closed-form expression for the price of a European-style option on the value of the asset at the given intermediate time. The results obtained make use of remarkable properties of the gamma bridge process, and are applicable to a wide variety of financial products based on cumulative gains processes such as aggregate claims, credit portfolio losses, defined benefit pension schemes, emissions and rainfall.
Brody DC, Crosby J, Li H, 2008, Convexity adjustments in inflation-linked derivatives, Risk Magazine, Vol: September, Pages: 124-129
Dorje Brody, John Crosby and Hongyun Li value several types of inflation-linked derivatives using a multi-factor version of the Hughston (1998) and Jarrow & Yildirim (2003) model. Expressions for the prices of zero-coupon inflation swaps with delayed payment and period-on-period inflation swaps with delayed payments are obtained in closed form by explicitly calculating the relevant convexity adjustments. These results are then applied to value limited price indexation swaps using Ryten’s (2007) common factor representation methodology.
BRODY DORJEC, HUGHSTON LANEP, MACRINA ANDREA, 2008, INFORMATION-BASED ASSET PRICING, International Journal of Theoretical and Applied Finance, Vol: 11, Pages: 107-142
A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the corresponding price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such "X-factor" we associate a market information process, the values of which we assume are accessible to market participants. Each information process consists of a sum of two terms; one contains true information about the value of the associated market factor, and the other represents "noise". The noise term is modelled by an independent Brownian bridge that spans the interval from the present to the time at which the value of the factor is revealed. The market filtration is assumed to be that generated by the aggregate of the independent information processes. The price of an asset is given by the expectation of the discounted cash flows in the risk-neutral measure, conditional on the information provided by the market filtration. In the case where the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price process. Dividend growth is taken into account by introducing appropriate structure on the market factors. The prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European-style call option is of the Black–Scholes–Merton type. We consider the case where the rate at which information is revealed to the market is constant, and the case where the information rate varies in time. Option pricing formulae are obtained for both cases. The information-based framework generates a natural explanation for the origin of stochastic volatility in financial markets, without the need for specifying on an ad hoc basis the dynamics of
Brody DC, Hughston LP, Macrina A, 2008, Information-based asset pricing, Int J Theo App Finance, Vol: 11, Pages: 107-142, ISSN: 0219-0249
A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the corresponding price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such "X-factor" we associate a market information process, the values of which we assume are accessible to market participants. Each information process consists of a sum of two terms; one contains true information about the value of the associated market factor, and the other represents "noise". The noise term is modelled by an independent Brownian bridge that spans the interval from the present to the time at which the value of the factor is revealed. The market filtration is assumed to be that generated by the aggregate of the independent information processes. The price of anasset is given by the expectation of the discounted cash flows in the risk-neutral measure, conditional on the information provided by the market filtration. In the case where the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price process. Dividend growth is taken into account by introducing appropriate structure on the market factors. The prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European-style call option is of the Black–Scholes–Merton type. We consider the case where the rate at which information is revealed to the market is constant, and the case where the information rate varies in time. Option pricing formulae are obtained for both cases. The information-based framework generates a natural explanation for the origin of stochastic volatility in financial markets, without the need for specifying on an ad hoc basis the dynamics of t
Brody DC, 2008, Comment on "Typicality for Generalized Microcanonical Ensembles", Phys Rev Lett, Vol: 100, ISSN: 0031-9007
Brody DC, Gustavsson ACT, Hughston LP, 2008, Symplectic approach to quantum constraint, J PHYS A-MATH THEOR, Vol: 41, Pages: 1-11
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions to the constrained dynamics of systems of multiple spin-1/2 particles. When the motion is constrained to a certain product space containing all of the energy eigenstates, the dynamics thus obtained are quasi-unitary in the sense that the equations of motion take a form identical to that of unitary motion, but with different boundary conditions. When the constrained subspace is a product space of disentangled states, the associated motion is more intricate. Nevertheless, the equations of motion satisfied by the dynamical variables are obtained in closed form.
Brody DC, Hook DW, 2007, On optimum Hamiltonians for state transformation (vol 39, pg L167, 2006), JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 40, Pages: 10949-10949, ISSN: 1751-8113
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- Citations: 11
DCBrody, DWHook, 2007, Lattice Boltzman simulations of the acoustic radiation from waveguides, Journal of Physics A: Mathematical and Theoretical, Vol: 40, Pages: 10949-10949, ISSN: 1751-8113
Brody DC, Hook DW, Hughston LP, 2007, Quantum phase transitions without thermodynamic limits, Proc Roy Soc A, Vol: 463, Pages: 2021-2030, ISSN: 1364-5021
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterized by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order phase transitions at finite temperatures.
Brody DC, 2007, Note on exponential families of distributions, J PHYS A-MATH THEO, Vol: 40, Pages: F691-F695, ISSN: 0305-4470
Brody DC, Hughston LP, Macrina A, 2007, Beyond hazard rates: a new framework for credit-risk modelling, Advances in Mathematical Finance, Editors: Fu, Jarrow, Yen, Elliott, Publisher: Birkhauser Verlag, Pages: 231-257, ISBN: 9780817645441
Dorje C Brody, Daniel W Hook, Lane P Hughston, 2007, Unitarity, ergodicity, and quantum thermodynamics., Journal of Physics A: Mathematical and Theoretical, Vol: 40, Pages: F503-F509, ISSN: 0305-4470
Brody DC, Gustavsson ACT, Hughston LP, 2007, Entanglement of three-qubit geometry, THIRD INTERNATIONAL WORKSHOP DICE2006, Publisher: IOP Publishing
Brody DC, Constantinou IC, Buckley IRC, 2007, Option price calibration from Renyi entropy, Phys Lett A, Vol: 366, Pages: 298-307, ISSN: 0375-9601
Bender CM, Brody DC, Chen JH, 2007, PT-symmetric extension of the Korteweg-de Vries equation, J PHYS A-MATH THEO, Vol: 40, Pages: F153-F160, ISSN: 0305-4470
Bender CM, Brody DC, Jones HF, et al., 2007, Faster than hermitian quantum mechanics, PHYSICAL REVIEW LETTERS, Vol: 98, ISSN: 0031-9007
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- Citations: 300
Dorje C Brody, Daniel W Hook, Lane P Hughston, 2007, On quantum microcanonical equilibrium, Journal of Physics: Conference Series, DICE 2006
BRODY D, ELLIS D, HOLM D, 2007, Random Hamiltonian in thermal equilibrium, Fourth International Workshop on Decoherence, Information, Complexity and Entropy
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