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.Comment: 9 figure

Pseudo Hermitian formulation of Black-Scholes equation

We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system

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.Comment: 5 figure

(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.Comment: 21 pages, no figures, latex. Minor change

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.Comment: 10 pages, 4 figures, presented by C.Coriano at the Intl. Workshop "Nonlinear Physics, THeory and Experiment II", Gallipoli, Lecce, June 28-July 6, 200

Superstrings, Gauge Fields and Black Holes

There has been spectacular progress in the development of string and superstring theories since its inception thirty years ago. Development in this area has never been impeded by the lack of experimental confirmation. Indeed, numerous bold and imaginative strides have been taken and the sheer elegance and logical consistency of the arguments have served as a primary motivation for string theorists to push their formulations ahead. In fact the development in this area has been so rapid that new ideas quickly become obsolete. On the other hand, this rapid development has proved to be the greatest hindrance for novices interested in this area. These notes serve as a gentle introduction to this topic. In these elementary notes, we briefly review the RNS formulation of superstring theory, GSO projection, $D$-branes, bosonic strings, dualities, dynamics of $D$-branes and the microscopic description of Bekenstein entropy of a black hole.Comment: Lecture notes for talk delivered at NUS in 1997-1998. Some recent updates added. The material may be somewhat outdated but it could still be useful for physicists new to the fiel

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.Comment: 18 figures, Invited Talk, International Econophysics Conference, Bali, 28-31 August 200