213 research outputs found
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
A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
The Black-Scholes formula for pricing options on stocks and other securities
has been generalized by Merton and Garman to the case when stock volatility is
stochastic. The derivation of the price of a security derivative with
stochastic volatility is reviewed starting from the first principles of
finance. The equation of Merton and Garman is then recast using the path
integration technique of theoretical physics. The price of the stock option is
shown to be the analogue of the Schrodinger wavefuction of quantum mechacnics
and the exact Hamiltonian and Lagrangian of the system is obtained. The results
of Hull and White are generalized results for pricing stock options for the
general correlated case are derived.Comment: Needs subeqnarray.sty. To appear in J. de Phys. I (Dec 97
(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
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
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
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, -branes, bosonic strings, dualities,
dynamics of -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
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