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

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

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

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.Comment: 28 pages, 4 figure

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

Maximum temperature for an Ideal Gas of U^(1)\hat U(1) Kac-Moody Fermions

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the $\hat U(1)$ case is shown to have a maximum temperature $kT_{M} = |\lambda| /\pi$, where $\lambda$ is the coupling of the super charge operator $G_0$ to the fermions. This result is similar to the case of strings but unlike strings the result is obtained from a well-defined lagrangian.Comment: Needs subeqnarray.sty; To be published in Phys. Rev. D, Dec 15, 1995. Some typographical errors have been corrected in the revised versio