Quantum field theory of forward rates with stochastic volatility

Baaquie, Belal E.

doi:10.1103/physreve.65.056122

Cited by 17 publications

(10 citation statements)

References 15 publications

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“…Obtaining fixed income options data to investigate the significance of correlated forward rates on option prices as well as its impact on their hedge parameters would also be valuable. An enhanced model with stochastic volatility where innovations in the term structure result from the product of two fields has been developed by Baaquie [2].…”

Section: Current and Future Researchmentioning

confidence: 99%

A Quantum Field Theory Term Structure Model Applied to Hedging

Baaquie

Srikant

Warachka

2003

Int. J. Theor. Appl. Finan.

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A quantum field theory generalization, Baaquie [1], of the Heath, Jarrow and Morton (HJM) [10] 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.

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Section: Current and Future Researchmentioning

confidence: 99%

A Quantum Field Theory Term Structure Model Applied to Hedging

Baaquie

Srikant

Warachka

2003

Int. J. Theor. Appl. Finan.

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“…58 55 If we have d Brownian motions, then D = d + 1, d spatial dimensions plus Euclidean time. 56 Note that this is not the same as quantum field theory of [Baaquie, 2001[Baaquie, , 2002. Nor is our proposal related to the "gauge theory of arbitrage" (GTA) of [Ilinski, 1997], [Ilinksi and Kalinin, 1997] -for a popular discussion of GTA, see [Dunbar, 1998]; for a critique of GTA, see [Sornette, 1998].…”

Section: Discussionmentioning

confidence: 98%

Volatility smile as relativistic effect

Kakushadze

2017

Physica A: Statistical Mechanics and its Applications

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We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution 1) is properly normalized and 2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of the Black-Scholes-Merton model. The new parameter is the analog of the speed of light in Special Relativity. However, in the financial context there is no "speed limit" and the new parameter has the meaning of a characteristic diffusion speed at which relativistic effects become important and lead to a much softer asymptotic behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a nonlocal stochastic description of such (Lévy) processes is inadequate and discuss a local description from physics. The presentation is intended to be pedagogical.

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“…In this paper, we compare field theory models of interest rate models with market data, and propose certain modified models inspired from theoretical considerations and observed facts about the interest rates. The theoretical framework for all these models is Baaquie's formulation [1], [2] of forward rates as a two dimensional quantum field theory. The Baaquie model is a generalization of the Heath-Jarrow-Morton (HJM) model; the key feature of the field theory model is that the forward rates f (t, x) are imperfectly correlated in the maturity direction x > t, and which is specified by a rigidity parameter µ.…”

Section: Introductionmentioning

confidence: 99%