# Fractional term structure models: No-arbitrage and consistency

@article{Ohashi2008FractionalTS,
title={Fractional term structure models: No-arbitrage and consistency},
author={Alberto Ohashi},
journal={arXiv: Pricing of Securities},
year={2008}
}
• A. Ohashi
• Published 9 February 2008
• Mathematics
• arXiv: Pricing of Securities
In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the…
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## References

SHOWING 1-10 OF 39 REFERENCES
A note on Wick products and the fractional Black-Scholes model
• Economics
Finance Stochastics
• 2005
It is pointed out that the definition of the self-financing trading strategies and/or thedefinition of the value of a portfolio used in the above papers does not have a reasonable economic interpretation, and thus that the results in these papers are not economically meaningful.
Interest Rate Dynamics and Consistent Forward Rate Curves
• Mathematics, Economics
• 1999
We consider as given an arbitrage‐free interest rate model M, and a parametrized family of forward rate curves G. We study the question as to when the given family G is consistent with the dynamics
Towards a general theory of bond markets
• Mathematics
Finance Stochastics
• 1997
It is shown that a market is approximately complete iff an equivalent martingale measure is unique and two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions are suggested.
Bond pricing and the term structure of interest rates
• Economics, Mathematics
• 1989
This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes
A Characterization of Hedging Portfolios for Interest Rate Contingent Claims
• Economics, Mathematics
• 2004
We consider the problem of hedging a European interest rate contingent claim with a portfolio of zero-coupon bonds and show that an HJM type Markovian model driven by an infinite number of sources of
FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
• Mathematics
• 2002
In this paper, stochastic differential equations in a Hilbert space with a standard, cylindrical fractional Brownian motion with the Hurst parameter in the interval (1/2,1) are investigated.
Ergodic theory for SDEs with extrinsic memory
• Mathematics
• 2007
We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological
The Fundamental Theorem of Asset Pricing
• Mathematics, Economics
• 1999
We saw in the previous chapter that the existence of a probability measure Q ~ P under which the (discounted) stock price process is a martingale is sufficient to ensure that the market model is
The fundamental theorem of asset pricing for continuous processes under small transaction costs
• Mathematics, Economics
• 2010
A version of the fundamental theorem of asset pricing is proved for continuous asset prices with small proportional transaction costs. Equivalence is established between: (a) the absence of arbitrage