Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper candidate for modelling this empirical phenomena. IBm. however. is not a semimartingale process. For this reason. it is very hard to apply such processes for asset price modelling.
Without using Ito formula, we investigate the IBm interest rate theory‘ We obtain a pure discount bond price. and Greeks by using Malllavin calculus.
Rhee, J.H. (2008), "Fractal Interest Rate Model without Ito Formula", Journal of Derivatives and Quantitative Studies: 선물연구, Vol. 16 No. 1, pp. 21-48. https://doi.org/10.1108/JDQS-01-2008-B0002
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