Advanced SearchSearch Tips
No Arbitrage Condition for Multi-Facor HJM Model under the Fractional Brownian Motion
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
No Arbitrage Condition for Multi-Facor HJM Model under the Fractional Brownian Motion
Rhee, Joon-Hee; Kim, Yoon-Tae;
  PDF(new window)
Fractional Brwonian motion(fBm) has properties of behaving tails and exhibiting long memory while remaining Gaussian. In particular, it is well known that interest rates show some long memories and non-Markovian. We present no aribitrage condition for HJM model under the multi-factor fBm reflecting the long range dependence in the interest rate model.
Fractional Brownian motion;HJM;wick Integral;Malliavin calculus;long memory;
 Cited by
Bender, C. (2003). An Ito formula for generalized functional of a fBm with arbitrary hurst parameters, Stochastic Processes and Their Applications, 104, 81-106 crossref(new window)

Biagini, F. and Oksendal, B. (2003). Minimal variacnce hedging for fractional Brownian motion, Methods and Applications of Analysis, 10, 347-362 crossref(new window)

Biagini, F. and Oksendal, B. (2004). Forward integrals and an Ito formula for fractional Brown-ian motion, Working Paper, Available from: biagini/ricerca/forwfbm.pdf

Bjork, T. and Hult, H. (2005). A note on Wick products and the fractional Black-Scholes model, Finance and Siochastics, 9, 197-209 crossref(new window)

Cajueiro, D. and Tabak, B. (2007). Testing for fractional dynamics in the Brazilian term structure of interest rates, Physics Letters, 1, 1-5

Duncan, T., Hu, Y. and Pasik-Duncan, B. (2000). Stochastic calculus for fBm, Journal on Control and Optimization 38, 582-612 crossref(new window)

Eberlein, E. and Raible, S. (1999). Term structure models deriven by general Levy processes, Mathe-matical Finance, 9, 31-53 crossref(new window)

Lim, J., Lee, K. and Song, H. (2008). Estimation of liquidity cost in financial markets, Communication of the Korean Statistical Society, 15, 111-118 crossref(new window)

Mandelbrot, B. B. (1971). When can price Be arbitraged efficiently? A limit to the validity of the random walk and martingale models, Review of Economics and Statistics, 53, 225-236 crossref(new window)

Oksendal, B. (2007). Fractional Brownian Motion in Finance, In Jensen, B. and Palokangs, T. (ed) Stochastic Economic Dynamics, Cambridge University Press, Cambridge

Rhee, J. H. and Kim, Y. T. (2008). Cap pricing under the fBm, Communication of the Korean Statis-tical Society, 15, 137-145 crossref(new window)