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Cap Pricings under the Fractional Brownian Motion

  • Rhee, Joon-Hee (Department of Business and Administration, Soong-Sil University) ;
  • Kim, Yoon-Tae (Department of Statistics, Hallym University)
  • Published : 2008.01.31

Abstract

We present formulas for two types of cap pricing under fBm-HJM model reflecting the empirical long range dependence in the interest rate model. In particular, we propose a new approach to pricing the cap with the default risk.

Keywords

References

  1. Bender, C. (2003). An Ito formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameters. Stochastic Processes and Their Applications, 104, 81-106 https://doi.org/10.1016/S0304-4149(02)00212-0
  2. Cajueiro, D. and Tabak, B. (2007). Long range dependence in interest rates and monetary policy. Physics Letters, 1, 1-5
  3. Duffie, D. and Lando, D. (2001). Term structures of credit spreads with incomplete accounting information. Econometrica, 69, 633-664 https://doi.org/10.1111/1468-0262.00208
  4. Duncan, T. E., Hu, Y. Z. and Pasik-Duncan, B. (2000). Stochastic Calculus for fractional Brownian motion: I. Theory. SIAM Journal on Control and Optimization, 38, 582-612 https://doi.org/10.1137/S036301299834171X
  5. Oksendal, B. (2004). Fractional Brownian motion in finance. Working paper
  6. Rhee, J. H. (2007). fBm interest rate theory. Submitted for Publication