• Communications for Statistical Applications and Methods
• /
• v.17 no.1
• /
• pp.47-54
• /
• 2010

By using the white noise theory for fractional Brownian sheet, we give new representations of the Wick integrals of various types with respect to fractional Brownian sheet with Hurst parameters $H_1,H_2{\in}$(0, 1).

• The Korean Journal of Financial Management
• /
• v.25 no.1
• /
• pp.85-108
• /
• 2008

In this paper, the fBm interest rate theory is investigated by using Wick integral. The well-known Affine, Quadratic and HJM are derived from fBm framework, respectively. We obtain new theoretical results, and zero coupon bond pricing formula from newly obtained probability measure.

• Communications for Statistical Applications and Methods
• /
• v.15 no.1
• /
• pp.137-145
• /
• 2008

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.

• Communications for Statistical Applications and Methods
• /
• v.16 no.4
• /
• pp.639-645
• /
• 2009

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.