논문KCI 등재
Fractional Brownian Motion을 이용한 이자율 모형
No-Arbitrage Interest Rate Models Under the Fractional Brownian Motion
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
주제분류경영학
초록
본 연구는 Bender(2003), Duncan et al.(2000)등의 Wick 적분을 이용하여, fBm을 이자율모형의 불확실성으로 사용하였다. Affine 모형에 대표적인 CIR, Hull and White 모형, Quadratic 모형, 그리고 HJM 모형에 차례로 적용한 결과 이론적으로 새로운 결과를 얻었으며, 특히 새로운 확률측도(probability measure)를 정의하여, 할인채권의 옵션가격을 제시하였다.
Abstract
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.
참고문헌 (24)
- 이준희, "Fractal 이자율 모형, Working Paper", ~ (2007)
- Ait-Sahalia, Y., "Transition Densities for Interest Rates and Other Nonlinear Diffusions", Journal of Finance, 54, pp.499~547 (1999)
- Bakus, D., "Long Memory Inflation Uncertainty：Evidence of the Term Structure of Interest Rate", Journal of Money and Credit and Banking, 25, pp.687~700 (1993)
- Baillie, R., "Long Memory Processes and Fractional Integration in Econometrics", Journal of Econometrics, 73, pp.5~59 (1996)
- Baroulas, J., "Fractional Dynamics in Japanese Financial Time Series", Pacific-Basin Finance Journal, 6, pp.115~124 (1998)
- Bender, C., "An Ito Formula for Generalized Functional of a fBm with Arbitrary Hurst Parameters", Stochastic Processes and Their Applications, 104, pp.81~106 (2003)
- Benth, F., "On Arbitrage Free Pricing of Weather Derivatives Based on Fractional Brownian Motion,” University of Oslo, Working paper", ~ (2003)
- Bjork, T., "A Note on Wick Products and the Fractional Black-Scholes Model", Finance and Stochastics, 9, pp.197~209
- Brigo, D., "A Deterministic-Shift Extension of Analytically Tractable and Time Homogeneous Short Rate Model,” To appear Finance and Stochastics", ~ (2001)
- Brody, D., "Dynamical Pricing of Weather Derivatives,” Working paper", ~ (2003)
- Cajueriro D., "Testing for Fractional Dynamics in the Brazilian Term Structure of Interest Rates,” Working paper", ~ (2003)
- Comte F., "Long Memory Continuous Time Model", Journal of Econometrics, 73, pp.101~149 (1996)
- Decreusefond, L., "Stochastic Analysis of the Fractional Brownian Motion", Potential Analysis, 10, pp.177~214 (1999)
- Duncan, T., "Duncan, Stochastic Calculus for fBm, SIAM", Journal of Control and Optimization, 38(2), pp.582~612 (2000)
- Elliot, R., "A General Fractional White Noise Theory and Application to Finance", Mathematical Finance, 13(2), pp.301~303 (2003)
- GilBazo J., "A Nonparametic Dimension Test of Term Structure,” Working paper", ~ (2003)
- Granger, C, "Long Memory Relationships and the Aggregation of Dynamic Models", Journal of Econometrics, 14, pp.227~238 (1980)
- Hog, E., "The Fractional O-U Process：Term Structure Theory and Application,” Working paper", ~ (2006)
- MaCarthy, J., "Test Long Range Dependence in Interest Rate Using Wavelet", The Quarterly Review of Economics and Finance, 44, pp.180~189 (2004)
- Mandelbrot, B., "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models", Review of Economics and Statistics, 53, pp.2~25 (1971)
- Norros, I., "An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions,” Working paper", ~ (2000)
- Oksendal, B., "Fractional Brownian Motion in Finance,” Working paper", ~ (2003)
- Rogers, C. C., "Arbitrage with fBm", Mathematical Finance, 7(1), pp.95~105 (1997)
- Tsay, W., "Long Memory Story of the Real Interest Rate", Economics Letters, 67, pp.325~330 (2000)
관련 논문AI추천
한국 금리기간구조의 장기 기억성에 대한 연구이명호, 이준희한국금융공학회 · 金融工學硏究2009 · 제8권 제3호비모수적 이자율모형 추정과 시장위험가격 결정에 관한 연구안성학, 이필상한국재무관리학회 · 재무관리연구2003 · 제20권 제2호국면 전환 2요인 이자율 기간구조에 대한 이론적 고찰현정순한국경제통상학회 · 경제연구2005 · 제23권 제1호Heath-Jarrow-Morton모형을 이용한 우리나라 이자율 기간구조 추정이병근, 현정순한국은행 · 경제분석2002 · 제8권 제2호Generating sample paths and their convergence of the geometric fractional Brownian motion김종은, 최희준, 추정호대한수학회 · 대한수학회보2018 · 제55권 제4호차익거래 기회가 없는 이자율 변동모형 하에서 확률적 평균만기 및 선물가격과 선도가격과의 관계에 관한 연구강병호, 최종연한국재무관리학회 · 재무관리연구2002 · 제19권 제2호