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Journal of the Korean Statistical Society v.33 no.2, 2004년, pp.245 - 254   피인용횟수: 2

A JOINT DISTRIBUTION OF TWO-DIMENSIONAL BROWNIAN MOTION WITH AN APPLICATION TO AN OUTSIDE BARRIER OPTION

Lee, Hang-Suck   (Department of Statistics, Soongsil UniversityUU0000851  );
  • 초록

    This paper derives a distribution function of the terminal value and running maximum of two-dimensional Brownian motion {X( $\tau$ ) = (X $_1$ ( $\tau$ ), X $_2$ ( $\tau$ ))', $\tau$ 〉0}. One random variable of the joint distribution is the terminal time value, X $_1$ (T). The other random variable is the maximum of the Brownian motion {X $_2$ ( $\tau$ ), $\tau$ 〉} between time s and time t. With this distribution function, this paper also derives an explicit pricing formula for an outside barrier option whose monitoring period starts at an arbitrary date and ends at another arbitrary date before maturity.


  • 주제어

    Brownian motion .   terminal time value .   running maximum .   barrier option .   trivariate normal distribution.  

  • 참고문헌 (18)

    1. BAXTER,M.;RENNIE,A. , Financial Calculus : An Introduction to Dervative Pricing / v.,pp.,
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    3. Computation of the trivariate normal interal , DREZNER,Z. , Mathematics of Computation / v.62,pp.289-294,
    4. Actuarial bridges to dynamic hedging and option pricing , GERBER,H.U.;SHIU,E.S.W. , Insurance : Mathematics and Economics / v.18,pp.183-218,
    5. LAMBERTON,D.;LAPEYRE,B. , Introduction to Stochastic Calculus Applied to Finance / v.,pp.,
    6. Pricing equity-indexed annuities embedded with exotic options , LEE,H. , Contingencies January/February / v.,pp.34-38,
    7. ZHANG,P.G. , Exotic Options : A Guide to Second Generation Options(2nd ed.) / v.,pp.,
    8. HARRISON,J.M. , Brownian Motion and Stochastic Flow Systems / v.,pp.,
    9. Time and path dependent options : The case of time dependent inside and outside barrier options , BERMIN,H.P. , The Thrid Nordic Symposium on Contingent Claims Analysis in Finance / v.,pp.,
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    11. Discussion of valuing equity-indexed annuities , LEE,H. , North American Actuarial Journal / v.5,pp.133-136,
    12. The theory of rational option pricing , MERTON,R. , The Bell Journal of Economics and Management Science / v.4,pp.141-183,
    13. Pricing equity-indexed annuities with path-dependent options , LEE,H. , Insurance : Mathematics and Economics / v.33,pp.677-690,
    14. Partial barrier options , HEYNEN,R.C.;KAT.H.M. , Journal of Financial Engineering / v.3,pp.253-274,
    15. Breaking down the barrier , REINER,E.;RUBINSTEIN,M. , RISK / v.4,pp.28-35,
    16. Computation of the bivariate normal integral , DREZNER,Z. , Mathematics of Computation / v.32,pp.277-279,
    17. Crossing barriers , HEYNEN,R.C.;KAT,H.M. , Risk / v.7,pp.46-50,
    18. Option pricing by Esscher tracsoforms (with discussion) , GERBER,H.U.;SHIU,E.S.W. , Transactions of the Society of Actuaries / v.46,pp.99-191,
  • 이 논문을 인용한 문헌 (2)

    1. 2009. "" 응용통계연구 = The Korean journal of applied statistics, 22(1): 59~73     
    2. Shin, Seung-Hee ; Lee, Hang-Suck 2009. "Pricing an Outside Barrier Equity-Indexed Annuity with Flexible Monitoring Period" 한국통계학회 논문집 = Communications of the Korean Statistical Society, 16(2): 249~264     

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