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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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• #### 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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