TY - GEN

T1 - Pricing double barrier options by combinatorial approaches

AU - Dai, Tian-Shyr

AU - Lyuu, Yuh Dauh

PY - 2005/12/1

Y1 - 2005/12/1

N2 - Double barrier options are important path-dependent derivatives in the financial market. How to price them efficiently and accurately is thus important. Until now, no simple closed-form pricing formula for double barrier options is reported. Double barrier options can be priced on a lattice that divides a certain time interval (from option initial date to maturity date) into n equal-length time steps. The pricing results obtained by the lattice algorithm converge to the true option value as n ← ∞, and the results oscillate significantly especially when n is not large enough. To obtain an accurate pricing result without suffering from price oscillation, n is required to be a large number. Unfortunately, the lattice pricing algorithm runs in O(n2) time. This paper proposes a linear-time combinatorial algorithm that can generate the same pricing results as the lattice algorithm. Thus our algorithm can handle very large n's efficiently. This algorithm uses a novel technique based on the re ection principle and the inclusion-exclusion principle. Numerical experiments are given to verify the excellent performance of our algorithm.

AB - Double barrier options are important path-dependent derivatives in the financial market. How to price them efficiently and accurately is thus important. Until now, no simple closed-form pricing formula for double barrier options is reported. Double barrier options can be priced on a lattice that divides a certain time interval (from option initial date to maturity date) into n equal-length time steps. The pricing results obtained by the lattice algorithm converge to the true option value as n ← ∞, and the results oscillate significantly especially when n is not large enough. To obtain an accurate pricing result without suffering from price oscillation, n is required to be a large number. Unfortunately, the lattice pricing algorithm runs in O(n2) time. This paper proposes a linear-time combinatorial algorithm that can generate the same pricing results as the lattice algorithm. Thus our algorithm can handle very large n's efficiently. This algorithm uses a novel technique based on the re ection principle and the inclusion-exclusion principle. Numerical experiments are given to verify the excellent performance of our algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84867276628&partnerID=8YFLogxK

U2 - 10.1007/3-540-32391-0_116

DO - 10.1007/3-540-32391-0_116

M3 - Conference contribution

AN - SCOPUS:84867276628

SN - 3540250557

SN - 9783540250555

T3 - Advances in Soft Computing

SP - 1131

EP - 1140

BT - Soft Computing as Transdisciplinary Science and Technology - Proceedings of the 4th IEEE International Workshop, WSTST 2005

Y2 - 25 May 2005 through 27 May 2005

ER -