Efficient Procedure for Valuing American Lookback Put Options

American Lookback Put Option;Binomial Lattice Model;uniformity;exercise barrier;monotonicity;exercise propagation;Actuarial Science

Wang, Xuyan

University of Waterloo

关键词: American Lookback Put Option;    Binomial Lattice Model;    uniformity;    exercise barrier;    monotonicity;    exercise propagation;    Actuarial Science;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3075/1/course9.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Lookback option is a well-known path-dependent option where itspayoff depends on the historical extremum prices. The thesis focuseson the binomial pricing of the American floating strike lookback putoptions with payoff at time $t$ (if exercise) characterized by[ max_{k=0, ldots, t} S_k - S_t,]where $S_t$ denotes the price of the underlying stock at time $t$.Build upon the idea of hyperlink{RBCV}{Reiner Babbs Cheuk andVorst} (RBCV, 1992) who proposed a transformed binomial latticemodel for efficient pricing of this class of option, this thesisextends and enhances their binomial recursive algorithm byexploiting the additional combinatorial properties of the latticestructure. The proposed algorithm is not only computationalefficient but it also significantly reduces the memory constraint.As a result, the proposed algorithm is more than 1000 times fasterthan the original RBCV algorithm and it can compute a binomiallattice with one million time steps in less than two seconds. Thisalgorithm enables us to extrapolate the limiting (American) optionvalue up to 4 or 5 decimal accuracy in real time.