臺灣博碩士論文加值系統

Barrier options are options that are either extinguished (“out”) or established (“in”), when the price of the underlying asset crosses a particular level (“barrier”). Common examples are “down-and-out,” “down-and-in,” “up-and-out” and “up-and-in” options, which can be calls or puts. An additional feature of some barrier options is that a rebate is paid when the option is extinguished or an additional premium is due when the option is established. Closed-form formulas for European barrier options are known in the literature. This is not the case for American barrier options, for which no closed-form formulas have been published. One has therefore had to resort to numerical methods. Using lattice models on binomial or trinomial trees for the valuation of barrier options is known to converge extremely slowly compared to plain vanilla options. In this thesis we show how to apply a simple, yet powerful, least-square Monte Carlo algorithm to approximate the value of American barrier options.

Contents
1 Introduction …………………………………….. 2
2 The Decomposition Technique for American Options
2.1 Valuing American Puts ………………………. 5
2.2 Valuing American Barrier Put Options……. 11
3 The LSM Methodology
3.1 The Valuation Framework ……………………. 16
3.2 Valuing American Puts ………………………..17
3.3 Valuing American Barrier Put Options …….21
3.3.1 The Homogeneous Property of American
Barrier Options …………………………23
4 Conclusion ………………………………………... 25
Bibliography ………………………………………….. 26

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