臺灣博碩士論文加值系統

The payoff of a barrier option depends on whether a specified underlying asset price crosses a specified level (called a barrier) during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier. However, in practice, many real contracts with barrier provisions specify discrete monitoring times. Such options are called discrete barrier options. Broadie et al. (1997) showed that discrete barrier options can be priced using continuous barrier formulas by applying a simple continuity correction to the barrier under the geometric Brownian motion setting. In this article, we focus on the connection between the discrete and continuous barrier options using the same method of correction to the barrier but under the constant jump diffusion model. The correction is justified theoretically by applying the techniques from sequential analysis, particularly Siegmund (1985). And we also give numerical results.

1 Introduction 1
2 Pricing Barrier Options 6
2.1 Continuous-monitoring case 6
2.2 Discrete-monitoring case 8
3 Proof of the Main Result 11
3.1 Distribution of 11
3.2 Some known results 14
3.3 Limit distribution of the overshoot and tau_t 16
3.4 Proof of Theorem 2.1 for the up-and-in put case 22
4 Numerical Results 26
5 Conclusion Remarks and Further Researches 37
References 38

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