跳躍擴散模型下之彩虹選擇權評價

The Valuation of Rainbow Options under the Jump-Diffusion Process

莊雅筑(Ya-Chu Chuang)

指導教授 ： 王之彥

國立臺灣大學/管理學院/國際企業學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201603455

摘要

在既有的文獻中，關於彩虹選擇權的評價以及跳躍擴散模型下的單一資產評價文獻都已發展得相當成熟，但卻沒有文獻推導在跳躍擴散模型下的彩虹選擇權評價公式。為解決此問題，我以機率測度轉換方式以及平賭評價方法，於本論文提出跳躍擴散模型下之彩虹選擇權評價公式，並以蒙特卡羅模擬法驗證。

關鍵字

跳躍擴散模型 ； 選擇權評價 ； 彩虹選擇權

並列摘要

There are existing literatures about analytic solutions for rainbow options and single-asset vanilla options under jump-diffusion processes. However, there is no literature about analytic solution of rainbow options under the jump-diffusion process. For the purpose of solving this problem, I propose a pricing formula to evaluate the rainbow options under the jump-diffusion process with the technique of change-of-probability-measure and the martingale pricing method in this paper.

並列關鍵字

Jump-diffusion process ； Option pricing ； Rainbow options

參考文獻

C.-Y. Chen, H.-C. Wang, J.-Y. Wang (2015). The valuation of forward-start rainbow options. Review of Derivatives Research, Vol. 18, No. 2, pp. 145-189.

Johnson, H. (1987). Options on the maximum or the minimum of several assets. Journal of Financial and Quantitative Analysis, 22, 277–283.

Margrabe, W. (1978). The value of an option to exchange one asset for another. The Journal of Finance, 33, 177–186.

Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.

Ouwehand, P., & West, G. (2006). Pricing rainbow options. Wilmott Magazine, 5, 74–80.