(第一年)本文利用一個多變量複合卜瓦松模型(Multivariate compound Poisson diffusion model)來描述資產價格的動態過程，此模型不僅能解釋資產跳躍亦能解釋資產間共同跳躍情況，並利用Esscher測度轉換得到一個風險中利的資產動態過程，並將此模型應用到互換選擇權評價來探討共同跳躍對於選擇權評價之影響。研究發現當資產間共同跳躍次數愈高，選擇權價值愈高。(第二年)隨著資產間的共同移動與共同跳躍的現象加劇，過去建構在資產動態服從幾何布朗運動的情況將無法描繪。本文提出一個多變量複合卜瓦松跳躍擴散進一步捕捉資產間的共同移動現象，同時也將共同跳躍的現象納入到模型中，並透過Markovwitz的平均數-變異數法則來建構投資組合。研究結果發現當共同跳躍次數的增加，將增加資產間的相關係數，這使得投資組合的風險分散的效果遞減，此外，當有重大的系統性風險發生時，共同跳躍的次數也會增加，且當共同跳躍的頻率增加至某一程度時，資產間的相關係數將達到1，此時，投資組合的建構將無法達到風險分散的效果。 (First Year) In this study, we investigate the valuation of European exchange options under a two-asset jump-diffusion process with correlations, where both individual jumps and cojumps in the underlying stock price dynamics are modeled by two independent compound Poisson processes with log-normal jump sizes. The Esscher transform technique is applied to provide an efficient way for exchange option valuation under an incomplete market setting. The estimated results and numerical examples are provided to illustrate the impact of cojumps on option prices. (Second Year) The phenomena of co-movement and co-jump among assets become more and more frequent and result in the dynamic process built basing on the geometric Brownian motion cannot depict these anymore. For the sake of taking comovement and co-jump among assets, we propose a new process called multivariate compound poisson diffusion model to more accurately model the dynamics of asset price. In addition, we use the mean-variance method proposed by Markovwitz to construct the portfolio and investigate the impacts of the co-jump on the portfolio construction. We find the increasing of co-jump intensity will also increase the correlation between assets and result in decreasing the effect of risk diversification through portfolio construction. Further, we also find the major systematic risk occurs, such as subprime crisis, the intensity of cojump will also increase.