本研究提出了兩個選擇權投資組合模型,以Horasanli (2008) 的選擇權定價模型為基礎,保留原模型計算報酬、避險比率的部分,首先加入模糊理論處理在Horasanli (2008) 模型中的假設變動性參數(如r、σ、S)為固定數值的部分,使模型能夠實際計算選擇權在真實市場中隨時間而變動的各種參數;其次運用多目標達成度的技術來表示投資者所能接受的風險範圍,使其可以根據達成度高低而彈性調整風險比率,改進風險規避的作用;最後比照真實市場的交易方式考量交易成本的計算。為驗證以上所提之模型貢獻,本研究運用兩個實例來實證提出的模型具有在考量交易成本下,處理模糊環境中的投資組合選擇權定價、避險問題的能力,結果顯示所提出的模型能夠更符合真實的市場交易情況,且在風險規避上能夠配合投資者對風險的偏好,彈性調整風險比率區間的寬度,提升模型風險規避的作用。
Two option portfolio models are proposed in this paper. Based on Horasanli (2008)’s option pricing model, we employ the fuzzy sets theorem to deal with the violation of fixed parameters (such as risk ratio and stock price) in the Black-Scholes model, and using multiple objective programming to represent the acceptable range of risks, we make sure it can adjust the risk ratio flexibly and improve the ability of risk aversion with transaction cost. Two examples are demonstrated to show that the proposed model 1 is more in line with actual market transactions to deal with option portfolios and the violation of parameters in a portfolio. The contribution of model 2 is to make risk aversion more flexible than that in Horasanli (2008)’s model for adjusting the range of risk neutralization. It can provide investors with an optimal solution for return and risk values that fit in the corresponding option portfolios.