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題名 | 動態複製性投資組合保險之模擬研究=A Simulation of Dynamic Synthetic Portfolio Insurance |
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作者姓名(中文) | 王雍智; 周建新; 陳振遠; | 書刊名 | 中華管理評論 |
卷期 | 5:1 2002.01[民91.01] |
頁次 | 頁130-141 |
分類號 | 563.5 |
關鍵詞 | 投資組合保險; 保護性賣權; Hull-White模型; Black-Scholes模型; Portfolio insurance; Protective put; Hull-White model; Black-Scholes model; |
語文 | 中文(Chinese) |
中文摘要 | 投資組合保險(Portfolio Insurance)乃是保障投資組合原始價值的一種風險管理策略,其最簡單的方式是向投資組合保險公司購買保險或購買保護性責權(Protective Put)達到避險的效果 然而,若是以上方式皆不可得,複製性責權(Synthetic Put)便成為達到投資組合保險的必要選擇。複製性責權乃是利用股票現貨及無風險債券來複製責權的損益結構,並隨著現貨價格及時間的演變動態調整此投資組合 傳統上,此種複製性投資組合保險(Synthetic Portfolio Insurance)皆以 Black-Scholes的責權公式來決定股票及債券的持有比例,但 Black-Scholes公式忽略了隨機變動及交易成本,不僅與現實明顯不符,且造成複製性投資組合與要保價值的巨大誤差。本文之研究目的,除了以股票現貨與無風險債券來複製保護性責權外,另外亦利用股價指數來複製責權策略 同時為了彌補前述 Black-Scholes公式缺點以減低誤差達到較佳的保險效果,本研究以 Hull-White的雙隨機過程模型為基礎,利用泰勒序列擴展的方式(Taylor Series Expansion),推導出一個新的股票與無風險債券的配置比例,此一新公式並通用於交易成本存在與不存在兩種不同的情況。電腦模擬研究結果顯示,此一新的避險比例較傳統的 Black-Scholes公式為佳,可以降低責權的價格誤差及複製性責權的配置誤差,並且更進一步減少投資組合與要保價值的複製誤差。 |
英文摘要 | Synthetic portfolio insurance is referred to as a risk management strategy that systematically replicates the payoff structure of a put option position on the entire financial portfolio with the underlying asset and the riskless asset. Traditionall the Black-Scholes put option formula has been used to determine allocation ratio between the risky and riskless assets. Howevery the Black-Scholes formula fails to capture the existence of stochastic volatility and transaction cost in the real life. In this papery we first generate different kinds of stock prices and stock index and replicate the insurance portfolio strategy using underlying stock price and index futures. By the wa this paper is to deal with the drawbacks of the Black-Scholes model in portfolio insurance. The study utilized the Hull and White model with two state variables. By solving the partial differential equation with approximation of Taylor series expansiony we derive the hedge ratio in the synthetic portfolio insurance under stochastic volatility. Two additional terms were added to the Black-Scholes formula for correction. Computer simulation was conducted to testify the effectiveness of the formula. The result of the simulation showed that with the new formulay not only protection level error was reducedy but also mispricing error and misallocation error. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。