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題名：考量基差風險下之期貨及期貨選擇權：理論與實證
作者：吳訂宜
作者(外文)：Ting-Yi Wu
校院名稱：國立高雄第一科技大學
系所名稱：管理研究所
指導教授：王昭文
學位類別：博士
出版日期：2007
主題關鍵詞：期貨；期貨選擇權；布朗橋；基差；futures；futures options；Brownian bridge；basis
原始連結：連回原系統網址new window
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假設基差風險服從修正之布朗橋過程，本文首先推導出在隨機利率下具基差風險之期貨及期貨選擇權封閉解。布朗橋除了在起迄點的值為已知外，其為類似布朗運動之隨機過程。在無套利假設下，期貨價格和其標的資產價格於期貨契約到期時將會收斂；換言之，基差值在此時為零。修正之布朗橋過程可確保基差值在期貨契約到期時為零。然而傳統之布朗運動的波動度只為存續期間的函數，故本文修正其波動度為具時變的型態。
本文的第二個目的為以數值模擬方法探討具基差風險之期貨選擇權特性。期貨選擇權與現貨價格和基差的相關係數及利率和基差的相關係數具正向關係，但和基差起始值具反向關係。另外，現貨價格和基差相關係數的正負符號會影響基差波動度和期貨買權價格的關係。最後，本文以S&P 500期貨買權驗證所推導之期貨選擇權模型。以隨機利率下的Black模型為比較模型，實證結果支持期貨買權具基差風險；且，具基差風險之期貨選擇權能去除存續期間及價內、外的偏誤。全體樣本之指數及百分比平均誤差，本文之模型分別為0.930及0.92%，Black模型分別為-4.466及-27.04%。
Assuming the stochastic process of basis to behavior as a modified Brownian bridge process, this article provides the closed-form solutions of futures and futures options with basis risk (FOBR) under stochastic interest rate. Under no arbitrage assumption, the spot price and the futures price will converge at the expiration of the futures contract; this means that the basis is zero at that time. The modified Brownian bridge process ensures the basis to be zero at maturity of futures contract.
The FOBR model was empirically tested with daily data of S&P 500 futures and futures call options. Compared with the Black model under stochastic interest rate, the empirical test shows evidence that supports the occurrence of basis risk in the futures call options. The overall mean errors in terms of index-point and percentage are 0.930 and 0.92% for the FOBR model and -4.466 and -27.04% for the Black model.
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