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題名 | Heath-Jarrow-Morton架構下之利率差額交換的評價與避險:以第三國貨幣為本金和評價對偶性之探討=Pricing and Hedging of Diff Swaps under the Heath-Jarrow-Morton Model: Principal Denominated in the 3rd Country Currency and Pricing Duality |
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作者姓名(中文) | 謝承熹; 李賢源; | 書刊名 | 管理學報 |
卷期 | 20:1 2003.02[民92.02] |
頁次 | 頁31-65 |
分類號 | 561.71 |
關鍵詞 | 利率差額交換; Heath-Jarrow-Morton模型; 評價對偶性; Diff swap; Heath-Jarrow-Morton model; Pricing duality; |
語文 | 中文(Chinese) |
中文摘要 | 假設三個國家的瞬間遠期利率皆遵循Heath-Jarrow-Morton(以下簡稱HJM)模型及匯率遵循幾何布朗運動 (geometric Brownian motion),本文探討以第三國貨幣為本金的利率差額交換 (diff swap) 之評價與避險。本文首先證明存在唯一等價平賭測度 (equivalent martingale measure) Q,使得所有以本國貨幣計價的資產,其價格行為在本國貨幣市場帳戶 (money market account) 的平準下皆為平賭過程 (martingale process);接著在此一平賭測度下,推導以第三國貨幣為本金的利率差額交換之評價公式,並且假設瞬間遠期利率的波動結構具指數型遞減的函數形式,在此假設之下證明Turnbull (1993),Wei (1994),Chang、Chung and Yu (2001) 的評價公式皆為本文的特殊解。又根據公式的模擬結果顯示:加諸於國內指標利率的固定價差 (constant spread),不因第三國的利率水準及利率期限結構形狀之不同而有太大的改變,而且固定價差的絕對值通常小於兩國當期瞬間即期利率差的絕對值,並隨著交換期限的增長而減小;此外,與各國間利率的相關性相比,各國間匯率與利率的相關性對利率差額交換的評價影響較大。最後,本文說明評價匯率相關衍生性商品時存在評價對偶性,並說明應用評價對偶性的概念,可使以外國及第三國貨幣為本金的利率差額交換很容易被評價。 |
英文摘要 | Within the Heath-Jarrow-Morton model and given the geometric Brownian motion processes for all currency exchange rates, this paper studies: (1) the pricing and hedging of diff swap which notional principal is denominated in the 3rd country currency, and (2) the concept of pricing duality. A pricing formula for such a diff swap is derived under a unique equivalent martingale measure Q. This pricing formula includes that derived in Turnbull (1993), Wei (1994), and Chang, Chung and Yu (2001) as a special case. Moreover, simulations are performed to study the constant spread rate and correlation parameters. Finally, this paper discusses the concept of pricing duality. With this concept, diff swaps with notional principal denominated in foreign and the 3rd country currencies can be easily priced. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。