價差選擇權之定價

Pricing of Spread Options

謝進修(Chin-Hsiu Hsieh)

指導教授 ： 吳庭斌

國立臺北大學/商學院/統計學系/碩士(2009年)

摘要

在現在金融市場中，新奇衍生性商品不斷推出，尤其在各國開放金融市場的同時，為了能夠方便投資外國資產或是對其避險，匯率連動商
品的發行受到歡迎。匯率連動衍生性商品顧名思義，可知其商品於到期日時之現金流量當中，當期之匯率為重要因子。之所以採隨機利率
評價，乃因匯率的波動又與本國以及外國之利率有一定的關係。況且衍生性商品的標的資產並非與利率的波動完全無關，部分的資產價格亦
會隨著利率波動而波動。因此若將利率假設為一常數來評價，不計利率波動造成衍生性商品價格的影響，則評價上會忽略實際的市場中存
在的因素。故此，如果在隨機利率的模型下來進行評價，是比較合適的。本文在使用 Heath, Jarrow and Morton (1992) 的利率模型下，
來評價隨機利率下 Reiner(1992) 所提出的四種匯率連動選擇權，並將其擴展成價差選擇權 (spread option)，是為匯率連動價差選擇權。
由於價差選擇權無法直接求得封閉解，因此使用 Borovkova, Permana and Weide (2007) 提出的求價差選擇權價格的近似方法，來求取近
似封閉解以及避險參數。

關鍵字

HJM 利率模型 ； 匯率連動衍生性商品 ； 價差選擇權 ； 近似封閉解

並列摘要

This paper presents the introduction and valuation of quanto spread options. We price with Heath, Jarrow and Morton (1992)
interest rate model because of the volatilities of interest rate, correlations between exchange rate and interest rate and correlations between underlying assets and interest. This fact makes pricing formula more accurate. Although quanto spread option have no closed-form solutions, we try to find the approximate closed-form by using the method from Borovkova, Permana and Weide (2007).
The approximate closed-form will compare with the result of Monte Carlo numercial, and comfirm the accuracy of the approximate closed-form.

並列關鍵字

HJM interest rate model ； Quanto options ； spread options ； approximate closed-form

參考文獻

13. Wu, T. P., "Pricing and Hedging Quanto Forward Contracts under H.J.M. Model." Joural of the Chinese Statistical Association (2008), Vol. 46, pp. 288-308.

1. Amin, K. and Jarrow, R., "Pricing Foreign Currency Options under Stochastic Interest Rates." Journal of International Money and Finance (1991), pp. 310-329.

2. Black, F. and Scholes, M., "The Pricing of Options and Corporate Liabilities." Journal of Political Economy (1973), Vol. 81, pp. 637-654.

3. Borovkova, S. and Permana, F. and Weide, H., "A Closed Form Approach to the Valuation and Hedging of Basket and Spread Options." The Journal of Derivates, Vol. 14, No. 4 (2007), pp. 8-24.

4. Carmona, R. and Durrelman, V., "Pricing and Hedging Spread Options." SIAM Review, Vol. 45, No. 4 (2003), pp. 627-685.