隨機利率下匯率連動遠期契約之評價與避險

Pricing and Hedging Quanto Forward Contracts under Hjm Model

10.29973/JCSA.200812.0003

吳庭斌(Ting-Pin Wu)

匯率連動遠期契約 ； 風險中立評價方法 ； 利率模型 ； Quanto forward contracts ； risk-neutral pricing method ； interest rate model

中國統計學報

46卷4期（2008 / 12 / 01）

288 - 308

繁體中文

匯率連動遠期契約的到期現金流量涉及匯率，而匯率與利率的相關性甚高，因此假設利率爲常數會忽略利率與匯率相關性對評價的影響。若契約的標的資產與利率相關性甚高，例如：保險類股與金融類股，假設利率爲常數亦會忽略標的資產與利率相關性對評價的影響。近年來利率變動幅度大增，在固定利率假設下進行評價，會忽略利率波動對評價的影響。因此，匯率連動遠期契約的評價與避險參數的探討，應在隨機利率設定下進行較合理。本文在Heath, Jarrow and Morton (1992)利率模型架構下，求得隨機利率下匯率連動遠期契約的評價公式與避險參數，以期提供金融業界評價與避險之參考。

Quanto forward contracts are priced within Heath, Jarrow and Morton (1992) interest rate model. The advantages of the pricing formulas are that the formulas capture the impacts of the volatilities of interest rates and the correlations between exchange rates and interest rates and underlying assets and interest rates. These advantages makes the pricing formulas more reasonable and accurate and worthy to be recommended to financial practitioners.

1. Hsieh, C. H.(2002).Pricing and hedging of European forward start options under stochastic interest rate.Journal of Financial Studies,10(1),1-22.
   連結：
2. Amin, K. I.,Jarrow, R. A.(1991).Pricing foreign currency options under stochastic interest rates.Journal of International Money and Finance,10,310-329.
3. Black, F.,Scholes, M.(1973).The pricing of options and corporate liabilities.Journal of Political Economy,81,637-654.
4. Brigo, D.,Mercurio, F.(2006).Interest Rate Models Theory and Practice.Springer.
5. Elliott, R. J.,Kopp, P. E.(1999).Mathematics of Financial Markets.Springer.
6. Geman, H.,Nicole, E. K.,Rochet, J. C.(1995).Changes of Numeraire, Changes of Probability Measure and Option Pricing.Journal of Applied Probability,32,443-458.
7. Harrison, J.M.,Kreps, D.M.(1979).Martingales and Arbitrage in Multiperiod Securities Markets.Journal of Economic Theory,20,381-408.
8. Heath, D.,Jarrow, R.,Morton, A.(1992).Bond pricing and the term structure of interest rates: A new methodology for contingent claim valuations.Econometrica,60,77-105.
9. Hsieh, C. H.(2003).Pricing and hedging of four European foreign bond call options.Review of Securities and Futures Markets,15(2),101-130.
10. Nunes, J.(2004).Multifactor valuation of Floating Range Notes.Mathematical Finance,14,79-97.
11. Reiner, E.(1992).Quanto Mechanics, from Black-Scholes to Black Holes.Risk Magazine,5,147-151.
12. Svoboda, S.(2004).Interest Rate Modelling.Palgrave Macmillan.
13. Vasicek, O.(1977).An equilibrium characterization of the term structure.Journal of Financial Economics,5,177-188.
14. 陳松男(2002)。金融工程學：金融商品創新與選擇權理論。華泰。
15. 陳松男(1996)。選擇權與期貨：衍生性商品理論與實務。新陸書局。