国内外利率为随机的双币种重置型期权定价  

Pricing Quanto Reset Options with Stochastic Domestic and Foreign Interest Rates

作　　者：黄国安[1,2] 邓国和[1] 

机构地区：[1]广西师范大学数学科学学院,桂林541004 [2]桂林航天工业高等专科学校计算机系,桂林541004

出　　处：《大学数学》2011年第2期125-132,共8页College Mathematics

基　　金：国家自然基金(40675023);广西自然科学基金(桂科自0991091)

摘　　要：双币种重置期权的特征是指在终端期T时的收益依赖于预先设定的t0时刻标的资产的价格与执行价K>0(事先给定)的大小关系重新设置期权的执行价从而给出其定价,这种期权是投资于外国资产的一种合约,其风险不仅依赖外国资产价格的变化,还受外国货币的汇率以及国内外两种利率波动的影响,所以在实际应用方面十分广泛.本文首先就标的资产是外国股票和汇率两种情形下分别定义了双币种重置型欧式看涨期权的定价类型,建立了金融市场模型,其次利用鞅方法和多维联合正态分布在国内外利率是随机的情形下给出了双币种重置型欧式看涨期权的定价公式,最后利用数值算例比较了定价公式的行为特征.The reset feature in a quanto option refers to the payoff structure where the terminal payoff of the quanto option depends on resetting the strike price of either the foreign stock price or the exchange rate at a predetermined time t0∈.The option is a contract which invests to foreign assets and its payoff depends on not only the price of foreign asset,but also the affect of exchange rate and domestic and foreign interest rates.In this paper,we first establish the financial market model and define pricing formulas on quanto reset option of European call option in case of either foreign stock or exchange rates.Second,we derive the analytic price formulas for two types of above with stochastic domestic and foreign interest rates by using martingale method and multivariate jointly normal distribution functions.Finally,we analyze the pricing behaviours with numerical example.

关 键 词：双币种期权 重置型期权 随机利率 HULL-WHITE模型 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]