系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2009年
11期
76~83
,共null页
虹式几何平均亚洲期权 虹式算术平均亚洲期权 蒙特卡罗模拟
虹式幾何平均亞洲期權 虹式算術平均亞洲期權 矇特卡囉模擬
홍식궤하평균아주기권 홍식산술평균아주기권 몽특잡라모의
rainbow geometric average Asian option rainbow arithmetic average Asian option Monte Carlo simulation
研究了一种奇异路径依赖型期权——具有虹式特征的亚洲期权的定价问题.基于Black-Scholes模型的假设条件,利用多维ITO引理和无套利原理,构建了基于两个资产支付红利的虹式亚洲期权多因素路径依赖型期权定价模型,并结合边界条件,导出虹式几何平均亚洲看涨期权的解析定价公式以及虹式几何平均亚洲期权看涨-看跌平价关系式,以此为控制变量模拟计算虹式算术平均亚洲期权,数值实验表明虹式几何平均控制变量法有效地提高了蒙特卡罗模拟虹式算术平均亚洲期权定价的精确度.
研究瞭一種奇異路徑依賴型期權——具有虹式特徵的亞洲期權的定價問題.基于Black-Scholes模型的假設條件,利用多維ITO引理和無套利原理,構建瞭基于兩箇資產支付紅利的虹式亞洲期權多因素路徑依賴型期權定價模型,併結閤邊界條件,導齣虹式幾何平均亞洲看漲期權的解析定價公式以及虹式幾何平均亞洲期權看漲-看跌平價關繫式,以此為控製變量模擬計算虹式算術平均亞洲期權,數值實驗錶明虹式幾何平均控製變量法有效地提高瞭矇特卡囉模擬虹式算術平均亞洲期權定價的精確度.
연구료일충기이로경의뢰형기권——구유홍식특정적아주기권적정개문제.기우Black-Scholes모형적가설조건,이용다유ITO인리화무투리원리,구건료기우량개자산지부홍리적홍식아주기권다인소로경의뢰형기권정개모형,병결합변계조건,도출홍식궤하평균아주간창기권적해석정개공식이급홍식궤하평균아주기권간창-간질평개관계식,이차위공제변량모의계산홍식산술평균아주기권,수치실험표명홍식궤하평균공제변량법유효지제고료몽특잡라모의홍식산술평균아주기권정개적정학도.
This paper studies the pricing of a kind of exotic path-dependent options,i.e.,Asian options with feature based on rainbow.On the basis of the hypotheses of the Black-Scholes model,we construct the rainbow Asian options on two assets paying dividends with multi-factors path-dependent option pricing model using the multidimensional ITO lemma and the arbitrage-free principle.With the boundary conditions,we derive the analytic formula of the rainbow geometric average Asian call option and call-put parity relationship on rainbow geometric average Asian options.With the help of the above analytic fomulae as the control variate,we further simulate the rainbow arithmetic average Asian options.The numerical evidence is shown that rainbow geometric average control variable method effectively improves the accuracy on Monte Carlo simulation of rainbow arithmetic average Asian option pricing.
