(實驗)標(biāo)準(zhǔn)歐式看漲期權(quán)定價的蒙特卡洛模擬實驗報告

1、曜陜西科技大學(xué)實驗報告成績課程：數(shù)理金融實驗日期：2015年6月11日班級：數(shù)學(xué)122交報告日期：2015年6月12日姓名：才器退發(fā)：（訂正、重做）學(xué)號：201212010119教師：劉利明實驗名稱：標(biāo)準(zhǔn)歐式看漲期權(quán)定價的蒙得卡洛模擬一、實驗預(yù)習(xí)：1.標(biāo)準(zhǔn)歐式看漲期權(quán)的定價模型。2.標(biāo)的資產(chǎn)到期日價格的運動軌跡或分布.3.蒙特卡洛模擬的過程二、實驗的目的和要求：通過對標(biāo)準(zhǔn)的歐式期權(quán)進行定價模擬，掌握標(biāo)的資產(chǎn)到期日價格的分布，會熟練運用蒙特卡洛模擬進行期權(quán)的定價模擬，并學(xué)會分析模擬次數(shù)、模擬精度之間的關(guān)系，最后和標(biāo)準(zhǔn)的歐式期權(quán)的解析解比較給出相對誤差。三、實驗過程：（實驗步驟、原理和實驗數(shù)據(jù)記錄

2、等）參數(shù)：起初（或0時刻）S取學(xué)號后3位除以10取整，然后加上學(xué)號最后一位（例如： 201212010119,S=119/10+9=20） ;X取S加3;r取0.03;T取0.25;b 取0.5。 （模擬100次取最后結(jié)果平均值）注意：實驗為標(biāo)準(zhǔn)的歐式看漲期權(quán)。實驗步驟、原理蒙特卡羅模擬進行期權(quán)定價的核心在丁生成股票價格的隨機過程。模型假定在期權(quán)到期的T時刻。標(biāo)的股票價格的隨機方程為：STSexpYTSepUTT其中，隨機變量服從標(biāo)準(zhǔn)正態(tài)分布，即服從N（0,1），隨機變量YT服從正態(tài)分布，其均值為UTU0.52T，方差為TVT,u為股票的收益率，b為股票的波動率。期權(quán)的收益依賴丁ST在風(fēng)險中性

3、世界里的期望值，因此對丁風(fēng)險中性定價， 股票的收益率U可以用無風(fēng)險利率r減去連續(xù)紅利收益率q代替， 也就是 （r-q）o風(fēng)險中性定價的隨機方程為：STSexorq0.52T折其中服從標(biāo)準(zhǔn)正態(tài)分布。陜西科技大學(xué)理學(xué)院實驗報告-2-實驗數(shù)據(jù)記錄表1期權(quán)基本信息股票現(xiàn)價期權(quán)執(zhí)行價格無風(fēng)險連續(xù)復(fù)利有效期年波動率（標(biāo)準(zhǔn)差度量）股票每年紅利期權(quán)類型代碼期權(quán)類型20.0023.003.00%0.2550.00%3.00%1看漲期權(quán)表2蒙特卡洛參數(shù)1TbSqrt(T)Exp(-rT)Nsim-0.03130.25000.9925100表3期權(quán)價格期權(quán)價格|0.78表4蒙特卡洛模擬表模擬次數(shù)均勻分布隨機數(shù)標(biāo)準(zhǔn)正

4、態(tài)隨機變量值股票價格期權(quán)收益10.3650-0.345117.78220.000020.4899-0.025319.26230.000030.1557-1.012415.04990.000040.4745-0.064119.07670.000050.2573-0.651816.46990.000060.62880.328521.04410.000070.54210.105719.90350.000080.1563-1.009815.06000.000090.93851.542728.50705.5070100.65450.397521.41000.0000110.50610.015319.45

5、880.0000120.3905-0.278118.08280.0000130.1074-1.240614.21550.0000140.78400.785823.59230.5923150.4596-0.101318.89970.0000160.75370.686123.01200.0120170.59610.243320.60010.0000180.83270.965024.67361.6736190.0188-2.080111.52430.0000200.2104-0.805115.85040.0000210.0740-1.447013.50070.0000220.1055-1.25111

6、4.17830.0000230.3317-0.435217.38610.0000240.1282-1.134714.59690.0000250.0002-3.49038.10030.0000260.53680.092419.83750.0000期權(quán)價格0.78-3-270.65710.404421.44720.0000陜西科技大學(xué)理學(xué)院實驗報告-4-280.54400.110619.92790.0000290.82740.944024.54431.5443300.0819-1.392413.68600.0000310.1919-0.870815.59220.0000320.67890.4647

7、21.77250.0000330.4542-0.115018.83510.0000340.3570-0.366417.68780.0000350.1500-1.036514.95960.0000360.70440.537122.17030.0000370.92881.466827.97154.9715380.53020.075819.75550.0000390.0896-1.343013.85630.0000400.75770.699023.08620.0862410.4018-0.248618.21670.0000420.4619-0.095718.92630.0000430.4922-0.

8、019619.28970.0000440.2076-0.814715.81270.0000450.3297-0.440617.36270.0000460.0954-1.308013.97780.0000470.58980.227020.51660.0000480.1699-0.954715.26890.0000490.92761.458327.91184.9118500.0979-1.293414.02890.0000510.4439-0.141218.71240.0000520.2729-0.603916.66820.0000530.87251.138525.76742.7674540.75

9、070.676722.95750.0000550.2729-0.603916.66810.0000560.67360.450021.69290.0000570.2566-0.653816.46170.0000580.0899-1.341413.86180.0000590.0310-1.867012.15490.0000600.3227-0.460117.27830.0000610.79010.806923.71720.7172620.2973-0.532316.96930.0000630.2353-0.721616.18510.0000640.4805-0.049019.14880.00006

10、50.2546-0.660116.43580.0000660.3406-0.410817.49260.0000670.0449-1.696112.68550.0000680.4824-0.044119.17230.0000690.2060-0.820315.79040.0000700.86451.100925.52642.5264-5-710.58860.224020.50130.0000720.75490.690023.03440.0344730.92791.460227.92534.9253740.3310-0.437117.37800.0000750.54290.107819.91440

11、.0000760.0807-1.400413.65870.0000770.63440.343521.12270.0000780.4100-0.227518.31320.0000790.96041.755630.06577.0657800.1146-1.202314.35230.0000810.92341.428627.70584.7058820.62020.306020.92600.0000830.3477-0.391517.57740.0000840.1492-1.039714.94780.0000850.4800-0.050219.14290.0000860.2194-0.774215.9

12、7360.0000870.99372.496636.185013.1850880.1304-1.124414.63450.0000890.0289-1.897412.06280.0000900.3454-0.397817.54970.0000910.54770.119819.97390.0000920.92301.425227.68224.6822930.53820.096019.85560.0000940.4064-0.236818.27060.0000950.84721.024725.04452.0445960.82620.939424.51591.5159970.67240.446621.67460.0000980.72190.588522.45700.0000990.99682.723638.297515.29751000.