MATLAB金融计算试题

1、.MATLAB 金融计算试题（ 2014 级研究生用）(上机操作使用）一、 利率期限结构 （ 20 分）已知国债面值是100 美元，各期收益率为国债品种票息到期日当期收益3个月17-Apr-20131.156个月17-Jul-20131.182年1.7531-Dec-20141.685年3.0015-Nov-20172.9710 年4.0015-Nov-20224.0130 年5.37515-Feb-20414.92试分析其利率期限结构。MATLAB命令：bonds=datenum('04/17/2013')0 100;datenum('07/17/2013')

2、0100;datenum('12/31/2014')0.0175100;datenum('11/15/2017')0.03100;datenum('11/15/2022')0.04100;datenum('02/15/2041')0.0537100;yield=0.0115 0.0118 0.0168 0.0297 0.0401 0.0492'settle=datenum('01/17/2013'); %结算日zerorates,curvedates=zbtyield(bonds,yield,settle)

3、datestr(curvedates)plot(zerorates)运行结果：zerorates =0.01150.01180.01680.03020.04180.0550curvedates =7353417354327359647370147388407455070.0550.050.0450.040.0350.030.0250.020.0150.0111.522.533.544.555.56.ans =17-Apr-201317-Jul-201331-Dec-201415-Nov-201715-Nov-202215-Feb-2041二、期权定价（30 分）若股票现在价格为$50 ，期权执

4、行价格为$52 ，无风险利率为0.1 ，股票波动标准差为0.4 ，期权的到期日为6 个月 , 且若这一卖权在3.5 月时有一次股息支付$2。（ 1）使用 Black-Scholes 定价公式计算欧式卖权和买权的价值;MATLAB命令：price=50;strike=52;rate=0.1;time=6/12;volatility=0.4;callprice,putprice=blsprice(price,strike,rate,time,volatility)运行结果：callprice =5.8651putprice =5.3290（ 2）利用二项式期权定价（二叉树（CRR ）模型定价数值解

5、）计算看涨看跌期权价格;MATLAB命令：price=50;strike=52;rate=0.1;time=6/12;increment=1/12;volatility=0.4;flag=0;dividentrate=0;divident=2;exdiv=3.5;price,option=binprice(price,strike,rate,time,increment,volatility,flag,dividentrate,divident,exdiv)运行结果：得出二叉树每个交点处的资产价格和期权价值.price =50.000055.898562.517269.944176.26998

6、5.605496.0836044.775550.032655.931560.542067.952476.26990040.122644.808448.057553.939860.5420.00035.979038.147442.816748.0575000030.280933.987338978730.280900000024.0366option =6.70163.93081.76520.459800009.66866.22753.13930.9412000013.37629.51325.45601.9263000017.581113.85269.18333.942

7、5000021.719118.012713.85260000025.021321.719100000027.9634由结果可知， option 第一行第一列就是看跌期权价格，该期权价格为6.7016 元。MATLAB命令：price=50;strike=52;rate=0.1;time=6/12;increment=1/12;volatility=0.4;flag=1;dividentrate=0;divident=2;exdiv=3.5;price,option=binprice(price,strike,rate,time,increment,volatility,flag,dividen

8、trate,divident,exdiv)运行结果：得出二叉树每个交点处的资产价格和期权价值.price =50.000055.898562.517269.944176.269985.605496.0836044.775550.032655.931560.542067.952476.26990040.122644.808448.057553.939860.542000035.979038.147442.816748.0575000030.280933.987338978730.280900000024.0366option =4.99967.879212.086417

9、.944125.129434.036944.083602.11933.68096.259910.342716.384024.2699000.54731.08782.16224.29768.54200000000000000000000000000000.由结果可知， option 第一行第一列就是看涨期权价格，该期权价格为4.9996 元。(3) 假设股票价格服从几何布朗运动，试用蒙特卡洛模拟方法计算该期权价格。MATLAB 命令：s0=50;K=52;r=0.1;T=0.5;sigma=0.4;Nu=1000;randn('seed',0);%定义随机数发生器种子是0,%这样

10、保证每次模拟的结果相同nuT=(r-0.5*sigma2)*Tsit=sigma*sqrt(T)discpayoff=exp(-r*T)*max(0,s0*exp(nuT+sit*randn(Nu,1)-K);%期权到期时的现金流eucall,varprice,ci=normfit(discpayoff)运行结果：nuT =0.0100sit =0.2828eucall =6.1478varprice =10.2924ci =5.50916.7865三、搜集数据并计算画图（50 分）按照自己的研究生学号后两位数，在锐思金融数据库中搜集4 种股票信息，包括最高价、最低价、收盘价和开盘价，数据个数

11、2 个月左右，建立数据表格。要求使用MATLAB编程解决以下问题：（ 1）将 4 种股票的收盘价格转化为收益率，并画出收益率直方图海虹控股MATLAB命令：TickSeries=31.6332.1731.5830.7130.7730.9331.7931.583233.9133.1234.9835.335.534.6535.4635.9535.3937.6736.6436.7736.8536.5935.8135.1835.7636.6638.3538.2638.3438.8541.2740.9940.742.28'RetSeries=tick2ret(TickSeries)bar(Ret

12、Series)xlabel(' 天数');ylabel(' 收益率');title('海虹控股对数收益率直方图');运行结果：.RetSeries =0.0171-0.0183-0.02750.00200.00520.0278-0.00660.01330.0597-0.02330.05620.00910.0057-0.02390.02340.0138-0.01560.0644-0.02730.00350.0022-0.0071-0.0213-0.01760.01650.02520.0461-0.00230.00210.01330.0623-0.0

13、068-0.00710.0388盛达矿业MATLAB命令：海虹控股对数收益率直方图0.070.060.050.040.03率益 0.02收0.010-0.01-0.02-0.0305101520253035天 数TickSeries=13.07 12.88 13.19 12.98 12.78 12.49 12.73 12.51 12.97 13.06 12.68 13.17 13.93 14.39 14.08 14.3414.1914.2413.7413.5713.813.7613.7613.5213.313.2813.4413.3713.2813.7413.9314.1613.9914.73

14、14.7'RetSeries=tick2ret(TickSeries)bar(RetSeries).xlabel(' 天数 ' );ylabel(' 收益率 ' );title(' 盛达矿业对数收益率直方图' );运行结果：RetSeries =-0.01450.0241-0.0159-0.0154-0.02270.0192-0.01730.03680.0069-0.02910.03860.05770.0330-0.02150.0185-0.01050.0035-0.0351-0.01240.0169-0.00290-0.0174-0.0

15、163-0.00150.0120-0.0052-0.00670.03460.01380.0165-0.01200.0529-0.0020恒逸石化MATLAB命令：盛达矿业对数收益率直方图0.060.050.040.030.02率益 0.01收0-0.01-0.02-0.03-0.0405101520253035天 数TickSeries=9.439.148.998.678.6 8.428.498.4 8.538.978.618.919.119.129.069.149.048.798.78.788.839.379.479.3 9.559.899.699.649.589.529.8810.2210

16、.310.4510.84'.RetSeries=tick2ret(TickSeries)bar(RetSeries)xlabel(' 天数 ' );ylabel(' 收益率 ' );title(' 恒逸石化对数收益率直方图' );运行结果：RetSeries =-0.0308-0.0164-0.0356-0.0081-0.02090.0083-0.01060.01550.0516-0.04010.03480.02240.0011-0.00660.0088-0.0109-0.0277-0.01020.00920.00570.06120.01

17、07-0.01800.02690.0356-0.0202-0.0052-0.0062-0.00630.03780.03440.00780.01460.0373金宇车城MATLAB命令：恒逸石化对数收益率直方图0.080.060.040.02率益收0-0.02-0.04-0.0605101520253035天 数TickSeries=10.911.1711.3211.3211.2211.0811.2711.1911.3111.5211.2511.7812.0712.1112.1512.29.12.4512.8712.7712.6312.5612.7112.7112.512.1512.2312.1

18、212.4812.612.8712.913.3313.513.513.42'RetSeries=tick2ret(TickSeries)bar(RetSeries)xlabel(' 天数 ' );ylabel(' 收益率 ' );title(' 金宇车城对数收益率直方图' );运行结果：RetSeries =0.02480.01340-0.0088-0.01250.0171-0.00710.01070.0186-0.02340.04710.02460.00330.00330.01150.01300.0337-0.0078-0.0110-0

19、.00550.01190-0.0165-0.02800.0066-0.00900.02970.00960.02140.00230.03330.01280-0.0059金宇车城对数收益率直方图0.050.040.030.02率益 0.01收0-0.01-0.02-0.0305101520253035天 数.（ 2）计算 4 种股票收盘价的协方差矩阵；MATLAB命令：A=31.6313.079.4310.932.1712.889.1411.1731.5813.198.9911.3230.7112.988.6711.3230.7712.788.6 11.2230.9312.498.4211.083

20、1.7912.738.4911.2731.5812.518.4 11.1932 12.978.5311.3133.9113.068.9711.5233.1212.688.6111.2534.9813.178.9111.7835.313.939.1112.0735.514.399.1212.1134.6514.089.0612.1535.4614.349.1412.2935.9514.199.0412.4535.3914.248.7912.8737.6713.748.7 12.7736.6413.578.7812.6336.7713.88.8312.5636.8513.769.3712.7136

21、.5913.769.4712.7135.8113.529.3 12.535.1813.39.5512.1535.7613.289.8912.2336.6613.449.6912.1238.3513.379.6412.4838.2613.289.5812.638.3413.749.5212.8738.8513.939.8812.941.2714.1610.2213.3340.9913.9910.313.540.714.7310.4513.542.2814.710.8413.42cov(A)运行结果：ans =10.06081.47511.56872.30591.47510.37110.22700

22、.38571.56870.22700.36820.33262.30590.38570.33260.5837.（ 3）若给出这4 种股票预期收益率分别为0.3、0.25、0.2 和 0.15，且购买权重分别0.35、0. 25、 0.25 和 0.15 ，求总资产的标准差和期望收益；MATLAB命令：ExpReturn=0.3,0.25,0.2,0.15;ExpCovariance= 10.06081.47511.56872.30591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.5837;PortWts=0

23、.35 0.25 0.25 0.15;PortRisk,PortReturn=portstats(ExpReturn, ExpCovariance,PortWts)运行结果：PortRisk =1.4659PortReturn =0.2400（ 4）求该资产组合有效前沿（有效前沿的个数选为5）；MATLAB命令：ExpReturn=0.3 0.25 0.2 0.15;ExpCovariance=10.06081.47511.56872.30591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.5837;Num

24、Ports=5;PortRink,PortReturn,PortWts=frontcon(ExpReturn,ExpCovariance,NumPorts)运行结果：PortRink =0.54620.58201.17292.15853.1719PortReturn =0.22470.24360.26240.28120.3000PortWts =-0.00000.49490.50510.000000.87120.1288-0.00000.24750.75250-0.00000.62370.37630-0.00001.000000.0000-0.0000.（ 5）无风险利率为 0.35，借贷利率

25、为 0.5，投资者风险厌恶系数为 3，求考虑无风险资产及借贷情况下的最优资产配置。MATLAB命令：ExpReturn=0.3 0.25 0.2 0.15;ExpCovariance=10.06081.47511.56872.30591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.5837;RisklessRate=0.035;BorrowRate=0.5;RiskAversion=3;PortRisk,PortReturn,PortWts=portopt(ExpReturn,ExpCovariance)R

26、iskyRink, RiskyReturn, RiskyWts, RiskyFraction,OverallRick,OverallReturn=portalloc(PortRisk,.PortReturn, PortWts, RisklessRate,BorrowRate, RiskAversion)运行结果：PortRisk =0.54620.55340.57470.60840.96631.38641.82462.27042.72003.1719PortReturn =0.22470.23310.24150.24980.25820.26660.27490.28330.29160.3000P

27、ortWts =-0.00000.49490.50510.000000.66210.3379-0.00000.00000.82940.1706-0.000000.99660.0034-0.00000.16380.83620-0.0000.0.33110.668900.00000.49830.50170-0.00000.66550.33450-0.00000.83280.167200.00001.000000.0000-0.0000RiskyRink =0.5427RiskyReturn =0.2302RiskyWts =-0.00000.60400.3960-0.0000RiskyFracti

28、on =0.2209OverallRick =0.1199OverallReturn =0.0781（ 6）绘制这 4 种股票的最高价、最低价、收盘价和开盘价的烛型图。海虹控股MATLAB命令：a=31.9 30.5431.6331.2932.3530.7132.1731.332.631.5631.5832.083230.730.7131.8231.5930.4530.7730.5531.23030.9330.632.230.9431.7930.9432.1831.5231.5831.7832.1131.433231.633.9131.9133.9132.135.5732.533.1232.8

29、335.433.2634.9833.2635.5734.2835.334.9636.4935.135.535.335.834.4534.6535.335.634.635.4634.7536.3535.3335.9535.6636.2634.935.3935.737.93537.6735.0137.6636.4236.6437.338.2936.336.7736.6437.583636.8537.337.3236.3536.5937.2536.8935.835.8136.59.36.4134.7535.1835.936.0335.1835.7635.437.2235.536.6635.738.5

30、536.7238.3537.0538.6538.0838.2638.4439.1738.0338.3438.2539.238.0738.8538.541.4939.0841.2739.0842.3940.6840.9941.240.9940.0140.740.7542.640.5942.2840.69;candle(a(:,1),a(:,2),a(:,3),a(:,4)candle(a(:,1),a(:,2),a(:,3),a(:,4),'r')title(' 海虹控股 ' );运行结果：海虹控股44424038363432300510152025303540盛

31、达矿业MATLAB命令：a=13.1112.0813.0712.212.9912.6512.8812.913.4912.8813.1912.9913.2712.8812.9813.113.112.7712.7812.9512.7712.4212.4912.712.812.4212.7312.4212.7712.3212.5112.7213.2212.512.9712.5113.3812.9513.0613.1513.2712.4612.6812.9813.2212.6513.1712.68.14.1213.2213.9313.2914.6513.714.3913.9514.841414.081

32、4.3514.3513.8814.341414.3413.9214.1914.1514.31414.2414.114.213.713.7414.1413.7613.513.5713.513.913.413.813.51413.7113.7613.7914.0113.7213.7613.813.9913.513.5213.9113.4713.213.313.313.4413.0313.2813.2713.4513.1813.4413.2513.5413.313.3713.4513.4113.0913.2813.3313.7713.2913.7413.3414.0513.7213.9313.814

33、.2313.8114.1613.9414.213.813.9914.0814.813.9314.7313.9314.9514.5614.714.78;candle(a(:,1),a(:,2),a(:,3),a(:,4)candle(a(:,1),a(:,2),a(:,3),a(:,4),'r')title(' 盛达矿业 ' );运行结果：盛达矿业1514.51413.51312.5120510152025303540.恒逸石化MATLAB命令：a=9.68.759.439.049.649.1 9.149.359.168.868.999.0898.658.678.

34、998.858.588.68.588.858.388.428.638.548.3 8.498.438.578.348.48.58.578.4 8.538.429.318.538.978.539.388.418.618.78.978.638.918.639.218.859.118.919.258.979.129.119.3 9.019.069.139.158.8 9.149.059.278.959.049.19.098.748.799.048.868.618.78.78.858.638.788.728.938.258.838.49.668.829.378.8210.29.469.479.589.9 9.289.3 9.479.759.259.559.310.199.379.899.4410.089.539.699