MATLAB金融计算试题.doc

。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) 0 100; datenum(12/31/2014) 0.0175 100; datenum(11/15/2017) 0.03 100; datenum(11/15/2022) 0.04 100; datenum(02/15/2041) 0.0537 100; 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) datestr(curvedates) plot(zerorates)运行结果：zerorates = 0.0115 0.0118 0.0168 0.0302 0.0418 0.0550curvedates = 735341 735432 735964 737014 738840 745507ans =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）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 = 50.0000 55.8985 62.5172 69.9441 76.2699 85.6054 96.0836 0 44.7755 50.0326 55.9315 60.5420 67.9524 76.2699 0 0 40.1226 44.8084 48.0575 53.9398 60.5420 0 0 0 35.9790 38.1474 42.8167 48.0575 0 0 0 0 30.2809 33.9873 38.1474 0 0 0 0 0 26.9787 30.2809 0 0 0 0 0 0 24.0366option = 6.7016 3.9308 1.7652 0.4598 0 0 0 0 9.6686 6.2275 3.1393 0.9412 0 0 0 0 13.3762 9.5132 5.4560 1.9263 0 0 0 0 17.5811 13.8526 9.1833 3.9425 0 0 0 0 21.7191 18.0127 13.8526 0 0 0 0 0 25.0213 21.7191 0 0 0 0 0 0 27.9634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,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 = 50.0000 55.8985 62.5172 69.9441 76.2699 85.6054 96.0836 0 44.7755 50.0326 55.9315 60.5420 67.9524 76.2699 0 0 40.1226 44.8084 48.0575 53.9398 60.5420 0 0 0 35.9790 38.1474 42.8167 48.0575 0 0 0 0 30.2809 33.9873 38.1474 0 0 0 0 0 26.9787 30.2809 0 0 0 0 0 0 24.0366option = 4.9996 7.8792 12.0864 17.9441 25.1294 34.0369 44.0836 0 2.1193 3.6809 6.2599 10.3427 16.3840 24.2699 0 0 0.5473 1.0878 2.1622 4.2976 8.5420 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0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 = 5.5091 6.7865三、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=31.63 32.17 31.58 30.71 30.77 30.93 31.79 31.58 32 33.91 33.12 34.98 35.3 35.5 34.65 35.46 35.95 35.39 37.67 36.64 36.77 36.85 36.59 35.81 35.18 35.76 36.66 38.35 38.26 38.34 38.85 41.27 40.99 40.7 42.28;RetSeries=tick2ret(TickSeries)bar(RetSeries)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 -0.0275 0.0020 0.0052 0.0278 -0.0066 0.0133 0.0597 -0.0233 0.0562 0.0091 0.0057 -0.0239 0.0234 0.0138 -0.0156 0.0644 -0.0273 0.0035 0.0022 -0.0071 -0.0213 -0.0176 0.0165 0.0252 0.0461 -0.0023 0.0021 0.0133 0.0623 -0.0068 -0.0071 0.0388盛达矿业MATLAB命令：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 14.34 14.19 14.24 13.74 13.57 13.8 13.76 13.76 13.52 13.3 13.28 13.44 13.37 13.28 13.74 13.93 14.16 13.99 14.73 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 = -0.0145 0.0241 -0.0159 -0.0154 -0.0227 0.0192 -0.0173 0.0368 0.0069 -0.0291 0.0386 0.0577 0.0330 -0.0215 0.0185 -0.0105 0.0035 -0.0351 -0.0124 0.0169 -0.0029 0 -0.0174 -0.0163 -0.0015 0.0120 -0.0052 -0.0067 0.0346 0.0138 0.0165 -0.0120 0.0529 -0.0020恒逸石化MATLAB命令：TickSeries=9.43 9.14 8.99 8.67 8.6 8.42 8.49 8.4 8.53 8.97 8.61 8.91 9.11 9.12 9.06 9.14 9.04 8.79 8.7 8.78 8.83 9.37 9.47 9.3 9.55 9.89 9.69 9.64 9.58 9.52 9.88 10.22 10.3 10.45 10.84;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 -0.0209 0.0083 -0.0106 0.0155 0.0516 -0.0401 0.0348 0.0224 0.0011 -0.0066 0.0088 -0.0109 -0.0277 -0.0102 0.0092 0.0057 0.0612 0.0107 -0.0180 0.0269 0.0356 -0.0202 -0.0052 -0.0062 -0.0063 0.0378 0.0344 0.0078 0.0146 0.0373金宇车城MATLAB命令：TickSeries=10.9 11.17 11.32 11.32 11.22 11.08 11.27 11.19 11.31 11.52 11.25 11.78 12.07 12.11 12.15 12.29 12.45 12.87 12.77 12.63 12.56 12.71 12.71 12.5 12.15 12.23 12.12 12.48 12.6 12.87 12.9 13.33 13.5 13.5 13.42;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 = 0.0248 0.0134 0 -0.0088 -0.0125 0.0171 -0.0071 0.0107 0.0186 -0.0234 0.0471 0.0246 0.0033 0.0033 0.0115 0.0130 0.0337 -0.0078 -0.0110 -0.0055 0.0119 0 -0.0165 -0.0280 0.0066 -0.0090 0.0297 0.0096 0.0214 0.0023 0.0333 0.0128 0 -0.0059（2） 计算4种股票收盘价的协方差矩阵；MATLAB命令：A=31.63 13.07 9.43 10.932.17 12.88 9.14 11.1731.58 13.19 8.99 11.3230.71 12.98 8.67 11.3230.77 12.78 8.6 11.2230.93 12.49 8.42 11.0831.79 12.73 8.49 11.2731.58 12.51 8.4 11.1932 12.97 8.53 11.3133.91 13.06 8.97 11.5233.12 12.68 8.61 11.2534.98 13.17 8.91 11.7835.3 13.93 9.11 12.0735.5 14.39 9.12 12.1134.65 14.08 9.06 12.1535.46 14.34 9.14 12.2935.95 14.19 9.04 12.4535.39 14.24 8.79 12.8737.67 13.74 8.7 12.7736.64 13.57 8.78 12.6336.77 13.8 8.83 12.5636.85 13.76 9.37 12.7136.59 13.76 9.47 12.7135.81 13.52 9.3 12.535.18 13.3 9.55 12.1535.76 13.28 9.89 12.2336.66 13.44 9.69 12.1238.35 13.37 9.64 12.4838.26 13.28 9.58 12.638.34 13.74 9.52 12.8738.85 13.93 9.88 12.941.27 14.16 10.22 13.3340.99 13.99 10.3 13.540.7 14.73 10.45 13.542.28 14.7 10.84 13.42cov(A)运行结果：ans = 10.0608 1.4751 1.5687 2.3059 1.4751 0.3711 0.2270 0.3857 1.5687 0.2270 0.3682 0.3326 2.3059 0.3857 0.3326 0.5837（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= 10.0608 1.4751 1.5687 2.3059 1.4751 0.3711 0.2270 0.3857 1.5687 0.2270 0.3682 0.3326 2.3059 0.3857 0.3326 0.5837;PortWts=0.35 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=10.0608 1.4751 1.5687 2.3059 1.4751 0.3711 0.2270 0.3857 1.5687 0.2270 0.3682 0.3326 2.3059 0.3857 0.3326 0.5837;NumPorts=5;PortRink,PortReturn,PortWts=frontcon(ExpReturn,ExpCovariance,NumPorts)运行结果：PortRink = 0.5462 0.5820 1.1729 2.1585 3.1719PortReturn = 0.2247 0.2436 0.2624 0.2812 0.3000PortWts = -0.0000 0.4949 0.5051 0.0000 0 0.8712 0.1288 -0.0000 0.2475 0.7525 0 -0.0000 0.6237 0.3763 0 -0.0000 1.0000 0 0.0000 -0.0000（5） 无风险利率为0.35，借贷利率为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=10.0608 1.4751 1.5687 2.3059 1.4751 0.3711 0.2270 0.3857 1.5687 0.2270 0.3682 0.3326 2.3059 0.3857 0.3326 0.5837;RisklessRate=0.035;BorrowRate=0.5;RiskAversion=3;PortRisk,PortReturn,PortWts=portopt(ExpReturn,ExpCovariance)RiskyRink, RiskyReturn, RiskyWts, RiskyFraction,OverallRick, OverallReturn=portalloc(PortRisk,.PortReturn, PortWts, RisklessRate,BorrowRate, RiskAversion)运行结果：PortRisk = 0.5462 0.5534 0.5747 0.6084 0.9663 1.3864 1.8246 2.2704 2.7200 3.1719PortReturn = 0.2247 0.2331 0.2415 0.2498 0.2582 0.2666 0.2749 0.2833 0.2916 0.3000PortWts = -0.0000 0.4949 0.5051 0.0000 0 0.6621 0.3379 -0.0000 0.0000 0.8294 0.1706 -0.0000 0 0.9966 0.0034 -0.0000 0.1638 0.8362 0 -0.0000 0.3311 0.6689 0 0.0000 0.4983 0.5017 0 -0.0000 0.6655 0.3345 0 -0.0000 0.8328 0.1672 0 0.0000 1.0000 0 0.0000 -0.0000RiskyRink = 0.5427RiskyReturn = 0.2302RiskyWts = -0.0000 0.6040 0.3960 -0.0000RiskyFraction = 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 30.54 31.63 31.2932.35 30.71 32.17 31.332.6 31.56 31.58 32.0832 30.7 30.71 31.8231.59 30.45 30.77 30.5531.2 30 30.93 30.632.2 30.94 31.79 30.9432.18 31.52 31.58 31.7832.11 31.43 32 31.633.91 31.91 33.91 32.135.57 32.5 33.12 32.8335.4 33.26 34.98 33.2635.57 34.28 35.3 34.9636.49 35.1 35.5 35.335.8 34.45 34.65 35.335.6 34.6 35.46 34.7536.35 35.33 35.95 35.6636.26 34.9 35.39 35.737.9 35 37.67 35.0137.66 36.42 36.64 37.338.29 36.3 36.77 36.6437.58 36 36.85 37.337.32 36.35 36.59 37.2536.89 35.8 35.81 36.5936.41 34.75 35.18 35.936.03 35.18 35.76 35.437.22 35.5 36.66 35.738.55 36.72 38.35 37.0538.65 38.08 38.26 38.4439.17 38.03 38.34 38.2539.2 38.07 38.85 38.541.49 39.08 41.27 39.0842.39 40.68 40.99 41.240.99 40.01 40.7 40.7542.6 40.59 42.28 40.69;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：盛达矿业MATLAB命令：a=13.11 12.08 13.07 12.212.99 12.65 12.88 12.913.49 12.88 13.19 12.9913.27 12.88 12.98 13.113.1 12.77 12.78 12.9512.77 12.42 12.49 12.712.8 12.42 12.73 12.4212.77 12.32 12.51 12.7213.22 12.5 12.97 12.5113.38 12.95 13.06 13.1513.27 12.46 12.68 12.9813.22 12.65 13.17 12.6814.12 13.22 13.93 13.2914.65 13.7 14.39 13.9514.84 14 14.08 14.3514.35 13.88 14.34 1414.34 13.92 14.19 14.1514.3 14 14.24 14.114.2 13.7 13.74 14.1413.76 13.5 13.57 13.513.9 13.4 13.8 13.514 13.71 13.76 13.7914.01 13.72 13.76 13.813.99 13.5 13.52 13.9113.47 13.2 13.3 13.313.44 13.03 13.28 13.2713.45 13.18 13.44 13.2513.54 13.3 13.37 13.4513.41 13.09 13.28 13.3313.77 13.29 13.74 13.3414.05 13.72 13.93 13.814.23 13.81 14.16 13.9414.2 13.8 13.99 14.0814.8 13.93 14.73 13.9314.95 14.56 14.7 14.78;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：恒逸石化MATLAB命令：a=9.6 8.75 9.43 9.049.64 9.1 9.14 9.359.16 8.86 8.99 9.089 8.65 8.67 8.998.85 8.58 8.6 8.588.85 8.38 8.42 8.638.54 8.3 8.49 8.438.57 8.34 8.4 8.58.57 8.4 8.53 8.429.31 8.53 8.97 8.539.38 8.41 8.61 8.78.97 8.63 8.91 8.639.21 8.85 9.11 8.919.25 8.97 9.12 9.119.3 9.01 9.06 9.139.15 8.8 9.14 9.059.27 8.95 9.04 9.19.09 8.74 8.79 9.048.86 8.61 8.7 8.78.85 8.63 8.78 8.728.93 8.25 8.83 8.49.66 8.82 9.37 8.8210.2 9.46 9.47 9.589.9 9.28 9.3 9.479.75 9.25 9.55 9.310.19 9.37 9.89 9.4410.08 9.53 9.69 9.839.71 9.3 9.64 9.69