MAAB金融計(jì)算試題

1、MATLAB金融計(jì)算試題（2014級(jí)研究生用）（上機(jī)操作使用）、利率期限結(jié)構(gòu)（20分）已知國(guó)債面值是100美元，各期收益率為國(guó)債品種票息到期日當(dāng)期收益3個(gè)月17-Apr-20131.156個(gè)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試分析其利率期限結(jié)構(gòu)MATLA酶令：bonds=datenum('04/17/2013')0100;datenum('07/17/2013')0100;datenum(&#

2、39;12/31/2014')0.0175100;datenum('11/15/2017')0.03100;datenum('11/15/2022')0.04100;datenum('02/15/2041')0.0537100;yield=0.01150.01180.01680.02970.04010.0492'settle=datenum('01/17/2013');%結(jié)算日zerorates,curvedates=zbtyield(bonds,yield,settle)datestr(curvedates)pl

3、ot(zerorates)運(yùn)行結(jié)果：0.0550.050.0450.040.0350.030.0250.020.0150.0111.522.533.544.555.56zerorates=0.01150.01180.01680.03020.04180.0550curvedates=735341735432735964737014738840745507ans=17-Apr-201317-Jul-201331-Dec-201415-Nov-201715-Nov-202215-Feb-2041二、期權(quán)定價(jià)（30分）若股票現(xiàn)在價(jià)格為$50，期權(quán)執(zhí)行價(jià)格為$52，無(wú)風(fēng)險(xiǎn)利率為0.1，股票波動(dòng)標(biāo)準(zhǔn)差為0

4、.4，期權(quán)的到期日為6個(gè)月,且若這一賣權(quán)在3.5月時(shí)有一次股息支付$2。（ 1） 使用Black-Scholes定價(jià)公式計(jì)算歐式賣權(quán)和買權(quán)的價(jià)值;MATLABr令：price=50;strike=52;rate=0.1;time=6/12;volatility=0.4;callprice,putprice=blsprice（price,strike,rate,time,volatility）運(yùn)行結(jié)果：callprice=5.8651putprice=5.3290計(jì)算看漲（ 2） 利用二項(xiàng)式期權(quán)定價(jià)（二叉樹(shù)（CRR）模型定價(jià)數(shù)值解）看跌期權(quán)價(jià)格;MATLABr令：price=50;strike=

5、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）運(yùn)行結(jié)果：得出二叉樹(shù)每個(gè)交點(diǎn)處的資產(chǎn)價(jià)格和期權(quán)價(jià)值.price=50.000055.898562.517269.944176.269985.605496.0836044.775550.032655.931560.

6、542067.952476.269940.122644.808448.057553.939860.542035.979038.147442.816748.057530.280933.987338.1474026.978730.280924.0366option=6.70163.93081.76520.459809.66866.22753.13930.9412013.37629.51325.45601.9263003.94250013.85260021.71910027.9634017.581113.85269.18330021.719118.012700025.0213option第一行第一列

7、就是看跌期權(quán)價(jià)格，該期權(quán)價(jià)格為6.7016元。MATLABr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)運(yùn)行結(jié)果：得出二叉樹(shù)每個(gè)交點(diǎn)處的資產(chǎn)價(jià)格和期權(quán)價(jià)值.price=50.000055.898562.517269.94

8、4176.269985.605496.0836044.775550.032655.931560.542067.952476.26990040.122644.808448.057553.939860.542000035.979038.147442.816748.0575000030.280933.987338978730.280900000024.0366option=4.99967.879212.086417.944125.129434.036944.083602.11933.68096.259910.342716.384024.26990.54731.0878 2.

9、1622 4.29768.5420由結(jié)果可知,option第一行第一列就是看漲期權(quán)價(jià)格，該期權(quán)價(jià)格為4.9996元。(3)假設(shè)股票價(jià)格服從幾何布朗運(yùn)動(dòng)，試用蒙特卡洛模擬方法計(jì)算該期權(quán)價(jià)格。MATLABr令:s0=50;K=52;r=0.1;T=0.5;sigma=0.4;Nu=1000;randn('seed',0);%定義隨機(jī)數(shù)發(fā)生器種子是0,%這樣保證每次模擬的結(jié)果相同nuT=(r-0.5*sigmaA2)*Tsit=sigma*sqrt(T)discpayoff=exp(-r*T)*max(0,s0*exp(nuT+sit*randn(Nu,1)-K);%期權(quán)到期時(shí)的現(xiàn)金

10、流eucall,varprice,ci=normfit(discpayoff)運(yùn)行結(jié)果：nuT=0.0100sit=0.2828eucall=6.1478varprice=10.2924ci=5.50916.7865三、搜集數(shù)據(jù)并計(jì)算畫圖（50分）按照自己的研究生學(xué)號(hào)后兩位數(shù)，在銳思金融數(shù)據(jù)庫(kù)中搜集4種股票信息，包括最高價(jià)、最低價(jià)、收盤價(jià)和開(kāi)盤價(jià)，數(shù)據(jù)個(gè)數(shù)2個(gè)月左右，建立數(shù)據(jù)表格。要求使用MATLA編程解決以下問(wèn)題：(1)將4種股票的收盤價(jià)格轉(zhuǎn)化為收益率，并畫出收益率直方圖海虹控股MATLABr令：TickSeries=31.6332.1731.5830.7130.7730.9331.7931

11、.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(RetSeries)xlabel('天數(shù)');ylabel('收益率');title('海虹控股對(duì)數(shù)收益率直方圖);運(yùn)行結(jié)果:RetSeries=0.0171-0.0183-0.02750.00200.0278-0.0

12、0660.01330.0597-0.02330.05620.00910.0057-0.02390.02340.0138-0.01560.0644-0.02730.00350.0022-0.0071-0.0213-0.01760.01650.02520.0461-0.00230.00210.01330.0623-0.0068-0.00710.0388盛達(dá)礦業(yè)MATLABr令:TickSeries=13.0712.8813.1912.9812.7812.4912.7312.5112.9713.0612.6813.1713.9314.3914.0814.3414.1914.2413.7413.571

13、3.813.7613.7613.5213.313.2813.4413.3713.2813.7413.9314.1613.9914.7314.7'RetSeries=tick2ret(TickSeries)bar(RetSeries)xlabel('天數(shù));ylabel('收益率)；title('盛達(dá)礦業(yè)對(duì)數(shù)收益率直方圖)；0.06運(yùn)行結(jié)果:RetSeries =-0.01450.040.03盛達(dá)礦業(yè)對(duì)數(shù)收益率直方圖0.05-0.01-0.02-0.03-0.040510152025天數(shù)30352 10 o oo o率益收0.0241-0.0159-0.0154-

14、0.02270.0192-0.01730.03680.0069-0.02910.03860.05770.0330-0.02150.0185-0.01050.0035-0.0351-0.01240.0169-0.00290-0.0163-0.00150.0120-0.0052-0.00670.03460.01380.0165-0.01200.0529-0.0020恒逸石化MATLABr令：TickSeries=9.439.148.998.678.68.428.498.48.538.978.618.919.119.129.069.149.048.798.78.788.839.379.479.39.

15、559.899.699.649.589.529.8810.2210.310.4510.84'RetSeries=tick2ret（TickSeries）bar（RetSeries）xlabel（'天數(shù)'）;ylabel（'收益率'）;title（'恒逸石化對(duì)數(shù)收益率直方圖'）;運(yùn)行結(jié)果：0.080.06恒逸石化對(duì)數(shù)收益率直方圖53305220數(shù) 天RetSeries=-0.0308-0.0164-0.0356-0.0081-0.02090.0083-0.01060.01550.0516-0.04010.03480.02240.0011-0

16、.00660.0088-0.0109-0.0277-0.01020.00920.06120.0107-0.01800.02690.0356-0.0202-0.0052-0.0062-0.00630.03780.03440.00780.01460.0373金宇車城MATLABr令：TickSeries=10.911.1711.3211.3211.2211.0811.2711.1911.3111.5211.2511.7812.0712.1112.1512.2912.4512.8712.7712.6312.5612.7112.7112.512.1512.2312.1212.4812.612.8712

17、.913.3313.513.513.42'RetSeries=tick2ret(TickSeries)bar(RetSeries)xlabel（'天數(shù)）;ylabel（'收益率）；title（'金宇車城對(duì)數(shù)收益率直方圖）;運(yùn)行結(jié)果:RetSeries=0.02480.01340-0.0088-0.01250.0171-0.00710.01070.0186-0.02340.04710.02460.00330.00330.01150.01300.0337-0.0110-0.00550.01190-0.0165-0.02800.0066-0.00900.02970.0

18、0960.02140.00230.03330.01280-0.0059（2）計(jì)算4種股票收盤價(jià)的協(xié)方差矩陣；MATLABr令：A=31.6313.079.4310.932.1712.889.1411.1730.7712.788.611.2230.9312.498.4211.0831.7912.738.4911.2731.5812.518.411.193212.978.5311.3133.9113.068.9711.5233.1212.688.6111.2534.9813.178.9111.7835.313.939.1112.0735.514.399.1212.1134.6514.089.061

19、2.1535.4614.349.1412.2935.9514.199.0412.4535.3914.248.7912.8737.6713.748.712.7736.6413.578.7812.6336.7713.88.8312.5636.8513.769.3712.7136.5913.769.4712.7135.8113.529.312.536.6613.449.6912.1238.3513.379.6412.4838.2613.289.5812.638.3413.749.5212.8738.8513.939.8812.941.2714.1610.2213.3340.9913.9910.313

20、.540.714.7310.4513.542.2814.710.8413.42cov(A)運(yùn)行結(jié)果：ans=10.06081.47511.56872.30591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.58373)若給出這4種股票預(yù)期收益率分別為0.3、0.25、0.2和0.15，且購(gòu)買權(quán)重分別0.35、0.25、0.25和0.15，求總資產(chǎn)的標(biāo)準(zhǔn)差和期望收益；MATLABr令:ExpReturn=0.3,0.25,0.2,0.15;ExpCovariance=10.06081.47511.56872.

21、30591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.5837;PortWts=0.350.250.250.15;PortRisk,PortReturn=portstats(ExpReturn,ExpCovariance,PortWts)運(yùn)行結(jié)果：PortRisk=1.4659PortReturn=0.2400 4） 4)求該資產(chǎn)組合有效前沿(有效前沿的個(gè)數(shù)選為5)；MATLABr令：ExpReturn=0.30.250.20.15;ExpCovariance=10.06081.47511.56872.3

22、0591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.5837;NumPorts=5;PortRink,PortReturn,PortWts=frontcon(ExpReturn,ExpCovariance,NumPorts)運(yùn)行結(jié)果：PortRink=0.54620.58201.17292.15853.1719PortReturn=0.22470.24360.26240.28120.3000PortWts=-0.00000.49490.50510.000000.87120.1288-0.00000.247

23、50.75250-0.00000.62370.37630-0.00001.000000.0000-0.0000 5） 無(wú)風(fēng)險(xiǎn)利率為0.35，借貸利率為0.5，投資者風(fēng)險(xiǎn)厭惡系數(shù)為3，求考慮無(wú)風(fēng)險(xiǎn)資產(chǎn)及借貸情況下的最優(yōu)資產(chǎn)配置。MATLABr令：ExpReturn=0.30.250.20.15;ExpCovariance=10.06081.47511.56872.30591.47510.37110.22700.38571.56870.22700.36820.33262.30590.38570.33260.5837;RisklessRate=0.035;BorrowRate=0.5;RiskAve

24、rsion=3;PortRisk,PortReturn,PortWts=portopt(ExpReturn,ExpCovariance)RiskyRink,RiskyReturn,RiskyWts,RiskyFraction,OverallRick,OverallReturn=portalloc(PortRisk,.PortReturn,PortWts,RisklessRate,BorrowRate,RiskAversion)運(yùn)行結(jié)果：PortRisk=0.54620.55340.57470.60840.96631.38641.82462.27042.72003.1719PortReturn=

25、0.22470.23310.24150.24980.25820.26660.27490.28330.29160.3000PortWts=-0.00000.49490.50510.000000.66210.3379-0.00000.00000.82940.1706-0.000000.99660.0034-0.00000.16380.83620-0.00000.33110.668900.00000.49830.50170-0.00000.83280.167200.00001.000000.0000-0.0000RiskyRink=0.5427RiskyReturn=0.2302RiskyWts=-

26、0.00000.60400.3960-0.0000RiskyFraction=0.2209OverallRick=0.1199OverallReturn=0.0781（6）繪制這4種股票的最高價(jià)、最低價(jià)、收盤價(jià)和開(kāi)盤價(jià)的燭型圖。海虹控股MATLABr令：a=31.930.5431.6331.2932.3530.7132.1731.332.631.5631.5832.083230.730.7131.8231.5930.4530.7730.5532.230.9431.7930.9432.1831.5231.5831.7832.1131.433231.633.9131.9133.9132.135.5

27、732.533.1232.8335.433.2634.9833.2635.5734.2835.334.9636.4935.135.535.335.834.4534.6535.335.634.635.4634.7536.3535.3335.9535.6636.2634.935.3935.737.93537.6735.0137.6636.4236.6437.338.2936.336.7736.6437.583636.8537.337.3236.3536.5937.2536.8935.835.8136.5936.4134.7535.1835.936.0335.1835.7635.438.6538.0

28、838.2638.4439.1738.0338.3438.2539.238.0738.8538.541.4939.0841.2739.0842.3940.6840.9941.240.9940.0140.740.7542.640.5942.2840.69;candle(a(:,1),a(:,2),a(:,3),a(:,4)candle(a(:,1),a(:,2),a(:,3),a(:,4),'r')title('海虹控股');運(yùn)行結(jié)果：盛達(dá)礦業(yè)MATLABr令：a=13.1112.0813.0712.212.9912.6512.8812.913.4912.8813

29、.1912.9913.2712.8812.9813.113.112.7712.7812.9512.7712.4212.4912.712.812.4212.7312.4213.3812.9513.0613.1513.2712.4612.6812.9813.2212.6513.1712.6814.1213.2213.9313.2914.6513.714.3913.9514.841414.0814.3514.3513.8814.341414.3413.9214.1914.1514.31414.2414.114.213.713.7414.1413.7613.513.5713.513.913.413.8

30、13.51413.7113.7613.7914.0113.7213.7613.813.9913.513.5213.9113.4713.213.313.313.4413.0313.2813.2713.4513.1813.4413.2513.5413.313.3713.4513.4113.0913.2813.3314.2313.8114.1613.9414.213.813.9914.0814.813.9314.7313.9314.9514.5614.714.78;candle(a(:,1),a(:,2),a(:,3),a(:,4)candle(a(:,1),a(:,2),a(:,3),a(:,4)

31、,'r')title('盛達(dá)礦業(yè)');運(yùn)行結(jié)果：恒逸石化MATLABr令：a=9.68.759.439.049.649.19.149.359.168.868.999.0898.658.678.998.858.588.68.588.858.388.428.638.548.38.498.438.578.348.48.58.578.48.538.429.318.538.978.539.218.859.118.919.258.979.129.119.39.019.069.139.158.89.149.059.278.959.049.19.098.748.799.048.868.618.78.78.858.638.788.728.938.25