金融MATLAB實驗報告三

1、安徽財經大學金融證券實驗室實 驗 報 告實驗課程名稱 金融MATLAB 開 課 系 部 金融學院 班 級 學 號 姓 名 指 導 教 師 2016年6月1日實驗名稱MATLAB基礎知識學院 金融學院學號姓名實驗準備實 驗 目 的Ø 學會使用MATLAB金融工具箱進行金融數(shù)量分析，如：期權定價分析、投資組合績效分析、收益和風險的計算、有效前沿的計算、固定收益證券的久期和凸度計算、利率的期限結構、技術指標計算等。 實 驗 設 計 方 案請使用MATLAB金融工具箱進行對以下6個主題進行數(shù)量分析，數(shù)據來源自行在網上搜尋，要求是2015年之后的數(shù)據。1.期權定價分析 （第10章）2.收益、風

2、險和有效前沿的計算 （第12章）3.投資組合績效分析 （第13章）4.固定收益證券的久期和凸度計算 （第17章）5.利率的期限結構 （第18章）6.技術指標分析 （第22章）實驗分析過程1.期權定價分析 （第10章） 1.Black-scholes方程求解例：假設歐式股票期權，六個月后到期，執(zhí)行價格92元，現(xiàn)價為102元，無股利支付，股價年化波動率為55%，無風險利率為10%，計算期權價格。代碼：Price=102; Strike=92; Rate=0.1 Time=6/12; Volatility=0.55 Call, Put = blsprice(Price,Strike,Rate,Tim

3、e,Volatility)結果：Call = 22.9551Put = 8.46822.期權價格與波動率關系分析代碼：Price=102; Strike=92; Rate=0.1 Time=6/12; Volatility=0.1:0.01:0.55;N=length(Volatility) Call=zeros(1,N);Put=zeros(1,N);for i=1:NCall(i), Put(i)=blsprice(Price, Strike, Rate, Time, Volatility(i);endplot(Call,'b-'); hold onplot(Put,

4、9;b');xlabel('Volatility') ylabel('price') legend('Call','Put')結果：3.計算期權的Dalta代碼：Price=102; Strike=92; Rate=0.1 Time=6/12; Volatility=0.55;CallDelta, PutDelta = blsdelta(Price, Strike, Rate, Time, Volatility, Yield)結果：CallDelta = 0.7027PutDelta = -0.28524.利用不同的Pri

5、ce與Time計算Datla三維關系代碼：Price=60:1:102;Strike=92;Rate=0.1； Time=(1:1:12)/12;Volatility=0.55;Price,Time=meshgrid(Price,Time);CallDelta, PutDelta = blsdelta(Price, Strike, Rate, Time, Volatility);mesh(Price,Time,PutDelta);xlabel('Stock Price');ylabel('Time(year)');zlabel('Delta')結

6、果：5 B-S公式隱含波動率計算例：假設歐式股票期權，一年后，執(zhí)行價格99元，現(xiàn)價為105元，無股利支付，股價年化波動率為50%，無風險利率為10%，則期權價格為？代碼：Price=105;Strike=99;Rate=0.1;Time=1; CallValue=15; CallVolatility = blsimpv(Price, Strike, Rate, Time, CallValue, , , , 'Call'結果：CallVolatility =NaN代碼：PutValue=7;PutVolatility = blsimpv(Price, Strike, Rate,

7、Time, PutValue, , , , 'Put')結果：PutVolatility = 0.34556期權二叉樹模型的計算例：假設歐式股票期權，三個月后到期，執(zhí)行價格95元，現(xiàn)價為100元，無股利支付，股價年化波動率為60%，無風險利率為10%代碼：Price=100;Strike=95;Rate=0.1;Time=3/12; flag=1;Increment=1/12;Volatility=0.6; AssetPrice, OptionValue = binprice(Price, Strike, Rate, Time, Increment, Volatility, f

8、lag)結果：AssetPrice = 100.0000 118.9110 141.3982 168.1381 0 84.0965 100.0000 118.9110 0 0 70.7222 84.0965 0 0 0 59.4749OptionValue = 16.3282 28.3714 47.1866 73.1381 0 5.4371 11.4020 23.9110 0 0 0 0 0 0 0 02.收益、風險和有效前沿的計算 （第12章）數(shù)據來源于網易財經，具體數(shù)據見附的Excel表將所收集的股票價格指數(shù)鄭麗麗得到收益率均值，收益率標準差和協(xié)方差矩陣程序： A=xlsread('

9、;股票.xlsx') %導入數(shù)據，注意數(shù)據放在MATLAB的工作文件夾內R1=price2ret(A(:,1); %R1為華北制藥的日收益率R2= price2ret (A(:,2); %R2為中國石化的日收益率R3= price2ret (A(:,3) %R3為上海機場的日收益率ExpReturn,ExpCovariance=ewstats(R1 R2 R2)std(R1),std(R2),std(R3)結果如下表：收益率均值收益率標準差協(xié)方差矩陣華北制藥0.29740.03250.0011 0.0000 0.0000中國石化-0.13550.02330.0000 0.0005 0.

10、0005上海機場-0.13550.02700.0000 0.0005 0.00051.收益率和風險計算函數(shù)假設等權重配置華北制藥、中國石化、上海機場，計算資產組合的風險和收益。代碼： ExpReturn=0.2974 -0.1355 -0.1355;ExpCovariance=0.0011,0.0000,0.0000;0.0000,0.0005,0.0005;0.0000,0.0005,0.0005;PortWts=1/3*ones(1,3);PortRisk,PortReturn=portstats(ExpReturn,ExpCovariance,PortWts)結果：PortRisk =

11、0.0186PortReturn =0.00882有效前沿計算函數(shù)（1）怎樣配置華北制藥、中國石化、上海機場，則資產組合為最優(yōu)組合代碼： ExpReturn=0.2974 -0.1355 -0.1355;ExpCovariance=0.0011,0.0000,0.0000;0.0000,0.0005,0.0005;0.0000,0.0005,0.0005;NumPorts=10;PortRisk,PortReturn,PortWts=frontcon(ExpReturn,ExpCovariance,NumPorts)結果：PortRisk = 0.0185 0.0188 0.0195 0.02

12、07 0.0222 0.0240 0.0261 0.0283 0.0307 0.0332PortReturn = -0.0002 0.0328 0.0659 0.0990 0.1321 0.1651 0.1982 0.2313 0.2643 0.2974PortWts = 0.3125 0.6875 0 0.3889 0.6111 0 0.4653 0.5347 0 0.5417 0.4583 0 0.6181 0.3819 0 0.6944 0.3056 0 0.7708 0.2292 0 0.8472 0.1528 0 0.9236 0.0764 0 1.0000 0 0代碼： front

13、con(ExpReturn,ExpCovariance, NumPorts)結果：（2）如果各個資產投資上限為50%，求解有效前沿？代碼：ExpReturn=0.2974 -0.1355 -0.1355;ExpCovariance=0.0011,0.0000,0.0000;0.0000,0.0005,0.0005;0.0000,0.0005,0.0005;NumPorts=10;AssetBounds=0,0,0;0.5,0.5,0.5;PortRisk, PortReturn, PortWts=frontcon(ExpReturn, ExpCovariance,NumPorts,AssetB

14、ounds)結果：PortRisk = 0.0185 0.0186 0.0186 0.0187 0.0188 0.0190 0.0192 0.0194 0.0197 0.0200PortReturn = -0.0002 0.0088 0.0178 0.0268 0.0359 0.0449 0.0539 0.0629 0.0719 0.0809PortWts = 0.3125 0.5000 0.1875 0.3333 0.5000 0.1667 0.3542 0.5000 0.1458 0.3750 0.5000 0.1250 0.3958 0.5000 0.1042 0.4167 0.5000

15、 0.0833 0.4375 0.5000 0.0625 0.4583 0.5000 0.0417 0.4792 0.5000 0.0208 0.5000 0.2500 0.25003約束條件下有效前沿例配置華北制藥、中國石化、上海機場三個資產，中央商場最大配置60%，國投安信最大配置70%，東興證券最大配置50%，中央商場為資產集合A，國投安信、東興證券組成資產計劃B，集合A的最大配置為700%，集合B的最大配置為50%，集合A的配置不能超過集合B的3倍，則如何配置？代碼： NumAssets=3;ExpReturn=0.2974 -0.1355 -0.1355;ExpCovariance=

16、0.0011,0.0000,0.0000;0.0000,0.0005,0.0005;0.0000,0.0005,0.0005;NumPorts=5;PVal = 1;AssetMin = 0;AssetMax = 0.6,0.7,0.5;GroupA = 1 0 0;GroupB = 0 1 1;GroupMax = 0.7,0.5;AtoBmax = 3;ConSet = portcons('PortValue', PVal, NumAssets, 'AssetLims', AssetMin, AssetMax, NumAssets, 'GroupCo

17、mparison',GroupA, NaN,AtoBmax, GroupB,GroupMax );PortRisk,PortReturn,PortWts=portopt(ExpReturn,ExpCovariance,NumPorts,ConSet)結果：PortRisk = 0.0185 0.0188 0.0194 0.0204 0.0218PortReturn = -0.0002 0.0309 0.0620 0.0931 0.1242PortWts = 0.3125 0.6875 0 0.3844 0.6156 0 0.4562 0.5438 0 0.5281 0.4719 00.

18、6000 0.2000 0.2000代碼：portopt(ExpReturn,ExpCovariance,NumPorts,ConSet)4.固定收益證券的久期和凸度計算 （第17章）下列數(shù)據來源于網易財經：固定收益證券到期收益率（%）票面利率（%）結算日到期日計息方式16附息國債092.432.5528-Apr-1628-Apr-19每年付息一次16附息國債103.322.95-May-165-May-26每年付息一次16附息國債122.492.5119-May-1619-May-18每年付息一次1. 債券的價格及計算日的利息計算（1）計算16附息國債09的價格和日利息計算代碼：Yield=

19、0.0243;Couponrate=0.0255;Settle='28-Apr-16'Maturity='28-Apr-19'Period=1;basis=0;price,accruedlnt=bndprice(Yield, Couponrate,Settle,Maturity,Period,basis)結果：price = 100.3009accruedlnt = 0（2）計算16附息國債10的價格和日利息計算代碼：Yield=0.0332;Couponrate=0.0290;Settle='5-May-16'Maturity='5-M

20、ay-26'Period=1;basis=0;price,accruedlnt=bndprice(Yield, Couponrate,Settle,Maturity,Period,basis)結果：price = 96.2491accruedlnt = 0（3）計算16附息國債12的價格和日利息計算代碼：Yield=0.0249;Couponrate=0.0251;Settle='19-May-16'Maturity='19-May-18'Period=1;basis=0;price,accruedlnt=bndprice(Yield, Couponra

21、te,Settle,Maturity,Period,basis)結果：price = 100.0087accruedlnt = 02. 根據債券的價格計算久期（1）計算16附息債券09久期代碼：Price= 100.3009;Couponrate=0.0255;Settle='28-Apr-16'Maturity='28-Apr-19'Period=1;basis=0;ModDuration,YearDuration,PerDuration=bnddurp(Price,Couponrate,Settle,Maturity,Period,basis)結果：ModD

22、uration = 2.8910YearDuration = 2.9261PerDuration =5.8523（2）計算16附息債券10久期代碼：Price=96.2491;Couponrate=0.0290;Settle='5-May-16'Maturity='5-May-26'Period=1;basis=0;ModDuration,YearDuration,PerDuration=bnddurp(Price,Couponrate,Settle,Maturity,Period,basis)結果：ModDuration = 8.6516YearDuratio

23、n = 8.7952PerDuration = 17.5904（3）計算16附息債券12久期代碼：Price=100.0087;Couponrate=0.0251;Settle='19-May-16'Maturity='19-May-18'Period=1;basis=0;ModDuration,YearDuration,PerDuration=bnddurp(Price,Couponrate,Settle,Maturity,Period,basis)結果：ModDuration = 1.9512YearDuration = 1.9755PerDuration

24、=3.951033根據債券收益率計算久期（1）根據16附息國債09的收益率計算久期代碼：Yield=0.0243;Couponrate=0.0255;Settle='28-Apr-16'Maturity='28-Apr-19'Period=1;basis=0;ModDuration,YearDuration,PerDuration=bnddurp(Yield,Couponrate,Settle,Maturity,Period,basis)結果：ModDuration = 0.0986YearDuration = 1.0163PerDuration =2.0326

25、（2）根據16附息國債10的收益率計算久期代碼：Yield=0.0332;Couponrate=0.0290;Settle='5-May-16'Maturity='5-May-26'Period=1;basis=0;ModDuration,YearDuration,PerDuration=bnddurp(Yield,Couponrate,Settle,Maturity,Period,basis)結果：ModDuration = 0.1076YearDuration = 1.0114PerDuration = 2.0229（3）根據16附息國債12的收益率計算久期

26、代碼：Yield=0.0249;Couponrate=0.0251;Settle='19-May-16'Maturity='19-May-18'Period=1;basis=0;ModDuration,YearDuration,PerDuration=bnddurp(Yield,Couponrate,Settle,Maturity,Period,basis)結果：ModDuration = 0.1076YearDuration = 1.2363PerDuration = 2.47264根據價格計算凸度（1）根據價格計算16附息國債09的凸度代碼： Price=1

27、00.3009;Couponrate=0.0255;Settle='28-Apr-16'Maturity='28-Apr-19'Period=1;basis=0;YearConvexity,PerConvexity=bndconvp(Price,Couponrate,Settle,Maturity,Period,basis)結果YearConvexity = 9.9013PerConvexity = 39.6054（2）根據價格計算16附息國債10的凸度代碼：Price=96.2491;Couponrate=0.0290;Settle='5-May-16

28、'Maturity='5-May-26'Period=1;basis=0;YearConvexity,PerConvexity=bndconvp(Price,Couponrate,Settle,Maturity,Period,basis)結果：YearConvexity = 85.2674PerConvexity = 341.0698（3）根據價格計算16附息國債12的凸度代碼：Price=100.0087;Couponrate=0.0251;Settle='19-May-16'Maturity='19-May-18'Period=1;ba