Settle = datetime(2018,9,15);类型=“零”；ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';ZeroDates = Settle + ZeroTimes;比率曲线(“零”、结算、ZeroDates ZeroRates)

互换= fininstrument(“交换”，“成熟”datetime (2027 3 15),“LegRate”[0 0],“LegType”，.．.［“浮动”，“固定”),“名义上”, 100,StartDate可以的datetime (2022 3 15),“名字”，“swap_instrument”）

互换=仪器(“掉期期权”，“罢工”, 0.02,“ExerciseDate”datetime (2022 3 15),“交换”交换,“名字”，“swaption_option”）

SabrModel = finmodel(“SABR”，“α”, 0.032,“β”, 0.04,的ρ、。08“怒”, 0.49,“转变”, 0.002)

outPricer = finpricer(“分析”，“模型”SabrModel,“DiscountCurve”myRC)

价格=价格(outPricer,Swaption)

Settle = datetime(2018,9,15);类型=“零”；ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';ZeroDates = Settle + ZeroTimes;比率曲线(“零”、结算、ZeroDates ZeroRates)

互换= fininstrument(“交换”，“成熟”datetime (2027 3 15),“LegRate”[0 0],“LegType”，.．.［“浮动”，“固定”),“名义上”, 100,StartDate可以的datetime (2022 3 15),“名字”，“swap_instrument”）

互换=仪器(“掉期期权”，“罢工”, (0.02;0.03;0.04),“ExerciseDate”datetime([2022年,3,15;2022年,4,15;2022、5、15]),“交换”交换,“名字”，“swaption_option”）

SabrModel = finmodel(“SABR”，“α”, 0.032,“β”, 0.04,的ρ、。08“怒”, 0.49,“转变”, 0.002)

outPricer = finpricer(“分析”，“模型”SabrModel,“DiscountCurve”myRC)

价格=价格(outPricer,Swaption)

Settle = datetime(2018,9,15);类型=“零”；ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';ZeroDates = Settle + ZeroTimes;比率曲线(“零”、结算、ZeroDates ZeroRates)

互换= fininstrument(“交换”，“成熟”datetime (2027 3 15),“LegRate”[0 0],“LegType”，.．.［“浮动”，“固定”),“名义上”, 100,StartDate可以的datetime (2022 3 15),“名字”，“swap_instrument”）

互换=仪器(“掉期期权”，“罢工”, 0.02,“ExerciseDate”datetime (2022 3 15),“交换”交换,“名字”，“swaption_option”）

BlackModel = finmodel(“黑色”，“波动”, 0.032,“转变”, 0.002)

outPricer = finpricer(“分析”，“模型”BlackModel,“DiscountCurve”myRC)

价格=价格(outPricer,Swaption)

Settle = datetime(2018,9,15);类型=“零”；ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';ZeroDates = Settle + ZeroTimes;比率曲线(“零”、结算、ZeroDates ZeroRates)

互换= fininstrument(“交换”，“成熟”datetime (2027 3 15),“LegRate”[0 0],“LegType”，.．.［“浮动”，“固定”),“名义上”, 100,StartDate可以的datetime (2022 3 15),“名字”，“swap_instrument”）

互换=仪器(“掉期期权”，“罢工”, 0.02,“ExerciseDate”datetime (2022 3 15),“交换”交换,“名字”，“swaption_option”）

HullWhiteModel = finmodel(“HullWhite”，“α”, 0.032,“σ”, 0.04)

outPricer = finpricer(“IRTree”，“模型”HullWhiteModel,“DiscountCurve”myRC,“TreeDates”ZeroDates)

[Price, outPR] = Price (outprice,Swaption，[“所有”])

outPR。结果

Settle = datetime(2019,1,1);类型=“零”；ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';ZeroDates = Settle + ZeroTimes;比率曲线(“零”、结算、ZeroDates ZeroRates)

互换= fininstrument(“交换”，“成熟”datetime (2022, 1, 1),“LegRate”[0.05, 0.04],“名字”，“swap_instrument”）

互换=仪器(“掉期期权”，“罢工”, 0.02,“ExerciseDate”datetime (2021 7 1),“交换”交换,“名字”，“swaption_option”）

线性高斯2fmodel = finmodel(“LinearGaussian2F”，“α”, 0.07,“Sigma1”, 0.01,“Alpha2”, 0.5,“Sigma2”, 0.006,“相关”, -0.7)

simDates = datetime(2019,7,1)+calmonths(0:6:30);outPricer = finpricer(“IRMonteCarlo”，“模型”LinearGaussian2FModel,“DiscountCurve”myRC,“SimulationDates”simDates)

[Price,outPR] = Price (outprice,Swaption，[“所有”])

outPR。结果

%零曲线ValuationDate =日期时间(“5 - 3月- 2016，“场所”，“en_US”）;ZeroDates = datemnth(ValuationDate，[1 2 3 6 9 12*[1 2 3 4 5 6 7 8 9 10 12]])';ZeroRates = [-0.33 -0.28 -0.24 -0.12 -0.08 -0.03 0.015 0.028.．.0.033 0.042 0.056 0.095 0.194 0.299 0.415 0.525]'/100;复利= 1;零曲线=利率曲线(“零”, ZeroDates ValuationDate ZeroRates,“复合”复合)

定义交换SwaptionSettle = datetime(“5 - 3月- 2016，“场所”，“en_US”）;SwaptionExerciseDate =日期时间(“5 - 3月- 2017，“场所”，“en_US”）;SwaptionStrikes = (-0.6:0.01:1.6)'/100;%包括负面打击SwapMaturity = datetime(“5 - 3月- 2022，“场所”，“en_US”）;标的掉期期限%OptSpec =“电话”；

LegRate = [0 0];互换= fininstrument(“交换”，“成熟”SwapMaturity,“LegRate”LegRate,“LegType”，[“固定”“浮动”),.．.“ProjectionCurve”ZeroCurve,“StartDate可以”SwaptionExerciseDate)

ForwardValue = parswaprate(交换，零曲线)

StrikeGrid = [-0.5;-0.25;-0.125;0;0.125;0.25;0.5;1.0;1.5) / 100;MarketStrikes =远期价值+ StrikeGrid; Shift = 0.008;0.8%的变化marketshiftedblackvolatility = [21.1;15.3;14.0;14.6;16.0;17.7;19.8;23.9;26.2) / 100;ATMShiftedBlackVolatility = marketshiftedblackvolatility (StrikeGrid==0);

Beta = 0.5;校准Alpha, Rho和NuobjFun = @(X) marketshiftedblackvolatility -波动性(finpricer(“分析”，“模型”，.．.finmodel (“SABR”，“α”X (1),“β”,β,的ρ, X (2),“怒”, X (3),“转变”转变).．.“DiscountCurve”，零曲线)，SwaptionExerciseDate，远期价值，市场罢工);X = lsqnonlin(objFun， [0.5 0 0.5]， [0 -1 0]， [Inf 1 Inf]);

Alpha = X(1);罗= X(2);Nu = X(3);

SABRModel = finmodel(“SABR”，“α”α,“β”,β,的ρρ,“怒”ν,“转变”转变)

sabrprice = finpricer(“分析”，“模型”SABRModel,“DiscountCurve”ZeroCurve)

sabrshiftedblackvolatility =波动性(SABRPricer, SwaptionExerciseDate, ForwardValue, SwaptionStrikes)

图;情节(MarketStrikes MarketShiftedBlackVolatilities,“o”，.．.SwaptionStrikes SABRShiftedBlackVolatilities);H = gca;线([0],[min (h.YLim), max (h.YLim)],“线型”，“——”）;Ylim ([0.13 0.31]) xlabel(“罢工”）;传奇(“市场报价”，“转移SABR”，“位置”，“东南”）;标题([“平移黑色波动率(”num2str(* 100)转变,百分比变化)]);

创建交换工具NumInst =长度(SwaptionStrikes);Swaptions(NumInst, 1) = fininstrument(“掉期期权”，.．.“罢工”SwaptionStrikes (1)“ExerciseDate”SwaptionExerciseDate (1)“交换”、交换);为k = 1:NumInst Swaptions(k) = fininstrument(“掉期期权”，“罢工”SwaptionStrikes (k),.．.“ExerciseDate”SwaptionExerciseDate,“交换”交换,“OptionType”, OptSpec);结束掉期期权

%使用SABR定价器进行价格交换SwaptionPrices = price(sabrprice,Swaptions);图;情节(SwaptionStrikes SwaptionPrices,“r”）;H = gca;线([0],[min (h.YLim), max (h.YLim)],“线型”，“——”）;包含(“罢工”）;标题(“掉期期权价格”）;