%% Calibrate Shifted SABR Model Parameters for Swaption Instrument
% This example shows how to calibrate the shifted SABR model parameters for a Swaption instrument when you use a SABR pricing method.
%% Load Market Data

% Zero curve
ValuationDate = datetime("5-Mar-2016", 'Locale', '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;
Compounding = 1;
ZeroCurve = ratecurve("zero",ValuationDate,ZeroDates,ZeroRates,'Compounding',Compounding)
% Define the swaptions
SwaptionSettle = datetime("5-Mar-2016", 'Locale', 'en_US');
SwaptionExerciseDate = datetime("5-Mar-2017", 'Locale', 'en_US');
SwaptionStrikes = (-0.6:0.01:1.6)'/100; % Include negative strikes
SwapMaturity = datetime("5-Mar-2022", 'Locale', 'en_US'); % Maturity of underlying swap
OptSpec = 'call';

%
%% Compute Forward Swap Rate by Creating Swap Instrument
% Use fininstrument to create a Swap instrument object.

LegRate = [0 0];
Swap = fininstrument("Swap", 'Maturity', SwapMaturity, 'LegRate', LegRate, "LegType",["fixed" "float"],...
    "ProjectionCurve", ZeroCurve, "StartDate", SwaptionExerciseDate)

ForwardValue = parswaprate(Swap,ZeroCurve)

%% Load the Market Implied Volatility Data
% The market swaption volatilities are quoted in terms of shifted Black volatilities with a 0.8 percent shift.

StrikeGrid = [-0.5; -0.25; -0.125; 0; 0.125; 0.25; 0.5; 1.0; 1.5]/100;
MarketStrikes = ForwardValue + StrikeGrid;
Shift = 0.008;  % 0.8 percent shift
MarketShiftedBlackVolatilities = [21.1; 15.3; 14.0; 14.6; 16.0; 17.7; 19.8; 23.9; 26.2]/100;
ATMShiftedBlackVolatility = MarketShiftedBlackVolatilities(StrikeGrid==0);

%% Calibrate Shifted SABR Model Parameters
% The Beta parameter is predetermined at 0.5. Use volatilities to compute the implied volatility.

Beta = 0.5;

% Calibrate Alpha, Rho, and Nu
objFun = @(X) MarketShiftedBlackVolatilities - volatilities(finpricer("Analytic", 'Model', ...
    finmodel("SABR", 'Alpha', X(1), 'Beta', Beta, 'Rho', X(2), 'Nu', X(3), 'Shift', Shift), ...
    'DiscountCurve', ZeroCurve), SwaptionExerciseDate, ForwardValue, MarketStrikes);

X = lsqnonlin(objFun, [0.5 0 0.5], [0 -1 0], [Inf 1 Inf]);

Alpha = X(1);
Rho = X(2);
Nu = X(3);

%% Create SABR Model Using the Calibrated Parameters
% Use finmodel to create a SABR model object.

SABRModel = finmodel("SABR",'Alpha',Alpha,'Beta',Beta,'Rho',Rho,'Nu',Nu,'Shift',Shift)

%% Create SABR Pricer Using Calibrated SABR Model and Compute Volatilities
% Use finpricer to create a SABR pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

SABRPricer = finpricer("Analytic", 'Model', SABRModel, 'DiscountCurve', ZeroCurve)
SABRShiftedBlackVolatilities = volatilities(SABRPricer, SwaptionExerciseDate, ForwardValue, SwaptionStrikes)
figure;
plot(MarketStrikes, MarketShiftedBlackVolatilities, 'o', ...
    SwaptionStrikes, SABRShiftedBlackVolatilities);
h = gca;
line([0,0],[min(h.YLim),max(h.YLim)],'LineStyle','--');
ylim([0.13 0.31])
xlabel('Strike');
legend('Market quotes','Shifted SABR', 'location', 'southeast');
title (['Shifted Black Volatility (',num2str(Shift*100),' percent shift)']);

%% Price Swaption Instruments Using Calibrated SABR Model and SABR Pricer

% Create swaption instruments
NumInst = length(SwaptionStrikes);
Swaptions(NumInst, 1) = fininstrument("Swaption", ...
    'Strike', SwaptionStrikes(1), 'ExerciseDate', SwaptionExerciseDate(1), 'Swap', Swap);
for k = 1:NumInst
    Swaptions(k) = fininstrument("Swaption", 'Strike', SwaptionStrikes(k), ...
        'ExerciseDate', SwaptionExerciseDate, 'Swap', Swap, 'OptionType', OptSpec);
end
Swaptions
% Price swaptions using the SABR pricer
SwaptionPrices = price(SABRPricer,Swaptions);

figure;
plot(SwaptionStrikes, SwaptionPrices, 'r');
h = gca;
line([0,0],[min(h.YLim),max(h.YLim)],'LineStyle','--');
xlabel('Strike');
title ('Swaption Price');

% Copyright 2019 The MathWorks, Inc.