#SABR: Stochastic alpha beta rho

+   This is a port of Matlab code over to C++. Original matlab code is in matlab subdirectory.
+   This is a study in SABR.
+   This C++ code does not require any additional libraries.

#Issues: + (1) Results in Octave vs C++ VS2017 + Differences in decimals. Have not identified yet why?

#(1) This example first solves for SABR's alpha with the following constants:

* F = 100;            % Futures price
* T = 0.5;            % Maturity in years   
* b = 0.9999;         % beta SABR parameter
* v = 0.5;            % vol-of-vol SABR parameter
* ATMvol = 0.30;      % Market ATM volatility

• Computation loops across these strikes and correlation levels

  • K = 70 80 90 100 110 120 130
  • rho = -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75;

• Constants for Black 76 only

  • r = .02

#(2) Then SABR volatility is then computed with alpha's and constants

#(3) Black 76 Call/Put and PutCall Parity is computed with SABR vol.

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• Below are results from building and running this C++ console application.

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• SABR Black-76 Equivalent Volatilies (%). Agrees with results from Haug Book pg 270 (Agrees when rounded to two decimals):

• Alpha Parameter Values used by SABR Black-76 Equivalent Volatilities, above:

• Black-76 Put Prices r:0.020000:

• Black-76 Call Prices r:0.020000:

• diff in Black-76 Put Call Parity Eqn: (C-P) - (F-K)exp(-rT) r:0.020000 F: 100.000000 T:0.500000: