calcBSImpVol(cp,P,S,K,T,r,q)

version 1.13.0.0 (7.25 KB) by Mark Whirdy

Calculates Black-Scholes Implied Volatility for Full Surface at High Speed

4.3

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2.2K Downloads

Updated 11 Feb 2018

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Calculates Black-Scholes Implied Volatility Surface for an Option Price Matrix.
Uses Li's Rational Function Approximator for the Initial Estimate, followed by
3rd-Order Householder's Root Finder (i.e. using vega,vomma & ultima) for greater
convergence rate and wider domain-of-convergence relative to Newton-Raphson. Both
Li's Approximator and the Root Finder are calculated matrix-wise (i.e.
fully vectorized) for increased efficiency.

Cite As

Mark Whirdy (2022). calcBSImpVol(cp,P,S,K,T,r,q) (https://www.mathworks.com/matlabcentral/fileexchange/41473-calcbsimpvol-cp-p-s-k-t-r-q), MATLAB Central File Exchange. Retrieved August 14, 2022.

MATLAB Release Compatibility

Created with R2012b

Compatible with any release

Platform Compatibility

Windows macOS Linux

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Acknowledgements

Inspired: Merton Jump Diffusion Option Price (Matrixwise)

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calcBSImpVol(cp,P,S,K,T,r,q)

Download	11 Feb 2018	1.13.0.0	removed the linear regression code which estimates the initial vol for points lying outside Li's domain of approximation. this regression code required in-domain values to be passed-in by the user to work. Out-of-domain vols are now 0.8
Download	28 Apr 2015	1.12.0.0	Amended to facilitate input variables "cp", "q" & "r" as matrices cp Call[+1],Put[-1] [m x n],[1 x 1] r Continuous Risk-Free Rate [m x n],[1 x 1] q Continuous Div Yield [m x n],[1 x 1]
Download	28 Apr 2015	1.11.0.0	Amended Code allowing matrix inputs for "cp", "r" and "q" cp Call[+1],Put[-1] [m x n],[1 x 1] r Continuous Risk-Free Rate [m x n],[1 x 1] q Continuous Div Yield [m x n],[1 x 1]
Download	27 Jun 2013	1.9.0.0	Changed comment "S Underlying Price [m x n]" to "S Underlying Price [1 x 1]" .. as was misleading This version of the file handles S as a scalar only.
Download	1 May 2013	1.7.0.0	Re-factoring of anonymous functions in Householder root solver to re-calculate derivatives & for only those points which have not converged. This increases speed by 20-50% (depending on particular surface).
Download	25 Apr 2013	1.6.0.0	Added Comments
Download	24 Apr 2013	1.1.0.0	Fixed bug in Put-Call Parity line P = P + S.exp(-q.T) - K.exp(-r.T); % Convert Put to Call by Parity Relation
Download	23 Apr 2013	1.0.0.0