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
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2.3K 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 (2024). 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 .

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes
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
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]
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]
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.

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).
1.6.0.0

Added Comments
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
1.0.0.0