## Merton Jump Diffusion Option Price (Matrixwise)

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Calculates Merton's 1976 Jump Diffusion Model by Closed Form Matrixwise Calculation for Full Surface

Updated 28 May 2013

Calculates Option Prices by Merton's 1976 Jump Diffusion Model by Closed Form Matrixwise Calculation for Full Surface

Inputs:
cp [1,-1] Call,Put
S Current Price
K Strike Vector
T Time-to-Maturity Vector
sigma Volatility of Diffusion
r Risk-free-Rate
q Div Yield
lambda Poisson Rate
a Jump Mean
b Jump Std Deviation
n Event Count (Limited to 170 since factorial(170)=7.26e306)

Example:
S = 100; K = (20:5:180)'; T = (0.1:0.1:5)';
sigma = 0.2; r = 0.0075; q = 0; lambda = 0.01; a = -0.2; b = 0.6; n = 50;
P = ia_calcMJDOptionPrice(cp,S,K,T,sigma,r,q,lambda,a,b,n);

[mK,mT] = meshgrid(K,T); [sigma,C] = calcBSImpVol(cp,P,S,mK,mT,r,q);
subplot(2,1,1); mesh(mK,mT,P); subplot(2,1,2); mesh(mK,mT,sigma);

References:
Merton, 1976, Option Pricing When Underlying Stock Returns are Discontinuous
http://www.people.hbs.edu/rmerton/optionpricingwhenunderlingstock.pdf

### Cite As

Mark Whirdy (2022). Merton Jump Diffusion Option Price (Matrixwise) (https://www.mathworks.com/matlabcentral/fileexchange/41939-merton-jump-diffusion-option-price-matrixwise), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2012b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux