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## Merton Jump Diffusion Option Price (Matrixwise)

version 1.1.0.0 (1.97 KB) by Mark Whirdy

### Mark Whirdy (view profile)

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 (2019). Merton Jump Diffusion Option Price (Matrixwise) (https://www.mathworks.com/matlabcentral/fileexchange/41939-merton-jump-diffusion-option-price-matrixwise), MATLAB Central File Exchange. Retrieved .

Siyun Chen

### Siyun Chen (view profile)

run very good, the value matches to original BS model! Thanks.

Liqun

### Liqun (view profile)

Do you have matrixwise Black Scholes Option price?

Justin Rodrigues

### Justin Rodrigues (view profile)

Excellent program, well written and knowledgable author. Was kind enough to answer my questions and showed me how to execute the program to fit my needs. Very professional and kind.