# Can someone help me understand the heston model and its application.

#### noteverythingisok

Hey guys. I'm trying to simulate a Euro call option with volatility being stochastic and following the heston model. This is just for a course and I'm totally lost on how to do this when the volatility parameter is stochastic. I'm using STATA to simulate, and have code to simulate the call option when volatility is assumed constant. I have parameters k, theta, rho etc. given.

#### DMD

##### Active Member
To simulate the CIR model, refer to this paper: http://www.columbia.edu/~mh2078/MCS04/MCS_SDEs.pdf

To simulate two rho correlated r.v.s Y1 and Y2, let Z1 Z2 be independent r.v.s,

Y1=Z1
Y2=rho*Z1 + Sqrt(1-rho^2)*Z2.

Create a vector of your CIR process. Then just simulate your geometric Brownian motion using the exact solution of GBM, but in the place of the volatility put the corresponding entry of your CIR process vector.

Hope this helps..

#### Bastian Gross

##### German Mathquant
Did it works?

Did you compare your solution with the exact solution of the closed-form Heston?

#### Daniel Duffy

##### C++ author, trainer
Alan Lewis' book on Sto Vol is the standard reference.

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