Hi, I have chosen to do a project at undegrad level on the heston stochastic volatility model. my degree is math, so dont know too much on this area yet. can someone give me an idea of how i can simulate scenarios for the heston model..(im using MATLAB).. should i feed in some parameters and calculate the option price (european call) and then calculate the implied volatility when this price is put in to the black scholes formula. i can then plot 3-d graph varying strike,...and calculating implied volatilities.. Does this sound reasonable...and practical/useful to do.. maybe then i can try to calibrate some parameters from some data.. BY THE WAY,, Please tell me.. where i will need /can use monte carlo methods in this project thank you

It might be an instructive exercise, although I would start with the quasi-closed form (integral) solution in Heston's original paper, and then consider either consider finite differences (you can start with Explicit Euler), since for the Monte Carlo you really need C++. The integral would actually probably be easier to do with Mathematica or Maple, both of which you should have access to as a student.If you have time, you might consider comparing Heston to another stochastic vol model.

I agree with exotiq to start with the closed-form solution.Another suggestion, related to that, is to explore, in-depth theproblem of branch-cut crossings in that model. This requiresat most an under-graduate course in complex variables andsince you are a math major ...This branch-cut problem will become evident if you follow upexotiq's suggestion, then take a non-zero rho, and relatively largevolatility of volatility. It's a nice small problem for an under-graduatethesis and hasn't been studied much by the 'experts' at all. Butyou can find bits and pieces in articles on the web.If you can get a 'closed-form' solution for the location ofthe 'problem' spots in parameter space, you might even have enoughfor a publishable paper. Even without that, you can exlore theproblem numerically. Of course, you'll have to hurry regards,

Hi,If you have enough time, you can try to calibrate this model with some methods!see heston's calibrationI will be very pleased to hear you conclusions about your study!