In Heston model, If the parameters obey 2*kappa*theta> sig (known as the Feller condition) then the process volatility is strictly positive. When I run your codes even using your marketdata, calibrated parameters violate the feller condition. Could you please explain why it is so and probably fix it if possible.
Thanks in advance
Hi this is a really good practice. Thanks very much! Here I have some questions regarding the work:
1) Solver is very sensitive to the initial values. If I change it drastically, sometimes I got very different minimum target cell.. How did you deal with it? Do you think the algorithm in Matlab like fminunc() etc. gonna help?
2) I found the formulas for the two ---- V[lnS(T)] and V[lnF(T)] ---- are exactly same. Why? If they are theoretically same, why the calculations afterwards sometimes use V(lnS) sometimes use V(lnF)?
I'd like to appreciate your work anyways, hope can get back from you soon!
Following 9/4/2013 subject.
Thank you very much for your answer. I have two more comments/questions:
1) In your optimization problem, when you impose Var(S(T)_obs) = Var(S(T)) we could have written also
Var(log(S(T))) = marketvola^2*T
since the forward condition is already imposed. Maybe your setting is better because you dont need weights?
2) The market volatility you are using is Black volatility of an option on S(T) = F(T,T), the spot, isn't it?. We could also have imposed the volatility condition on options expiring at Ti on F(Ti,Tj) futures with Ti<Tj. Have you tried that?
I really like this work. Thanks.
I'm just a beginner in commodity derivatives. I d want to know what exactly is this 'market volatility', is it the Black volatility associated to an option with payoff (S_T-K)_+. Have you tried to calibrate volatility to options on futures? Thanks!
By initial parameters do you mean the forward and vol prices? If so I just used the current forward/vols prices from the market on the valuation date.
The correlation parameters could probably use a bit more analysis but I just took some rough estimates based off of historical movements.