# What parameters give a smile (not smirk) in Heston?

I am trying to create a smile in Heston model, however, as of yet, I have only been able to get smirks (i.e., big negative slope ITM that flattens out ATM, and then a very small positive slope OTM).

What parameters ($\kappa, \xi, \rho$ etc) should one use in Heston in order for the prices to actually show a proper smile? --> \_/

• As a guess, try $\rho=0, \kappa=0, \xi>0,\theta=$whatever. Essentially, no correlation between spot and vol, and vol of vol positive. – will Apr 6 '17 at 14:04
• This related question and its answer might be useful: quant.stackexchange.com/questions/17717. – LocalVolatility Apr 6 '17 at 16:45

The impact of all the 5 parameters to be calibrated are the following:

• $\rho$ impacts the skewness: try $\rho = 0$ to get a symmetric smile

• $\sigma$ impacts the smile effect: you may want to move this parameter in your case. Increasing it (try 0.5 or more for instance) will amplify the smile effect you want.

• $v_0$ and $\theta$: the initial volatility and its long term level. This will only impact the level of your smile

• $\kappa$: as for $\sigma$, this will also modify the smile effect. Increasing $\kappa$ will decrease the smile effect, so you may want to decrease it (to 1 for instance).

• The link to the paper is broken. Could you please update it? – Hans May 7 '17 at 0:21