I just checked this one. I saw the picture you are referring to and I think the frown is not real. Much of it looks like noise created by wide bid ask spreads and extremely high implied vols. The dat... Read More

I'll answer both of your questions in one go: Your ideas are correct. If the Black-Scholes model was true, the implied volatility surface would be flat but it is not in real life. Thus, the geometric... Read More

The reason is that, as shown in Proposition 2.1 of that paper, in order to exclude static calendar arbitrage, the total variance has to be strictly increasing in forward moneyness. See also the belo... Read More

Maybe it would help you to think of it the following way. The strike $\sigma^2(T)$ of a fresh-start variance swap of maturity $T$ in the Heston model only depends on parameters $(v_0,\theta,\kappa)$,... Read More

Let's take a step back to look at what implied volatility (IV) really is. If we know the price of a call option, the interest rate (we can use the spot rate corresponding the option maturity) then Im... Read More

You are an investment bank. You trade a multitude of vanilla and exotic options. You want to make sure the option prices you quote as a client are arbitrage-free with respect to liquid option prices... Read More

Here are my thoughts. Let's take for example the pair EURUSD and USDEUR. The fx rate for EURUSD will be $Xt$ and USDEUR $1/Xt$. Now assume that $d{Xt} = \mu{Xt} dt + \sigma{Xt} dWt $ then thanks to I... Read More

You can convert the implied volatility to local volatility using this formula: $\sigma^2 \left(T,y\right)=\frac{\frac{\partial w}{\partial T}}{1 -\frac{ y}{w} \frac{\partial w}{\partial y}+\frac{1}{2... Read More

Yes, that's what we wish to see from the correctly-specified model. Now, let me try to answer your 2nd and 3rd questions together as they are based on the same confusion. There are two different co... Read More

In short no you don't need to estimate the values for these quantities to calibrate the model. Instead what you want to do is to perform a least squares optimization on the model parameters against m... Read More