Assemble the data, consisting of a matrix of quoted option prices $\{C(Ti,Kj^i)\}{i=1}^{N}$ where $j=1,2,...,Mi$ together with the yield curve to determine $r$ . Interpolate and extrapolate these pr... Read More

At long maturities, the real problem tends more to be model error than volatility estimation: over that kind of time period most companies undergo significant capital structure changes, for which the... Read More

Nevermind, i'm just confusing myself. Now I understand what I misunderstood. The implied volatility surface of a prices of calls generated by a stochastic volatility model will not be constant since... Read More

Here is how I would approach such a calibration. Assuming we have the necessary market data one can easily construct the emprical distribution of the arrival rate. Let $\lambda_{emp}(\delta)$ be th... Read More

a = 0.05; b = 0.3; rho = -0.35; m = 0; sigma = 0.15; S0 = 100; r = 0.033; q = 0.0022; T = 0.26; F0 = S0*exp((r-q)*T); k = (50:0.5:120); x=log(k/F0); iv = a+b*(rho*(x-m)+((x-m).^2+sigma^2).^(1/2));... Read More

I am intrigued by this question because it gets at the heart of so many grey areas of the financial system in which it becomes almost impossible to know how many assets derive their values from some... Read More

Firstly I'm only concentrating on Sharpe, this is the most robust of your metrics. Consider the difference between sharpe and drawdown, sharpe contains a contribution from every return in your result... Read More

honestly your question is hard to understand. Are these two questions the same? "Does fitting sub-optimal option exercise strategies to market data yield better option values?" "which modeling appro... Read More

You generated only one realization of the GBM. The variance of a GBM increases with time and so you must generate more realizations to get accurate estimates. Here see a sample of Brownian simluation... Read More

Yes, you are correct. Consider the following toy example: 1) Log prices follow: $dpt=\mu dt+\sigma dWt$ 2) Then: $r{t+h,h}=p{r+h,h}-p_t ~ N(\mu h, \sigma^2 h)$ 3) standard ML estimators: $\hat{\mu}=... Read More