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6

The Hull-White model can represents the risk free rate as a stochastic process, that is, in terms of expected return and volatility. The zero curve only gives you expected returns and you have to find a source to calibrate volatility, as FQuant told you. Common volatility sources used for this calibration are historical series of the zero curve or ...


4

The one-factor Hull-White model is given by $$dr(t) = (\theta(t) - \alpha\; r(t))\,dt + \sigma\, dW(t)\,\!.$$ The zero curves are only sufficient for the calibration of the parameter $\theta(t)$, which is given in terms of them by $$\theta\mathrm{(t)=}\frac{\partial f(0,t)}{\partial T}+\alpha f(0,t)+\frac{\sigma^2}{2a}(1-e^{-2\alpha t}),$$ where ...


3

I highly recommend you to stick with the error function (RMSE) value minimization approach. I love MC techniques for this and related problem solving and thus do not recommend you to use anything else because of its simplicity and transparency. It comes down to using the right discretization function and to possibly implement variance reduction approaches. ...


3

Doesn't the Heston model have some Fourier transform formulae for pricing vanillas? I think one could use those to calibrate to the vanillas. Can't provide references at this moment, on the road. Edit: check out http://www.visixion.com/dok/Visixion_Calibrating_Heston.pdf -- I haven't read this closely but it sounds familiar


3

Jim Gatherals Book deals with the models you mention and gives an intuitive understanding about calibration and issues that arise. Mostly basic stuff, but very useful if you're just starting out. Also very understandable without an extensive math background.


3

You can find the derivation of the Heston characteristic function (its Fourier Transform) in Gatheral (2006). Using the characteristic function, you can optimize the model on the prices. There are multiple approaches to optimize, among others pattern search (which is very slow) and stochastic optimization (randomly jump around and stop after n iterations), ...


3

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 approach leads to better predictions and better relative value measures?" I think you want to ask 1 and I think it is similar to Setting the r in put-call parity? ...


2

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 the empirical distribution. Then one can define a metric by $$ m(k,A,N)=\sum_{i=1}^N |\lambda_{emp}(i)-\lambda^a(i)| $$ After you have decided upon a suitable ...


2

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 there are very few models.


2

GMM method is a powerful method to calibrate historically, only. Also, the historical Calibration is used in the banking industry for forecast an asset’s performances and not for replicating them. Mathematically, it's known that historical vs options calibration is equivalent to observing an asset through two different probabilities (historical vs the ...


1

Here's a decent study of calibration performance using fast fourier transforms versus other techniques. It concludes Gaussian quadrature works better than other techniques. http://www.frankfurt-school.de/dms/publications-cqf/CPQF_Arbeits6.pdf Edit: AZhu points out the link above is dead and that a working link is ...


1

Dealing with model error under stochastic volatility (in a more formal way) you could use the UVM (Uncertain Volatility Framework). Here are what i think are the most seminal references: Avellenada et al (1995) Pricing And Hedging Derivative Securities In Markets With Uncertain Volatilities http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3736 ...


1

In reality, you needn't bring exotics into consideration to think about this issue. Consider the case of a shop that has fundamental analysts but also trades options on those equities. The fact that the fundamental analysts trade stocks means they think those prices are somehow "wrong". So of course it seems from their point of view that the options ...


1

The starting point for your analysis should be to convert all your options bid/ask prices to implied volatilities, which are the invariant (time-homogeneous, i.i.d.) process in your case. Even though you do not have the dividend yield and other factors necessary to back out the implied volatility, so long as you use the same assumptions (and they are ...



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