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September 12th, 2021, 11:59 pm
Forum: General Forum
Topic: Calibration of displaced multi-factor short rate models
Replies: 1
Views: 1081

### Calibration of displaced multi-factor short rate models

Hello, I am reading about multi-factor short rate models, like CIR2++, CIR3++, 2-Factor Black-Karasinski model... Analytical solution to price derivatives such as caps/swaptions does not exist for such models. A possible approach is to calibrate these models using Monte Carlo simulation. We generate...
July 15th, 2021, 8:19 am
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

QE doesn't seem to be a nice scheme to calculate greeks using AAD. Glasserman 2004 page 397 allows one to differentiate SDE to get SDE for greeks. (Kunita). and Lykke Rasmussan'S PhD thesis discusses this as well, including AD and Complex Step Method. Yes, I read that QE is not a nice scheme for AA...
July 15th, 2021, 8:13 am
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

With SPX, there's little need. For some other underlying, if there are gross arbitrage violations at some mid-quotes, could be worth it. Or, you could just drop the offending quotes from the calibration.     In the end, the model does the smoothing and fixes the arb-violations, so it seems like ove...
July 14th, 2021, 10:50 am
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Hi, is it a good practice to smooth out the volatility surface before calibrating a model? There could be a significant loss of information, especially when fitting a model to away-from-the money options.

Thanks,
K
July 12th, 2021, 10:28 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Thanks for the chart -- looks good. Yes, minimizing the RMSE in the implied vol (IV) is a decent calibration strategy, esp if you want to see how different models are capable, or not, of  matching far otm behavior. You need to have a very robust implied vol function and need to choose your minimum ...
July 12th, 2021, 9:12 am
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Hi Alan, What about calibration in the volatility space? I mean can I consider an objective function where I minimize the squared distance between market vol and the Heston implied vol? Are there any limitations of such a calibration methodology? And how about calibration via Monte Carlo simulation?...
July 12th, 2021, 8:54 am
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Here it is...

July 9th, 2021, 8:29 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

>> It's also good practice to visually examine your integrand for smoothness along the contour. K: I am trying to visualize the integrand,  Just plot your (real) integrand vs. x for x=0 to xmax. Should be a smooth function -- ultimately very small near xmax.  Yes, it converges to 0. At xmax = 25 it...
July 9th, 2021, 5:13 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

>> If you include shorter-dated, well out of the money options, such as those available with SPX, a calibration will often violate the Feller condition in order to achieve a "best fit". I have seen it happen often, although I typically don't use MSE on prices as the objective function. In...
July 9th, 2021, 4:57 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

>> It's also good practice to visually examine your integrand for smoothness along the contour. K: I am trying to visualize the integrand, to see if the integral is not smooth when Im(z) is between 0 and 1. For a given set of model parameters, I generated a contour map. I don't get the feeling why ...
July 5th, 2021, 2:46 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Thanks, Cuchulainn. I am correctly using scipy.integrate.quad, did some test runs on standard cases.  I think the problem is the formula mentioned in the article that I am following. I am now following the book by Lewis. I think the contour variation that Alan has suggested above is a useful techni...
July 5th, 2021, 2:25 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

A few comments.  - The H function I posted uses z instead of k; otherwise, the parameters are the same as my previous post. - Mathematica documentation is online. - Commented out stuff mostly related to using  xmax =infinity;  sometimes you can get away with this; sometimes not. The code here uses ...
July 2nd, 2021, 1:33 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

You're welcome.
If you have time it would be nice how DE/SLSQP/(SHGO?) worked out to determine 'best practice' for this problem.
I'll definitely do that.
Krish
July 2nd, 2021, 1:04 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Thank you, Alan. I follow the steps that have you mentioned and come back with the results. Great help!

Krish
July 2nd, 2021, 12:59 pm
Forum: General Forum
Topic: Lewis Formula
Replies: 46
Views: 4583

### Re: Lewis Formula

Thanks, Cuchulainn. I am correctly using scipy.integrate.quad, did some test runs on standard cases.  I think the problem is the formula mentioned in the article that I am following. I am now following the book by Lewis. I think the contour variation that Alan has suggested above is a useful techniq...