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raoul-pietersz / cash_settled_swaptions

A module for valuation of cash-settled swaptions
MIT License
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Comparison with other models?! #1

Open AlexanderZvyagin opened 6 years ago

AlexanderZvyagin commented 6 years ago

Thanks, I just finished reading your article. I would like to know, have you tried to compare your results with the ones produced by other models?

The model which I have in mind is described in the article "Full implications for CMS convexity" by Simon Cedervall and Vladimir Piterbarg. https://www.yumpu.com/en/document/view/25786587/full-article-risknet

Alexander.

raoul-pietersz commented 6 years ago

Hi Alexander. Thank you for your comment. The paper to which you refer is a very interesting one. I've now read it in full. We did compare our results to the ones produced by other models, in particular, the model of Bermin & Williams, and suggestions in papers of Henrard and of Lutz to consider Hull-White, linear swap rate model, LIBOR market model. We also considered other methods. Not all of those comparisons were documented in the paper, but rather these were documented in Frank's Master's thesis. If I compare the model described in our paper to the one of Cedervall and Piterbarg, then I believe to observe the following difference: The annuity mapping function M(x) defined in equation (5) appears to be dependent on one stochastic variable (S(T)) whereas in our model we model two stochastic variables. One related to forecasting, the other to discounting. I hope my answer makes sense, I'm curious to find out your thoughts.

Raoul.

AlexanderZvyagin commented 6 years ago

Hi Raoul,

thank you for your answer!

Frank's Master's thesis

it is not referenced in the article, could you share a link, please?!

There are few things which worries me and a colleague of mine, with whom I have discussed your article. The first concern is about this section:

...Corollary 3.2 is paradoxical to the result of Mercurio (2008).... ...formula for cash-settled swaptions is not arbitrage-free ... ... Mercurio (2008) uses the terminal measure ... ... We use the physical measure ...

But the model is arbitrage-free (or not) regardless of the measure!

And one more thing about LEMMA 3.1:

...Assume there exists an additional process y∗ ... ... PVBP(t) = lambda * Ann(.) [formula 7]

I tend to agree that IF such process exists, your formula (8) is correct. But why it should exist?! It seems that you have found a special case with formula (7) when cash-settled swaptions can be calculated with (8). But there is no guarantee that this can be applied on the real market data. Or do we miss something?

With best wishes, Alexander