In this month’s Quantcast, Christian Fries, head of model development and methodology at DZ Bank in Frankfurt and a professor of mathematical finance at LMU University, talks about the qualities to look out for in algorithmic techniques, and the importance of simple and clean codes when developing good algorithms.
Fries introduces his new paper, Automatic backward differentiation for American Monte Carlo, which applies adjoint algorithmic differentiation (AAD) to calculate the sensitivities of Bermudan options and valuation adjustments in a quicker way.
Two key advantages of his technique include the ability to avoid a cumbersome regression step in the calculation of the sensitivities, and the fact that it is easy to code.
Fries says he doesn’t like debates around which algorithm is faster than the other, and that the more important results to look out for are whether an algorithm manages to perform within a given order of magnitude and whether it is straightforward to implement.
“What matters is if an algorithm performs within seconds, minutes, hours or days. It’s not so important if it performs within one second or four seconds…code complexity is a big issue. For example, in the industry, if you are heading a team, it is very important the code is clean, easy to understand and does not have many complicated special cases.”
He adds there are still outstanding issues with AAD in that it is difficult to code and not easy to develop on legacy systems.
“When I started to look at AAD I thought everything was done there, and to my surprise, [found that] there is a little bit more that can be done,” says Fries.
He added that in the future he will be working on a paper on obtaining forward sensitivities for calculating margin valuation adjustment using AAD, and another follow-up paper looking at how to approximate those sensitivities without the use of AAD.
02:30 Fundamental Review of the Trading Book
03:00 Discussion of previous paper on Monte Carlo method
04:24 Forthcoming paper
08:42 How AAD is adapted to Greeks calculation
11:40 Improvements brought by the methodology
14:26 Model performance
17:10 Where does the technique apply?
18:30 Option price boundaries
23:00 How the model is used at the bank
23:40 Future research
25:54 AAD’s potential still to be discovered
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