Heston expansions

Posted by Fabien Le Floc'h-2 on Apr 10, 2014; 11:57am
URL: http://quantlib.414.s1.nabble.com/Heston-expansions-tp15144.html

Hello,

I have added Heston expansion formulas along with unit tests from:
- M Forde, A Jacquier, R Lee, The small-time smile and term structure of implied volatility under the Heston model, SIAM Journal on Financial Mathematics, 2012 - SIAM
- M Lorig, S Pagliarani, A Pascucci, Explicit implied vols for multifactor local-stochastic vol models arXiv preprint arXiv:1306.5447v3, 2014 - arxiv.org

This can be particularly useful to find a good initial guess in the Heston calibration as described in this paper: http://papers.ssrn.com/abstract=2362968

In this context, I have found that in practice, the Lorig et al. second order formula is often more accurate than a numerical integration with a few number of points, while being an order of magnitude faster.

Attached is a patch file.

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