Re: AnaliticHestonEngine -- SV or SVJ

Posted by Klaus Spanderen-2 on Sep 08, 2008; 8:02pm
URL: http://quantlib.414.s1.nabble.com/AnaliticHestonEngine-SV-or-SVJ-tp6640p6649.html

Hi

sorry for the late answer.


On Monday 01 September 2008 17:57:02 nabbleuser2008 wrote:
> I also wanted to try what you're saying below, but I was not
> able to understand how to do what you were saying

I've attached a version of the LongstaffSchwartzPathPricer, which calculates
the average life time 'til exercise of an option instead of the price. (There
are better ways to do this but this was easy to implement). Just replace the
original file by the attached one and ran e.g. eamples like
MCLongstaffSchwartzEngineTest::testAmericanOption. The npv is the average
life time. Now (hopefully;-) the implied vols of calls and puts quoted in
terms of the average life time will be closer together than the implied vols
quoted in terms of the option maturity. Calibrate on "synth" european options
with maturity = avg. life time of the american options.

> I've used the FDDividendAmericanEngine to calculate the implied
> volatilities ( Even though I noticed the comment in the source file that
> impliedVolatility may not be accurate. I still used it as I couldn't find a
> better alternative in the QL librarary for my needs, as I'm interested in
> americans with discrete dividend payments.)
>

Be aware that the Heston model is using a dividend yield and that the
volatilities for a discrete dividend Black-Scholes models and dividend yield
BS-model aren't the same. See e.g.

 Bos, R. et al. (2003) Dealing with discrete dividends, Risk Magazine, 16, pp.
109–112.

to transfer volatility surfaces between both dividend models. The Heston
calibration helper assumes a dividend yield BS volatility. May be for the
time being you are better off using the FDAmericanEngine and a dividend
yield.

cheers
 Klaus

--
Klaus Spanderen
Ludwig Erhard Str. 12
48734 Reken (Germany)
EMail: [hidden email] (remove NOSPAM from the address)

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