Re: [Quantlib-dev] Bates Engine for American Options

[David B. <db...@ic...>]

Hi Klaus - I'll definitely take a look at that example.  I'm using your DAX
example right now as a base.  The research I've done has shown me that one
can-not neglect Jumps in the near-term, or the core Vol process becomes
over-estimated.  There are a number of facets to this problem which I've yet
to fully understand, but I've been reading a few papers on the topic which
have proved quite interesting:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=965248


There are a few issues which I'm currently having, conceptually.
1)  I don't believe I'm actually getting the clustering effects of a
GARCH-model.  To get that, error-propagation is necessary.  I would probably
like to handle it in some-fashion despite it not being needed to fit the
implied volatility surfaces accurately.  This would require me to further
understand the link between the P-measure / Q-measure and the cross-time
Surface Dynamics of a stochastic vol. model.
2)  To use the above paper, we'd need to figure out how to turn all of these
ruminations and thoughts into an analytic model.  In a GARCH-direction there
was some type of Mean Tracking Tree which is about 10-years old and
apparently has decent efficiency.  Kilin, in the above, uses a Gaussian
Quadrature, so something of that nature might be necessary to solve this.
3)  Supposing I'm willing to accept the risk-neutral log-normality of
options 1Y+ into the future, which from what I've read is not a bad
hypothesis, I could probably build some type of Brownian Bridge to
accelerate the calibration.  This far-future strike series could be used
(perhaps) like a shrinkage estimator, where if we turn on regularization to
the maximum, the output is the standard answer.


What do you think?



Best,
DB




Klaus Spanderen-2 wrote:
> 
> Hi
> 
> If for the time being you can set aside the jumps it might be worth
> looking at 
> the Heston finite difference pricing engine, e.g. the test case 
> testFdmHestonAmerican() in test-suite/fdheston.cpp ist a good starting
> point.
> 
> regards
> 
>  Klaus
> 
> On Thursday 19 February 2009 07:04:00 uptotibet wrote:
>> Hey Guys - I've looked through the list and was just wondering if anyone
>> has used the Bates Model to price American Options?  I started down this
>> path trying to find some connection for GARCH-based option pricing. 
>> After
>> a lot of meandering around, I realized I don't need "garch" per-se, but
>> some type of stochastic volatility model.
>>
>> I want to be able to handle the skews on options more accurately for
>> portfolio optimizations.  I don't care about arbing this stuff, but I
>> dont
>> want to get arbed - if that makes sense.
>>
>>
>> Any thoughts?
> 
> 
> 
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