[ quantlib-Bugs-2104135 ] HybridHestonHullWhiteProcess -> negative prices for a Call

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Bugs item #2104135, was opened at 2008-09-10 20:01
Message generated for change (Comment added) made by lballabio
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: HybridHestonHullWhiteProcess -> negative prices for a Call

Initial Comment:
I am getting negative prices for a call option (among other calibration problems) in the following example code.  (Almost entirely based on test-suite code.)



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>Comment By: Luigi Ballabio (lballabio)
Date: 2008-09-24 15:46

Message:
results.value = std::max(0.0, results.value);

at the end of the engine's calculate() method?

Luigi

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Comment By: Klaus Spanderen (klausspanderen)
Date: 2008-09-16 09:01

Message:
Hi Luigi,

I can also generate negative option NPVs with Monte-Carlo engines
we have in actual library code (I guess nearly all MC engines
supporting control variate can generate negative NPVs for deep
OTM options. At least for the MCAmericanEngine it was pretty easy to
find an example.).

The root of the problem is the control variate algorithm itself, which
might generate negative NPVs having a finite MC statistics, see line 104
in montecarlomodel.hpp. At the time being I don't see a one line fix for
this behaviour.

best regards
 Klaus

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Comment By: Luigi Ballabio (lballabio)
Date: 2008-09-15 18:08

Message:
Klaus,
    I hope you don't mind my stepping in. Is this an issue of the
MultiVanillaOption class you had in the example, or of an instrument/engine
we have in actual library code? If it's library code, I'd try and avoid
negative NPVs being returned--even if the calibration or the use of control
variates is not optimal. Maybe the engine can floor the option value at
zero?

Luigi


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Comment By: Klaus Spanderen (klausspanderen)
Date: 2008-09-13 14:27

Message:
Hi

The example is using control variate to reduce the statistical error. But
this method can also lead to small negative option NPV for deep OTM options
(as happen in your example). Therefore these options are ignored during the
calibration.

A few other thinks
- in line 751 a constant vol of 12% is added to initialize the calibration
helper. IMO that's a bug because the calibration helper does not match to
the impliedVols array.
- you are using only a few instruments to calibrate the Hull-WHite model.
The \sigma is IMO unrealistically high. Look e.g. into the BermudanSwaption
example to get more realistic values.  
- the targetQualityIndex of the test case is much too small for real world
problems. For real problems it is better to monitor the improvements of the
qualityIndex and exit if no further progress is made. (E.g. for your
example I'm getting a qualityIndex of around 100.)
- The algorithm is based on Monte-Carlo optimization and therefore by far
not as stable as a normal Heston calibration. That the reason why I've
removed the example a month ago.

best regards
 Klaus


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