RE: Problem by pricing quanto asian basket options with MC simulation (multipath)

Posted by Giorgio Pazmandi on Feb 13, 2006; 12:48am
URL: http://quantlib.414.s1.nabble.com/Problem-by-pricing-quanto-asian-basket-options-with-MC-simulation-multipath-tp4466p4468.html

>I'm not familiar with quantlib, but for a MC approach to work, you
>will need to ensure that you pick a measure in which all the
>tradeable assets are martingales with respect to the same (tradeable)
>numeraire. I would guess that your asset 2 doesn't satisfy this
>condition.

Thank you for your answer, I think that you are right and the condition that
you mentioned is not satisfied. That explains why our calculation doesn't
work

>Incidentally, the usual way to tackle these problems is to adjust the
>yield on the quanto underlying by the fx covariance.

I see, but how is the yield adjusted? Are there papers or books on this
subject?

Thank you again for your help

Giorgio

>On 10 Feb 2006, at 18:29, Giorgio Pazmandi wrote:
>
>> Hi, we are having some problems by using the (multi)path simulation
>> capabilities of quantlib for the  pricing of quanto asian basket
>> options
>> (these are asian basket options where the underlying are in  different
>> currencies but the payoff doesn't depend on any exchange rate). I
>> hope that
>> this problem is not "out of topic" in this mailing list.
>>
>> To simulate this options we let run a MC simulation with 3 stocastic
>> variables (the 2 underlying  prices and the exchange rate). We
>> compared our
>> results with a commercial product wich prices this  kind of
>> options. As long
>> as we put in the correlation matrix correlations beetwen the assets
>> our
>> results match very well. When we add a correlation between the
>> assets and
>> the exchange rate we get a  small effect on the price, while in the
>> commercial product we see a bigger effect.
>>
>>
>> test #1 (no correlation): Our simulation gives 8.65 +/- 0.09,
>> reference
>> value is 8.64 +/- 0.08
>>
>> test #2: (only correlation beetween the 2 asset): Our simulation
>> gives 9.66
>> +/- 0.10, reference  value is 9.65 +/- 0.09
>>
>> test #3: (only correlation between asset and ex.rate): Our
>> simulation gives
>> 8.66 +/- 0.09 (similar  to the simulation #1), reference value is
>> 8.22 +/-
>> 0.08
>>
>> test #4: (all the correlations): Our simulation gives 9.67 +/- 0.10
>> (similar
>> simulation #2),  reference value is 9.24 +/- 0.09
>>
>>
>> Maybe somebody has some experience with such kind of options and
>> can give us
>> a hint of what we are  doing wrong. Details on our test case and on
> our
>> aproach to price it follows below.
>>
>> Thank in advance for any help
>>
>> Giorgio