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

Posted by Ed Colley on
URL: http://quantlib.414.s1.nabble.com/Problem-by-pricing-quanto-asian-basket-options-with-MC-simulation-multipath-tp4466p4469.html

Pricing quanto options this way is fairly standard. You just add  
fxvol * eqvol * corr to the yield on the equity, and then treat it as  
a domestic stock. The original paper is:

Reiner, Eric (1992). Quanto mechanics, Risk, 5 (10), 59-63.

But you can find desriptions in plenty of textbooks, e.g.  
Baxter&Rennie or recent editions of Hull.

  - Ed

On 13 Feb 2006, at 08:47, Giorgio Pazmandi wrote:

>> 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
>