[R-SIG-Finance] American basket options

[Wojciech Slusarski]

I used it for american-asian options (also called hawaiian) and it was
quite stable. though there are two dimensions only of the problem -
spot price and average strike being path dependant. A friend of mine
used that for pricing bermudan swaptions, where you have to model the
whole interest rate term structure which results in higher
dimensionality and said that sometimes it gives strange results and
sometimes spurious. In the original L-S algorithm you conduct
regression only on paths on which the option is in-the-money. He
extended that, by runing regression on all paths. The main problem is
the selection of proper polynomials for the regression. Instead of
that, he was splitting the space for equally sized small pieces and
was fitting linear model. It was providing fine results, though was a
bit time consuming.

Best regards,
Wojciech

2007/10/10, Moshe Olshansky <m_olshansky at yahoo.com>:
> Thank you!
>
> I heard about that method. Now I will check it more
> carefully.
> Is is the only Monte Carlo based method?
> Any idea about it's accuracy?
>
> As to programming, I think that there is a version of
> it in QuantLib (the C++ version). Has anybody used it?
>
> I will share my experiences with the list.
>
> Regards,
>
> Moshe.
>
> --- Wojciech Slusarski <wojciech.slusarski at gmail.com>
> wrote:
>
> > There is an algorithm called OLS Monte Carlo, or
> > Longstaff-Schwarz
> > algorithm for valuation of american/bermudan options
> > using MC method,
> > though it can be a bit tricky to programm that for a
> > portfolio of 10
> > securities and be a bit unstable, though worth of
> > trying. If the
> > dividends are not high, it should not differ much
> > from a european
> > option priced using Monte Carlo. If dividends are
> > high, then the price
> > should be slightly higher.
> >
> > Regards,
> > Wojciech ¦lusarski
> >
> >
> > 2007/10/9, Moshe Olshansky <m_olshansky at yahoo.com>:
> > > This is an OTC traded option.
> > >
> > > For a European option one can estimate the
> > covariance
> > > matrix and then use Monte Carlo (taking into
> > account
> > > the dividends for each stock). This is pretty
> > > straightforward (well, there may be many ways to
> > > estimate the covariance matrix but let's use the
> > > simplest one).
> > >
> > > Regards,
> > >
> > > Moshe.
> > >
> > > --- Krishna Kumar <kriskumar at earthlink.net> wrote:
> > >
> > > > I am just curious as to if this is being traded
> > in
> > > > some market ?.
> > > >
> > > > This is probably not very helpful but I don't
> > think
> > > > a European style
> > > > basket is there in the existing packages.
> > European
> > > > style baskets are
> > > > themselves tricky if you want to get the basket
> > > > smile right etc.
> > > > American style baskets will be messy.
> > > >
> > > > Cheers
> > > > Krishna
> > > >
> > > >
> > > >
> > > >
> > > > Moshe Olshansky wrote:
> > > > > Hello,
> > > > >
> > > > > Is there any R code which allows to calculate
> > the
> > > > > price of an American basket option (option on
> > a
> > > > price
> > > > > of a portfolio)?
> > > > > If yes, are there any references to how
> > accurate
> > > > these
> > > > > calculations are?
> > > > > If no, can anybody recommend a relatively easy
> > to
> > > > use
> > > > > software doing this?
> > > > >
> > > > > Are there any non Monte Carlo methods to
> > compute
> > > > (even
> > > > > roughly) the price on an American basket put
> > > > option on
> > > > > a portfolio of 10 dividend paying stocks with
> > 6
> > > > months
> > > > > maturity?
> > > > >
> > > > > Thank you in advance,
> > > > >
> > > > > Moshe.
> > > > >
> > > > >
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