[R-SIG-Finance] American basket options

[Moshe Olshansky]

Dear Wojciech,

Thank you very much for your note!

As I understand, the polynomial regression is used in
Longstaff-Schwarz method to predict the expected
return from keeping the option between stages k and
k+1 (which allows one to decide whether to exercise it
at stage k), so any other type of prediction can be
used (like regression trees, neural networks, etc.). 
Has anyone tried to run a "mini Monte Carlo" from
stage k to k+1 (for every k from 1 to N) in order to
reduce the variance of expected returns if continued
to stage k+1?
In my case I am not concerned about the speed (even a
few hours for one run will be OK - but certainly not a
few millenniums!).

Regards,

Moshe.

--- Wojciech Slusarski <wojciech.slusarski at gmail.com>
wrote:

> 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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