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American basket options

8 messages · Krishna Kumar, Moshe Olshansky, Wojciech Slusarski +1 more

#
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.
#
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:
#
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:

            
#
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>:
#
For baskets of stocks larger than three or so, Monte Carlo methods outperform the best finite difference code. As mentioned below, there are Monte Carlo algorithms for the American case.

Dale Smith, Ph.D.
Vicis Capital, LLC

-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Wojciech Slusarski
Sent: Tuesday, October 09, 2007 6:00 AM
To: r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] American basket options

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>:
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#
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:
#
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>:
#
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: