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.
American basket options
8 messages · Krishna Kumar, Moshe Olshansky, Wojciech Slusarski +1 more
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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>:
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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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:
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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.
_______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing
list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.