[R-SIG-Finance] R-SIG-Finance Digest, Vol 41, Issue 8: American Basket Options
Matt Slezak
nocman43202 at yahoo.com
Thu Oct 11 15:25:58 CEST 2007
American Basket Options
Here is an efficient method I used to value European
options on a basket of securities. Maybe you can
piece together R code for the American basket option.
I have done something similar in Excel using
QuantLibXL. First calculate the correlation matrix
for the assets in the portfolio. Next, do a Cholesky
decomposition on this matrix. Generate 1000 random
numbers for each asset in the portfolio. Transform
these into correlated random numbers by multiplying
each by its factors from the Cholesky matrix. Next
generate quasi-random sequences (Halton or other,
range 0 to 1) and pull these numbers from the
cumalative normal distribution. Next you create
Geometric Brownian Motions for each asset using the
respective correlated random number, the asset's
volatility, and the asset's drift. Run the 1000
simulations for each asset over the time horizon, then
calculate the net present value (NPV) of the payoffs
for the whole portfolio (which is the maximum of the
postive NPV or 0, since the long option cannot have a
negative return). The average payoff of the portfolio
is the value of the basket option.
If someone can add how one determines whether the
option is exercised in each stage of the Monte Carlo
simulation for American exercise it would be
appreciated - I used this method for European options.
Hope this is helpful -Matt Slezak
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> > Today's Topics:
>
> 1. Re: American basket options (Dale Smith)
> 2. Re: Burns on Cramer (Patrick Burns)
> 3. Re: returns convention (david.jessop at ubs.com)
> 4. Re: Burns on Cramer (BBands)
> 5. Re: Burns on Cramer (Patrick Burns)
> 6. Black -Litterman Model
> (ngottlieb at marinercapital.com)
> 7. Re: Black -Litterman Model (Brian G. Peterson)
> 8. Re: Black -Litterman Model
> (ngottlieb at marinercapital.com)
> 9. Re: American basket options (Moshe Olshansky)
> 10. Re: American basket options (Wojciech
> Slusarski)
> > From: "Dale Smith" <dsmith at viciscapital.com>
> To: "Wojciech Slusarski"
> <wojciech.slusarski at gmail.com>,
> <r-sig-finance at stat.math.ethz.ch>
> Date: Tue, 9 Oct 2007 07:05:07 -0400
> Subject: Re: [R-SIG-Finance] American basket options
>
> 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
> > > >
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>
> > From: Patrick Burns <patrick at burns-stat.com>
> CC: R-sig-finance <r-sig-finance at stat.math.ethz.ch>,
> The New Markets List <marketslist at googlegroups.com>
> To: BBands <bbands at gmail.com>
> Date: Tue, 09 Oct 2007 12:30:14 +0100
> Subject: Re: [R-SIG-Finance] Burns on Cramer
>
> John,
>
> We definitely agree on one thing: Cramer's goals
> appear
> to be having fun and getting fame. I have no way of
> knowing
> if he is having fun, but he has certainly succeeded
> with fame.
> (Disclosure: Two of my top goals are having fun and
> not getting
> famous. At present I'm doing well with both these.)
>
> I think goals are of secondary rather than primary
> importance.
> Reading my horoscope in the newspaper may satisfy my
> goal
> of knowing how to run my life, but I think a more
> important
> question is whether that is the action of a rational
> person or not.
>
> What I am advocating is SCIENCE: What can we know?
> And
> then let's set about learning that.
>
> What we can learn with random portfolios is whether
> or not a
> fund or a market commentator exhibits skill over
> some period of
> time. (There are other things to learn with random
> portfolios as
> well, by the way.)
>
> Once we have information on skill (which as far as I
> know is
> uniquely available through random portfolios), then
> we can address
> the issue of goals. We can get a sense of how much
> skill was needed
> to meet the goal over the past period -- maybe a
> lot, maybe even
> negative skill would have done. More importantly we
> get a hint of
> how we might best set about to achieve our goals in
> the future.
>
> If we focus on goals rather than skill, we have very
> little basis on
> which to carry past performance into the future.
>
> If you wanted to pick a poker player to back, would
> you merely
> look at the player's winnings or would you try to
> evaluate if he or
> she outperformed given the hands that were dealt?
>
> In terms of what is contracted for, I have
> previously suggested that a
> good choice is to contract for exhibited skill as
> determined by random
> portfolios. This rewards fund managers that do
> exhibit skill, and allows
> the investor a mechanism that comes closer to paying
> for what they get.
>
> Pat
>
> Patrick Burns
> patrick at burns-stat.com
> +44 (0)20 8525 0696
> http://www.burns-stat.com
>
>
> BBands wrote:
>
> >I read this paper,
>
>http://www.burns-stat.com/pages/Working/cramer_vs_pseudocramer.pdf,
> >and found it to be interesting, however, the idea
> of judging
> >real-world results against artificially constructed
> portfolios leaves
> >me cold. The only reasonable way of judging
> performance is against
> >stated goals. Goals tend to be specified in terms
> of returns (relative
> >or absolute), variability (volatility, draw down
> and so forth) or a
> >combination (Sharpe, Sortino...) and the only
> reasonable question is
> >to what extent the goals are met. Judgment against
> a basket of random
> >portfolios, however cleverly constructed, is simply
> not defined in
> >relation to the efforts of the manager.
> >
> >(In this particular case, one might well ask what
> Cramer's goals are.
> >They would seem to be to have fun and gather fame.
> Since it seems that
> >he is eminently successful on both counts one is
> forced to acknowledge
> >that he is doing a good job.)
> >
> >As for the challenge to chartists in the paper's
> conclusion, they too
> >should be measured individually against their
> goals, not random
> >portfolios. Why this emphasis on goals? Because
> this goals are what
> >investors pay for. They may use past performance as
> a gage to
> >ascertain whether the goal is obtainable, but by
> and large investors
> >pay for specified goals and retain or fire managers
> on whether those
> >goals are met. Other assessment alternatives matter
> little, even if
> >they are 'better', unless investors agree and
> contract for them. This
> >is after all a contractual relationship and results
> need to be
> >evaluated in terms of expectations.
> >
> > jab
> >
> >
>
>
> > From: <david.jessop at ubs.com>
> To: <r-sig-finance at stat.math.ethz.ch>
> Date: Tue, 9 Oct 2007 12:40:06 +0100
> Subject: Re: [R-SIG-Finance] returns convention
>
> The answer of "it depends" is right. An example of
> when simple returns
> (i.e. price (t) / price (t-1)) are often used is in
> calculating tracking
> error. A related question is in calculating
> relative returns - should
> you do the ratio of returns or the difference?
>
> Regards,
>
> David Jessop
>
>
> Date: Mon, 08 Oct 2007 21:23:21 +1000
> From: paul sorenson <sf at metrak.com>
> Subject: [R-SIG-Finance] returns convention
> To: r-finance <r-sig-finance at stat.math.ethz.ch>
> Message-ID: <470A1329.2040102 at metrak.com>
> Content-Type: text/plain; charset=ISO-8859-1;
> format=flowed
>
> Is it usually assumed that references to "returns"
> are calculated as
> diff(log(prices))? Compared with say the simple
> fractional change from
> one price to the next?
>
> For example, in PerformanceAnalytics I notice that
> the default value of
> CalculateReturns is diff(log(prices)).
>
> I guess it probably doesn't matter much either way
> for small changes, I
> just wanted to know if there was some common
> convention when I see an R
> function that expects a returns vector.
>
> cheers
>
>
>
>
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>
> > From: BBands <bbands at gmail.com>
> To: R-sig-finance <r-sig-finance at stat.math.ethz.ch>
> Date: Tue, 9 Oct 2007 07:26:28 -0700
> Subject: Re: [R-SIG-Finance] Burns on Cramer
>
> On 10/9/07, Patrick Burns <patrick at burns-stat.com>
> wrote:
>
> > I think goals are of secondary rather than primary
> importance.
> > Reading my horoscope in the newspaper may satisfy
> my goal
> > of knowing how to run my life, but I think a more
> important
> > question is whether that is the action of a
> rational person or not.
>
> Ah, so we come to a divide. I suspect that in
> general we'll find
> practitioners on one side and analysts on the other.
> In any case, I
> got a lot out of a day spent thinking about it.
> Thanks for your
> papers, always interesting.
>
> As for your poker analogy, since the game most often
> comes down to a
> few, or less, key hands, I'd guess that overall
> results have better
> information than how the player performs on an
> average hand.
>
> By-the-by, we've been using bootstrap distributions
> to evaluate the
> probability of success for certain trades for a long
> time. Although we
> are happy with this approach, the issue to me is
> getting enough
> different kinds of environments in to the bootstrap
> sample. To wit, a
> sample composed of daily US stock market data from
> 2002 and 2003,
> yields rather different results than a sample
> composed of data from
> 2005 and 2006. We are currently using trailing two
> years, but there
> must be a better method of sampling.
>
> All the best,
>
> jab
> --
> John Bollinger, CFA, CMT
> www.BollingerBands.com
>
> If you advance far enough, you arrive at the
> beginning.
>
>
> > From: Patrick Burns <patrick at burns-stat.com>
> CC: R-sig-finance <r-sig-finance at stat.math.ethz.ch>
> To: BBands <bbands at gmail.com>
> Date: Tue, 09 Oct 2007 16:19:37 +0100
> Subject: Re: [R-SIG-Finance] Burns on Cramer
>
> BBands wrote:
>
> >On 10/9/07, Patrick Burns <patrick at burns-stat.com>
> wrote:
> >
> >
> >
> >>I think goals are of secondary rather than primary
> importance.
> >>Reading my horoscope in the newspaper may satisfy
> my goal
> >>of knowing how to run my life, but I think a more
> important
> >>question is whether that is the action of a
> rational person or not.
> >>
> >>
> >
> >Ah, so we come to a divide. I suspect that in
> general we'll find
> >practitioners on one side and analysts on the
> other. In any case, I
> >got a lot out of a day spent thinking about it.
> Thanks for your
> >papers, always interesting.
> >
> >As for your poker analogy, since the game most
> often comes down to a
> >few, or less, key hands, I'd guess that overall
> results have better
> >information than how the player performs on an
> average hand.
> >
> >
>
> I'm certainly no expert in poker so you may have it
> right for
> poker, but I would rather entrust my pension to a
> fund manager
> that has shown consistent positive skill rather than
> one showing
> erattic skill.
>
> >By-the-by, we've been using bootstrap distributions
> to evaluate the
> >probability of success for certain trades for a
> long time. Although we
> >are happy with this approach, the issue to me is
> getting enough
> >different kinds of environments in to the bootstrap
> sample. To wit, a
> >sample composed of daily US stock market data from
> 2002 and 2003,
> >yields rather different results than a sample
> composed of data from
> >2005 and 2006. We are currently using trailing two
> years, but there
> >must be a better method of sampling.
> >
> >
>
> The market changes over time. You might note that I
> emphasize
> the time period when speaking of exhibiting skill.
> It seems to me
> that there is no alternative but to do the testing
> over several periods.
> I would, of course, be keen to hear other solutions.
>
> Pat
>
> >All the best,
> >
> > jab
> >
> >
>
>
> > From: <ngottlieb at marinercapital.com>
> To: <r-sig-finance at stat.math.ethz.ch>
> Date: Tue, 9 Oct 2007 13:20:49 -0400
> Subject: [R-SIG-Finance] Black -Litterman Model
>
> Does anyone know if the Black Litterman Model for
> Optimization has been
> implemented in R?
>
> If in S would help also, and if in S how mushc would
> be involved in
> converting into an R package?
>
> Thanks,
> Neil
>
--------------------------------------------------------
>
>
>
> This information is being sent at the recipient's
> reques...{{dropped:16}}
>
>
> > From: "Brian G. Peterson" <brian at braverock.com>
> To: ngottlieb at marinercapital.com,
> r-sig-Finance <r-sig-finance at stat.math.ethz.ch>
> Date: Tue, 09 Oct 2007 12:41:19 -0500
> Subject: Re: [R-SIG-Finance] Black -Litterman Model
>
> ngottlieb at marinercapital.com wrote:
> > Does anyone know if the Black Litterman Model for
> Optimization has been
> > implemented in R?
> >
> > If in S would help also, and if in S how mushc
> would be involved in
> > converting into an R package?
>
> Black Litterman option pricing is certainly
> implemented in R.
>
> However, I *think* you are talking about the
> extended Black Litterman
> models often applied to CAPM portfolio optimization.
> I am not aware of
> anyone publishing code for an extended Black
> Litterman portfolio
> optimization model in R. I've looked at it a couple
> of times, but never
> implemented it.
>
> In the future, it would help if you would cite a
> reference that you are
> using as the basis for your question (web page,
> book, paper, etc.). It
> would help list members to evaluate your request.
>
> Regards,
>
> - Brian
>
>
> > From: <ngottlieb at marinercapital.com>
> To: <brian at braverock.com>,
> <r-sig-finance at stat.math.ethz.ch>
> Date: Tue, 9 Oct 2007 13:58:19 -0400
> Subject: Re: [R-SIG-Finance] Black -Litterman Model
>
> Thanks Brian for timely response.
>
> Precisely... regarding CAPM and Optimization even
> though CAPM is a
> little dated.
> Good point about citing a reference, something I
> usually always do
> when responding to questions from others.
>
> Here is two citations that is a decent start
> regarding BL Model:
>
http://www.mccombs.utexas.edu/faculty/keith.brown/ChileMaterial/Idzorek%
> 20WP
>
> http://www.fmpm.ch/files/2001_01_Drobetz.PDF
>
>
> The more recent approach is Arbitrage Pricing Theory
> (APT):
> CITATIONS:
> Ross and Roll Paper:
>
http://www.cfapubs.org/doi/pdf/10.2469/faj.v51.n1.1868?cookieSet=1
>
> William Goetzman Comments on APT:
>
http://viking.som.yale.edu/will/finman540/classnotes/class6.html
>
> One more on APT
>
http://www.ny.frb.org/research/economists/wang/APT-Huberman-Wang.pdf
>
>
> Regards,
> Neil
>
>
>
>
>
> -----Original Message-----
> From: Brian G. Peterson [mailto:brian at braverock.com]
>
> Sent: Tuesday, October 09, 2007 1:41 PM
> To: Gottlieb, Neil; r-sig-Finance
> Subject: Re: [R-SIG-Finance] Black -Litterman Model
>
> ngottlieb at marinercapital.com wrote:
> > Does anyone know if the Black Litterman Model for
> Optimization has
> > been implemented in R?
> >
> > If in S would help also, and if in S how mushc
> would be involved in
> > converting into an R package?
>
> Black Litterman option pricing is certainly
> implemented in R.
>
> However, I *think* you are talking about the
> extended Black Litterman
> models often applied to CAPM portfolio optimization.
> I am not aware of
> anyone publishing code for an extended Black
> Litterman portfolio
> optimization model in R. I've looked at it a couple
> of times, but never
> implemented it.
>
> In the future, it would help if you would cite a
> reference that you are
> using as the basis for your question (web page,
> book, paper, etc.). It
> would help list members to evaluate your request.
>
> Regards,
>
> - Brian
>
--------------------------------------------------------
>
>
>
> This information is being sent at the recipient's
> reques...{{dropped:16}}
>
>
> To: Wojciech Slusarski
> <wojciech.slusarski at gmail.com>,
> r-sig-finance at stat.math.ethz.ch
> Date: Tue, 9 Oct 2007 19:27:59 -0700 (PDT)
> Subject: Re: [R-SIG-Finance] American basket options
>
> 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
> > > 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
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> > > > >
> > > > >
> > > >
> > > >
> > >
> > > _______________________________________________
> > > R-SIG-Finance at stat.math.ethz.ch mailing list
> > >
> >
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> > >
> > _______________________________________________
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> >
>
>
> > From: "Wojciech Slusarski"
> <wojciech.slusarski at gmail.com>
> CC: r-sig-finance at stat.math.ethz.ch
> Date: Wed, 10 Oct 2007 08:58:30 +0200
> Subject: Re: [R-SIG-Finance] American basket options
>
> 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
>
> > 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
> > > > 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.
> > > > > >
> > > > > >
> > > > >
> > > > >
> > > >
> > > >
> _______________________________________________
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> > > >
> > >
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