R-SIG-Finance Digest, Vol 41, Issue 8: American Basket Options
Hi Matt, Thank you for your note. In R things are much easier - one can use mvrnorm function from MASS package to generate a sample from a multivariate normal distribution with a given covariance matrix. I did this to price European basket options. The main problem in using Monte Carlo for American options is not knowing when to exercise prior to expiration date. Regards, Moshe. P.S. as to covariance matrix, does it make sense to use a longer history to estimate the correlation matrix and a shorter one to estimate individual (marginal) variances?
--- Matt Slezak <nocman43202 at yahoo.com> wrote:
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 --- r-sig-finance-request at stat.math.ethz.ch wrote:
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https://stat.ethz.ch/mailman/listinfo/r-sig-finance or, via email, send a message with subject or body 'help' to r-sig-finance-request at stat.math.ethz.ch You can reach the person managing the list at r-sig-finance-owner at stat.math.ethz.ch When replying, please edit your Subject line so it is more specific than "Re: Contents of R-SIG-Finance digest..." 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.
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